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General => General Chat => Topic started by: EEVblog on November 05, 2018, 11:58:51 pm

I'm putting this here instead of in the other blog section, as it's an important technical discussion.
Mehdi claims Walter Lewin is wrong about his infamous KVL violation video, and I've always felt the same but have never investigated myself.
https://www.youtube.com/watch?v=0TTEFF0D8SA (https://www.youtube.com/watch?v=0TTEFF0D8SA)

Wow. I was not even aware that there is such a controversy over Kirchhoff's law.
I though Kirchhoff's laws were derivable from Faraday's law and Maxwell equations in general. But quick search shows that it is not very easy.

KVL only applies in static fields. KCL still applies in fields under flux.
A meter used to measure across points in an induction loop in field flux becomes part of the loop, and the voltage will depend on where the meter and leads are placed relative to the loop. Move it from one side to the other and the voltage reverses.
The current induced in a loop is fixed. The voltage depends on the impedance  the higher the impedance, the higher the voltage between any two points in the loop. This is actually normal inductor behavior if you think about it.

The worst part of this is the way Lewin is acting on YouTube on his own video. He's being pretty childish and refuses to discuss it at all.

When I first watched Walter Lewins video the first thing that struck me was the experimental setup and that the test leads were also part of the experiment. Mehdi's got it right an you can't fault his experimental setup and explanation. KVL still holds true in an varying magnetic field if you draw the circuit correctly by including the test leads. I think Walter Lewin knows this and is just being controversial to get students to think about the problem. Mehdi's experimental setup is nicely done and very easy to replicate and hopefully it will teach EEs a little about good wiring practice when there are stray magnetic fields.

Mehdi Sadaghdar's lecture and experiment is also a good way of showing how you should attach twisted pair into a circuit to make a measurement, think twice before you measure.
As an aside, I wonder how the electrostatic "dual" of the experiment would be arranged ?

The nub of the discussion seems to be do the sum of the voltages around a circuit always add to zero.
You have to admit MaxwellsFaradays law seem to be on Walter Lewins side.
Also
From Wikipedia
KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for highfrequency (shortwavelength) AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore, the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.
It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.[2] These are treated as imaginary circuit elements that produce a voltage drop equal to the rateofchange of the flux.
But then Electrobooms arguments are convincing too.
Maybe the demonstration by Walter Lewin doesn't really show what he is trying to show? the loop seems to include the path to the scope.
How would you measure EMF in a closed loop anyway?
IDK but I really would like to understand this better.

From Wikipedia
It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.
Et voila.
The crux of the matter is that Lewin didn't account for the fact that KCL require the EE equivalent of spherical cows. In the real world wires have resistance and inductance and mutual capacitance, and are not the simple indications of equivalence that they are assumed to be in KCL. So for the math to be accurate you have to consider them as lots of little spherical cows all stuck together in different ways.
If you have a whole lot of little spherical cows you get to call that finite element analysis.

Thanks HackedFridgeMagnet, "KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop" which is true and KVL only holds up for a static field. However, if you take into account all of the parasitic and stray circuit elements then KVL still holds up if you have a vaying magnetic field, however, you've got a different circuit than what you started with. Both Lewin and Electroboom are right, all depends on whether you model in the parasitics. KVL still holds for varying magnetic field if and only if you model in the parasitic circuit elements

Thanks HackedFridgeMagnet, "KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop" which is true and KVL only holds up for a static field. However, if you take into account all of the parasitic and stray circuit elements then KVL still holds up if you have a vaying magnetic field, however, you've got a different circuit than what you started with. Both Lewin and Electroboom are right, all depends on whether you model in the parasitics. KVL still holds for varying magnetic field if and only if you model in the parasitic circuit elements
Hmm.. it seems to say it differently below.
Apparently it needs to be in a conservative vector field but I can't even see that the field within a resistor is a conservative vector field because it is dissipating energy.
KVL is based on the assumption that there is no fluctuating magnetic field linking the closed loop. This is not a safe assumption for highfrequency (shortwavelength) AC circuits.[2] In the presence of a changing magnetic field the electric field is not a conservative vector field. Therefore, the electric field cannot be the gradient of any potential. That is to say, the line integral of the electric field around the loop is not zero, directly contradicting KVL.
It is often possible to improve the applicability of KVL by considering "parasitic inductances" (including mutual inductances) distributed along the conductors.[2] These are treated as imaginary circuit elements that produce a voltage drop equal to the rateofchange of the flux.
So is the line integral of the electric field around the loop zero in all cases (KVL) or not?
If it is non zero (Maxwell Faraday) then how would you measure it? Because measuring it with a scope would seem to prove KVL.
Of course there is also the unlikely scenario where Wikipedia is wrong. ;)

I have thought about this question way too much since high school, but I always convinced myself that KVL doesn't hold under external EMF.
BUT Walter's setup is really bad probing.
I will be working on getting a good experiment.

Maybe the demonstration by Walter Lewin doesn't really show what he is trying to show?
That's possible. He could be right in theory, but may be using a poorly thought out experiment to try and show it.
And maybe it's deliberately a bit dodgy because it's not easy to demonstrate?, and maybe he knows that?
Kinda reminds me of my current flowing through a capacitor video. That was bit of a troll on my part in order to show a "controversial" way of thinking about theoretic current and maxwells law. The old theoretical physicist vs practical engineer viewpoint discrepancy.

I would also say that both are right in a certain way.
Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.
If you have taken the DC voltage source in his lecture example and replaced it with a 1GHz AC source then Kirchoffs law again would not hold because your schematic is ignoring parasitic effects that the real circuit can't simply ignore.
A similar argument to this is how to calculate kinetic energy in physics. Its commonly used that kinetic energy E = (m*v^2)/2 and it turns out this works perfectly in practical experiments. However due to relativistic effects things appear heavier as they get closer to the speed of light, this is sort of a 'parasitic' effect that we are ignoring in that formula because the speeds we normally work with are so low that the effect is practically zero and everything works great. But when you get to these higher speeds this effect starts to contribute more and more to the total energy and then yes that equation is broken. But its not broken because the equation is wrong. Its just ignoring a insignificant detail of the physics model that turned out to become significant in this particular set of circumstances.
But i do have to say that Dr. Lewin explains it a slightly odd direction that is kinda misleading. Its not that this special case with magnetic fields breaks Kichhoffs law, but its just that the mathematical model of the cirucit ignores magnetic effects that should not be ignored in this case. Ideal wires with 0 voltage drop would need to also be 0 units long in the physical world so that they don't have inductance. If all the wires are 0 units long this means the physical circumference of the circuit must also be 0 (Resistors are considered to be 0 length too or they would also be inductors). A circle with 0 circumference must also have a surface area of 0 as such it has 0 magnetic loop area and as such can't get a voltage induced in it no matter how strong or fast changing of a magnetic field you place it in. With that that the voltage on both resistors would calculate to be 0V as you would get trough the analysts of the circuit because the circuit contains no voltage sources.
The correct model for his physical circuit would include inductors on all lengths of wire(including probes going to the scope) and all these inductors should have a dot marked on them showing if they go clockwise or counterclockwise along the magnetic field. Additionally arrows should be drawn between all of them to show they are all coupling together via a magnetic field and the coupling factor written on each arrow. This circuit now has a voltage source in it, its the voltage source that is powering the inductor representing the solenoid. You could then calculate the voltages at each point of the circuit and you would get results that are very close to what the scope is showing.
This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.

I would also say that both are right in a certain way.
Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.
This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.
I agree. Especially with the last part. This has been discussed before and it seems Dr. Lewin is just trolling.

I tend to approach this problem in the following way:
KVL holds true for infinite small dimensioning or as a logical concept  thats when you not happen to use a diagram that includes all inductances and capacitances in the circuit.
For everything else the dimensions and field strength would need to be specified, the logical concept of a circuit designed in a loop does not mean that it physically needs to be a flat loop.
Both are right by themselves, the discrepancy stems from taking the logical concept and converting it directly into a specific physical design.

It's easy to forget that wire is a component too, and also the scope with its probes. If you add a changing magnetic field you cant ignore the wire any longer.

All logical concepts ask for ideal elements, this means that side effects can be cancelled out somehow and you are left with the concept itself as the effect.
Ideal switches, ideal wires, ideal ... do obviously not exist, which makes it practically the base of the whole electronics trade to put concepts in physical reality without unwanted/inacceptable side effects (errors or mishaps) by design.
But don´t go ad hominem because of that, as it is just the kind of discrepancy that is thought provoking in a good way, presented as a right/wrong approach although the concept left the realm it was meant to be used in.

I would also say that both are right in a certain way.
Kirchoffs law doesn't hold in a magnetic field if you don't model the effect of the field on the inductance. But does work if you model the parasitics of the wire as instructors.
This is an excellent paradox to get people thinking. But Dr. Lewin should explain that the problem is a bad circuit model ignoring what should not be ignored rather than the ever so useful Kirchhoffs law being wrong.
I agree. Especially with the last part. This has been discussed before and it seems Dr. Lewin is just trolling.
Yeah i get the feeling that he explains it in a way that doesn't give the full picture on purpose. Using it as sort of a way to see what the student are thinking when they try to explain it and perhaps find the rare bright student who figures out the real reason behind this effect.
But it could also be just a case of being exposed to too much theory and too little practical electronics work. I noticed this with some teachers that they get a different perception of a certain subject due to approaching it from pure theory and sort of settle in to certain specific ways of mathematical problem solving that they personally find really neat.
One of my favorite electronics teachers turned out to be a old guy who has been repairing TVs and other equipment for many years. He had an incredible depth of practical knowledge of useful electronic circuits and knew exactly how they work and how to design them. I'm really not saying theory is a waste of time but instead that every bit of theory should be connected to something physical as well, otherwise you just end up going down a rabbit hole full of math describing mythical ideal components. Once enough math abstractions are stacked on top of each other you can get so far away from the physical world that it can be hard to find your way back to what a voltmeter is showing on the bench (Especially when the teacher in question only ever touched a physical voltmeter once a year).

I am wondering if there is one example KVL does not apply when every "parasitics" and "outer elements" are modeled?
Someone suggested superconductor without giving an example.
So maybe there is an edge case/singularity where KVL does not apply ://

I find it a bit nit picky.
Newtons laws also don't work everywhere, that doesn't make them false all of a sudden?
They have their limits, so has Kirchhoffs laws.
Nothing new, can we go on now with the real stuff?

https://www.eevblog.com/forum/chat/kirchhoff_sloopruleisforthebirds/ (https://www.eevblog.com/forum/chat/kirchhoff_sloopruleisforthebirds/)
https://www.eevblog.com/forum/beginners/arekirchofflawsuseless/msg920903/#msg920903 (https://www.eevblog.com/forum/beginners/arekirchofflawsuseless/msg920903/#msg920903)
https://www.eevblog.com/forum/beginners/walterlewin802lect16superdemo(correction)/ (https://www.eevblog.com/forum/beginners/walterlewin802lect16superdemo(correction)/)
Internet Rule #0: Search before you post ;D

I'll repeat the comment I made on the video (which I'm sure has been utterly buried under a torrent of less extensive comments, or suppressed outright by algorithm):
The way I see it is structural:
He's using a DC circuit in an AC field, and claiming that the DC circuit still holds, while forcing an AC behavior upon it.
As is always the case in proof by contradiction: we have only proven that our premises were wrong.
It's a similar fiction as the conservation of charge vs. energy when connecting charged capacitors together: if energy is conserved, where does it go? Well, it turns out that you can't simply short capacitors together without taking account of their resistance, or inductance. Or, more generally, of the loop area between them, which gives rise to both elements. So the charge is conserved (a more fundamental quantity), and energy is conserved whether or not you've written in a way for it to do so.
It would be more illustrative if he phrased it as a riddle to the student, to figure out where the disconnect is.
You are quite correct that merely adding a transformer, and keeping track of the probe wires in the field, is all that is missing!
As for failings of Kirchoff's laws: radio waves. One must get ever more particular about where (spatially speaking) one applies them. The current flowing into the feedpoint of a dipole antenna, for example, does not equate with the current conducted out of the element tips, which is zero. The disconnect here is concentrating on conduction, while ignoring displacement current. In effect, equivalent capacitance carries the current into free space. But more accurately, it's carried into the fields around every point of the antenna.
At their most general (but perhaps least useful), KVL/KCL reduce to a single point only: they are a differential relation, which must be integrated over the space of interest. (This, of course, is painful to do by hand for all but the simplest arrangements, so we usually have computers divide the space into millions of finite elements and apply the laws to them, for us. Hence, FEA (finite element analysis) tools.)
This, in turn, drive home another point about schematics: what we draw is an abstraction, a fiction, a model. The points are connected instantaneously in time and space, with no concept of distance, or the speed of light (namely, that the distance is effectively zero, or the speed of light is infinite). To build a realistic model, when the speed of light is relevant, we must introduce enough parameters (whether L and C approximations, or real transmission line elements) to match this.
Tim

Just for the fun of it, here is a LT Spice simulation recreating this cirucit.
The graph shows that the actual voltage between those two points is an average between the two scope readings(Since this cancels out the voltage added and subtracted by the test leads going one or the other way)
EDIT: Do note that this is not a accurate simulation as it still ignores stray capacitance and assumes a perfect coupling between all coils. In reality the coupling between the wires would be slightly less than 1 due to the wires not being able to exist in the same physical location and the coupling to the solenoid coil in the middle should be even less due to it being far away from the current path of all the other wires.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=565039;image)

The reason for the apparent difference in readings is that the magnetic field also induces a voltage into the meter or scope leads. Kirchhoff's Law still holds if you take this into account.
As a relevant point of interest, you cannot have a halfturn transformer winding. It is always an integer number of turns. You have to connect the ends of your 'half turn' winding together somehow, for current to flow. Making the wire longer, as in including the test leads of a meter for example, does not alter the fact that the circuit still completes the same magnetic path as a complete turn would do. The longer wire intercepts a more diffuse magnetic field but over a longer distance, and the induced EMF is the same as if it were a tightly wound turn.
In this case a fail, but unless people challenge established science there will never be any more breakthroughs. The problem these days is that science has become more like a religion whose tenets MUST NOT be questioned. This is just as bad as allowing complete pseudoscience.

Interesting question, but I find Dr. Lewin's experimental setup kind of a disgrace for an MIT professor. Anecdotally, the MIT revoked his "professor emeritus" title, but apparently not based on anything related to his scientific merits. Anyway.
I think he hasn't proved anything here. Is there anything else than induced voltages in the probing wires and scope probe in play?
Devising a completely neutral probing setup seems pretty difficult to do, and you won't achieve it with a couple flying wires (however twisted they may be) and basic scope probes.
That said, even if we consider a perfect setup and a real discrepancy, my take here would be that KVL could still perfectly apply. We would just have to consider the loop having extra voltage sources from any induced voltage. That wouldn't defeat it, but make us consider that our circuit model is incomplete.
Just my 2 cents.

A lot of older academics become kooks or cranks because they have been sniffing their own farts so long and no one dares to say they stink. (Because that would jeopardize their own path towards their autofartsniffing career)
Old people should be viewed with suspicion, especially academics. It's sad but true. Look at the ideas that come out of 20something brains versus the ossified crap and egostroking narcissism from older people.

It is not like he taught advanced physics. From what I've seen his lectures were more like physically themed performances rather than actual lectures. This was fine for the first year EEs that have never seen physics before.

That said, even if we consider a perfect setup and a real discrepancy, my take here would be that KVL could still perfectly apply. We would just have to consider the loop having extra voltage sources from any induced voltage. That wouldn't defeat it, but make us consider that our circuit model is incomplete.
Simply put:
You don't get to pick and choose when you follow a law and when you don't.
This is physics, not politics~~
Tim

That said, even if we consider a perfect setup and a real discrepancy, my take here would be that KVL could still perfectly apply. We would just have to consider the loop having extra voltage sources from any induced voltage. That wouldn't defeat it, but make us consider that our circuit model is incomplete.
Simply put:
You don't get to pick and choose when you follow a law and when you don't.
This is physics, not politics~~
Tim
Not sure I got your point, nor that you got mine.
I've yet to agree with KVL not being met, until I get a consistent and formal proof of that.
Any electrical circuit made of physical, nonideal components and nonzero length, nonzero impedance connections between them will get inductive and capacitive coupling with its surroundings. If you devise the real, physical circuit that it actually is, including its surrounding environment, you get equivalents of transformers and capacitors added to the ideal circuit. Taking those into account makes up the real circuit IMO, and KVL is most likely met in any case. I'm saying "most likely" because this is what makes the most sense to me, but as others here, I would of course consider a different view as long as it's rigorously proven.
Not considering those "parasitics" (in the sense that they are not part of our idea of the ideal circuit we designed) is ignoring basic laws of physics. Still don't get how KVL would not apply, until I get a formal explanation and a rigorous experiment that shows that the observed discrepancies are not due to basic inductive and capacitive coupling.

I have a hard time believing that Lewin is "just trolling" or trying to get students to think as some have suggested, after reading his responses to Mehdi and others on his original video. I think this link will work, if not just look for ElectroBOOM's comment on the video, it should be near the top: https://goo.gl/JsKHb8.
If Lewin has a more subtle point he's trying to make, he's doing a good job of hiding it.
[EDIT: link shortened to avoid the automatic Youtube embed]

Not sure I got your point, nor that you got mine.
I've yet to agree with KVL not being met, until I get a consistent and formal proof of that.
Any electrical circuit made of physical, nonideal components and nonzero length, nonzero impedance connections between them will get inductive and capacitive coupling with its surroundings. If you devise the real, physical circuit that it actually is...
Precisely  you can't construct a supposed circuit (following one law), then probe it with another circuit (following a different law). While you can find such corruption in some domains, physics is a domain where this is strictly prohibited. :)
Tim

https://www.youtube.com/watch?v=b7i2uMx7gHo (https://www.youtube.com/watch?v=b7i2uMx7gHo)

physics is a domain where this is strictly prohibited. :)
Well, it is in violation of the law! :DD

Neato, I would imagine you need to remove the effects of the wires coming back to the scope to get a clearer picture. The only way I can think of is by using something like an LED. Would need to do a bunch of tests to figure out the LED intensity as a function of peak EMF induced voltage

Just to be clear, the Professor is correct.
To understand why in the intuitive way, remember what is voltage: By definition, voltage between points A and B is the work necessary to move a unit of charge from A to B.
1. In a constant (conservative) field, it does NOT matter the path I choose to walk my charge between A and B. It will cost me the same amount of energy, no matter how straight or how twisted my way from A to B was. Imagine dropping a ball from a mountain. No matter the path of the ball from top to the bottom, the ball will gain the same energy. All it matters is the height between the top and the bottom. In electric engineering language we say, it does NOT matter how I twist or coil the leads of my voltmeter, the measured voltage will be the same.
2. In a variable (nonconservative) field, it DOES matter the path I choose to walk between A and B. Imagine the same ball and the same mountain from case 1, except this time, while the ball is going downhill, somebody is tweaking the knob of "gravity". Now, the final energy of the ball will vary not only with the height between top and bottom, but also with how much and when the "gravity knob" was adjusted, so it is not the same any more if the ball take a shorter or a longer path.
In electric engineering terms we say, it DOES matter how I twist or coil the leads of my voltmeter.
For case 2 we say "in a variable field a voltage is induced in the voltmeter's leads", or "the leads act as voltage sources, too", or whatever, which is nothing more than (a wrong way of) saying that "the path DOES matter when moving charges in a variable (nonconservative) field".

I have a hard time believing that Lewin is "just trolling" or trying to get students to think as some have suggested, after reading his responses to Mehdi and others on his original video. I think this link will work, if not just look for ElectroBOOM's comment on the video, it should be near the top: https://goo.gl/JsKHb8.
If Lewin has a more subtle point he's trying to make, he's doing a good job of hiding it.
Wow, the spam link responses :o
I posted a comment, will see if I'll get the spam link reply honor too.

In electric engineering terms we say, it DOES matter how I twist or coil the leads of my voltmeter.
In the real world it can (and in this case demonstrably does) matter how you twist or coil the leads. There is transformer coupling happening which is not shown on your theoretical circuit.

Just trying to scroll through all the replies, I have learned something thru osmosis.
...in an induced EMF...
....loop...
...determined by path....
...Kirchoff's law is not valid....
...Special case...
...Thus, Faradays Law is always valid...
...basic physics...
...not going to argue about it....
see lecture 8, 5, 11, 7, 15

He'll do a video when he gets back from vacation in a week :popcorn:
(https://i.imgur.com/6bDVfdr.png)

He'll do a video when he gets back from vacation in a week :popcorn:
(https://i.imgur.com/6bDVfdr.png)
Thanks for you polite request on our behalf.
Yes, Dr. Lewin's says he will do a video, but, the way he worded his response, it is as if he is clearly refusing to watch or acknowledge ElectroBoom's video in any way. This may be understandable as it is clearly possible that Dr. Lewin's may have been hit with so many disruptive responses over the years on the subject which he may have won his argument so many times that he is now immune to any new views on what ElectroBoom's has measured and it may unfortunately be a pure one tone response. I hope he points out truly where ElectroBoom has made an error from his point of view, otherwise, we will most likely see a repeat of his early videos.

In electric engineering terms we say, it DOES matter how I twist or coil the leads of my voltmeter.
In the real world it can (and in this case demonstrably does) matter how you twist or coil the leads. There is transformer coupling happening which is not shown on your theoretical circuit.
Good point, let's simplify the circuit. Let's get rid of the voltmeter. We will use an electron to probe the voltage for each half of our loop. Even more, let's look only at the sign of the voltage for each half of the loop.
1. We have our loop of 2 resistors in an increasing magnetic field.
2. Electrons will flow through our loop, let's say clockwise.
3. Let's measure the voltage. By definition, voltage is the work required to move the unit of charge between our measuring points.
4. We don't have a voltmeter, so we grab an electron, and start moving it through each half of the loop, in order to see how much work do we need to accomplish that  or other said to probe the voltage for each half of the loop, lefthand half, and righthand half.
5. Starting from top, when we circulate our grabbed electron through the lefthand half of the loop, we will need to put some work to move our electron against the flow of all the other electrons in the loop, so negative voltage on the lefthand half.
6. Starting from top, when we circulate our grabbed electron through the righthand side of the loop, we don't need to put any work, our electron will move by itself, it will go with the flow of all the other electrons, it will generate some work, so positive voltage on the righthand half.
7. From 5 and 6 we observe the voltage between the same points is once positive, once negative, depending on which half of the loop we measure. The sum of voltages in our closed loop is Vpositive  Vnegative, which is NOT zero. E.g. 3V  (5V) = 8V.
8. We just seen the sum of voltages for our loop is NOT zero, yet Kirchhoff's Voltage Law predicts it to be ZERO, so Kirchhoff is broken for our setup.

He'll do a video when he gets back from vacation in a week :popcorn:
(https://i.imgur.com/6bDVfdr.png)
There may be moderation. I see the prof’s answer in the thread, but not your comment.

As a relevant point of interest, you cannot have a halfturn transformer winding. It is always an integer number of turns. You have to connect the ends of your 'half turn' winding together somehow, for current to flow. Making the wire longer, as in including the test leads of a meter for example, does not alter the fact that the circuit still completes the same magnetic path as a complete turn would do. The longer wire intercepts a more diffuse magnetic field but over a longer distance, and the induced EMF is the same as if it were a tightly wound turn.
Fractional turns can be done. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.2764&rep=rep1&type=pdf (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.2764&rep=rep1&type=pdf)

Dr. Lewin repeats the same answer in the comments:
In the case of an induced emf the potentials in a circuit are no longer determined, they depend on the path and thus Kirchhoff's Loop Rule is not valid. Kirchhoff's Loop Rule is a special case of Faraday's Law (namely when phi/dt=0). Thus Faraday's Law is always valid.
The thing is, he's not wrong, and it is fundamental.
That's the beginning and end of his argument. He's not interested in "you are not measuring it right".
He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf (http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf)
He claims this is where almost all the electrical engineering textbooks are dead wrong.
As Dave says, a case of theoretical physics vs practical engineering approaches.

For case 2 we say "in a variable field a voltage is induced in the voltmeter's leads", or "the leads act as voltage sources, too", or whatever, which is nothing more than (a wrong way of) saying that "the path DOES matter when moving charges in a variable (nonconservative) field".
He says "two voltmeters connected to the same two points can have two different readings." And he does an experiment where this is not only the case, but these two different reading are repeatable. If this was caused by consistently placing the probe wires (either intentionally or unwittingly) in a different orientation, most of the world, including physicists, would say this is a wrong way of saying that the path DOES matter when moving charges in a variable (nonconservative) field." Especially when he does not include the reason the scopes give the consistently (if you believe the results) different readings. For someone interested in the theory, as an educator or physicist, you would not make this comment (two voltmeters connected to the same two points can have two different readings) in the first place, unless the topic at hand is the potential deficiencies in common voltage measuring devices. You would say the voltage between those two points is in fact quantifiable and repeatable at any given point in time in the experiment.
Professor stretched things. If this were intentionally done to make his students think about the problem, his video would congratulate the student who figures out the omission/trick of how he produced this result. Apparently we shall see if/when the promised video is published.
If you want to play this "path" game, and insist that voltage is not by default the lowest energy path between the two points, then you have to say that the voltage between those point is undefinable, no?

If this were intentionally done to make his students think about the problem, his video would congratulate the student who figures out the omission/trick of how he produced this result
I agree completely, but Lewin's subsequent behavior suggests that he managed to fool himself, as well as the unwary student.
I always thought that the failure to take into account the probe placement was the problem, and am pleased to see this excellent video making that case!

Come to rethink of it, and as he's clearly not an idiot, I was then willing to believe that he actually did that on purpose, just to make young students aware of the question: using simplistic models while thinking they hold true in the real world, which is a very common pitfall. This would be all good if he made it clear in the end that it was his intent instead of making it even more confusing, to the point that he even managed to confuse some very experienced engineers, using his position of authority.
Now if he was genuinely trying to instill advanced physics notions in young heads, I think this was a very bad way of doing it from a pedagogical standpoint.

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf (http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf)
Thanks for the reference. This helps making it much clearer what he was meaning  especially on page 3.
From what I got and summing it up quickly, his fundamental point is that we EE use an "adapted" version of Kirchhoff's law which actually describes things correctly but is NOT what Kirchhoff intended.
This is why we don't seem to agree  we actually do agree for all practical matters but for a professor in physics, we're just abusively using the term "KVL". The lecture extract that rfeecs posted explains that a lot more clearly than Lewin's oral lectures and misleading experiments.

If you want to play this "path" game, and insist that voltage is not by default the lowest energy path between the two points, then you have to say that the voltage between those point is undefinable, no?
Yes.
I'm intrigued, where can I find this definition of voltage as "the lowest energy path"? (With the battery, any path between two given points requires the same energy.)
The wires and the resistors are nothing more than a way to force the charges to flow through a specific path. When there is no variable magnetic field, the path does not matter. When there is a variable magnetic field, the path is essential.
A good intuitive understanding is the old analogy with the water flow. If we have our loop inside the variable field, all the water will flow through our loop in a circle, always in the same direction. If we swim from the top to the bottom of our loop against the water flow, we will spend a lot of energy. If we swim again from top to bottom, but this time the other way around (with the water flow) we will gain some energy from the water flow. The energy spent or gained is our voltage. Once is negative, once is positive. Obviously they are not equal, so it is important if we choose to swim clockwise or counterclockwise.
For the case where the current flow is caused only by the battery, it doesn't matter if we choose to swim clockwise or counterclockwise. It matters only the start point and the end point.

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf (http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf)
Thanks for the reference. This helps making it much clearer what he was meaning  especially on page 3.
We've discussed this many times in previous threads. Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess. But he didn't invent it. It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
In the paper, everything is explained very simply without drama. It's no mystery. The meter wires are part of the circuit and the orientation of the wires determines the results.

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf (http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf)
From that same supplement, emphasis mine:
Suppose you put the probes of a voltmeter across the terminals of an inductor (with very small resistance) in a circuit. What will you measure? What you will measure on the meter of the voltmeter is a "voltage drop" of Ldi/dt. But that is not because there is an electric field in the inductor! It is because putting the voltmeter in the circuit will result in a time changing magnetic flux through the voltmeter circuit, consisting of the inductor, the voltmeter leads, and the large internal resistor in the voltmeter
I think that shows pretty clearly that he is not making a measurement mistake, and that he understands exactly why he got the result he did in his demonstration. So I guess he's so dismissive of KVL not because it's wrong, but because it gets the right answer via an insufficiently rigorous method, even when lumped inductors are added to his resistor model.
a case of theoretical physics vs practical engineering approaches.
Just so.

The meter wires are part of the circuit and the orientation of the wires determines the results.
What happens if we remove the voltmeters? How do we measure the voltage without the voltmeters? We will need to take an electric charge and drag it through the circuit from A to B. How much energy do we need to move our charge from A to B?
The answer is: it depends. If we go from A to B through the left side, or through the right side. Not only that the energy is different for each half of the circuit, but it has an opposite sign. No chance to get a zero for the whole loop.

He even takes this argument so far to the point of saying that Kirchoff's voltage law does not apply to circuits with inductors, because they have a changing magnetic field:
http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf (http://web.mit.edu/8.02/www/Spring02/lectures/lecsup41.pdf)
Thanks for the reference. This helps making it much clearer what he was meaning  especially on page 3.
We've discussed this many times in previous threads. Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess. But he didn't invent it. It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
In the paper, everything is explained very simply without drama. It's no mystery. The meter wires are part of the circuit and the orientation of the wires determines the results.
Absolutely, and this is exactly what several of us have been saying all along.
The experiment itself and the drama add no value.
There's still one valid point in what he says in how EEs interpret Kirchhoff's 2nd law. This doesn't change anything in practice.

The meter wires are part of the circuit and the orientation of the wires determines the results.
What happens if we remove the voltmeters? How do we measure the voltage without the voltmeters? We will need to take an electric charge and drag it through the circuit from A to B. How much energy do we need to move our charge from A to B?
The answer is: it depends. If we go from A to B through the left side, or through the right side. Not only that the energy is different for each half of the circuit, but it has an opposite sign. No chance to get a zero for the whole loop.
Yes, the wires are determining the path from A to B.
So you are supposed to get the amount of work by multiplying the charge by the E field and integrating that over the path. But that only works for electrostatics. We have a changing magnetic field so the electrostatic potential is not defined. We can make up a potential that still works for electrodynamics and Faraday's law, the magnetic vector potential:
https://en.wikipedia.org/wiki/Electric_potential (https://en.wikipedia.org/wiki/Electric_potential)
As the article points out, there is confusion over the language. What is meant by potential, voltage drop, potential difference, EMF? They tend to be used interchangeably but they can mean different things.

http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
Question:
If we remove the voltmeters and their leads, what is the voltage between A and B?
An even simpler question:
No voltmeters, no leads, no wires. Is the voltage between A and B positive, or negative? < drama, it's both! :o

As a relevant point of interest, you cannot have a halfturn transformer winding.
Other than the previous link on fractional turns dated 2003, an engineer named Franklin d'Entremont who worked for GE in Somersworth, NH got a patent in 1942 for fractional turns in line frequency transformers.
http://www.freepatentsonline.com/2284406.html (http://www.freepatentsonline.com/2284406.html)
An easy way to get a half turn on a winding with multiple turns is to have 2 windings in parallel with 1 turn difference between the two windings. If one winding has 100 turns and the other has 101 turns, the average is 100.5 turns. It does waste a little power but if there are quite a few turns for the two windings it won't make much difference.

http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
Question:
If we remove the voltmeters and their leads, what is the voltage between A and B?
An even simpler question:
No voltmeters, no leads, no wires. Is the voltage between A and B positive, or negative? < drama, it's both! :o
OK, no voltmeter, no wires. Calculate the voltage between A and B (using physics, Maxwell's equations or whatever). You will probably need to know the length of the wire segments. Assume 4 equal segments and the resistors have negligible length. Do you get more than one number? No.

The problem with Kirchhoff is that he's not thinking fourthdimensionally. The strict adherence to Kirchhoff's laws is what makes it difficult for people to grasp RF.

It is not like he taught advanced physics. From what I've seen his lectures were more like physically themed perfo rmances rather than actual lectures. This was fine for the first year EEs that have never seen physics before.
Yes I have to admit that the videos I have seen don't go into anything too profound and I guess with the more public profile that he has if that is what he is into then it's far enough for educating the average person. He has always striked me as a fairly decent fellow and of his lectures that I have seen I enjoyed most the ones that were indeed more performance in nature. I think he did an excellent job at giving physics a practical angle and perhaps inspiring people. I found his parting public lecture very entertaining and a little informative and greatly enjoyed the lecture he gave to children on the nature of sounds.
In this case though he has suffered the beginner mistake of poor probing and allowing his probe to become part of the circuit.
It is fairly a common problem with people that don't have to deal with the hard physics to miss "real world" factors like stray capacitance. I tried in vain to explain this to a guy at work that has just gotten into radio and is going by rules he is being taught in radio class. He thought that he could solve my EMC issue with standard aerial chokes until I explained what common mode noise is and that that inductor in real life is not an inductor but a tuned circuit and that for RFI purposes 2 inductors of the same value could behave differently because of this thing called stray capacitance.

What happens if we remove the voltmeters? How do we measure the voltage without the voltmeters? We will need to take an electric charge and drag it through the circuit from A to B. How much energy do we need to move our charge from A to B?
The answer is: it depends. If we go from A to B through the left side, or through the right side. Not only that the energy is different for each half of the circuit, but it has an opposite sign. No chance to get a zero for the whole loop.
Well, when measuring voltage, why are we "dragging the electron" where it doesn't want to go? Isn't the usual way to do this to let the electron go where it wants? If you have to drag it one way and input energy, and the opposite is true for the other direction, it will take the other way every time. This is why the electrons go in a circle, here, right? From A to B via route 1, and B to A via route 2? You make it sound like there's some random chance electricity will spontaneously take the uphill direction against the merrygoround and is therefore the voltage undefined. The electron is not going to go A to B via route 2, because it doesn't want to. Oh.. wait. yeah. i'm in way over my head, here. I think I'm starting to see where I have no idea what the grown ups are talking about. >:D
I should probably watch lectures 8, 5, 11, 7 and 15.

We've discussed this many times in previous threads. Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess. But he didn't invent it. It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
In the paper, everything is explained very simply without drama. It's no mystery. The meter wires are part of the circuit and the orientation of the wires determines the results.
LOL this Lewin guy is sounding more and more like the typical academic bitter old crank. Not attributing previous work and acting like a fool? Time to push him out on an ice floe, seems to me.
He's the Leo Kronecker of the physics world...

What happens if we remove the voltmeters? How do we measure the voltage without the voltmeters? We will need to take an electric charge and drag it through the circuit from A to B. How much energy do we need to move our charge from A to B?
The answer is: it depends. If we go from A to B through the left side, or through the right side. Not only that the energy is different for each half of the circuit, but it has an opposite sign. No chance to get a zero for the whole loop.
Well, when measuring voltage, why are we "dragging the electron" where it doesn't want to go? Isn't the usual way to do this to let the electron go where it wants? If you have to drag it one way and input energy, and the opposite is true for the other direction, it will take the other way every time. This is why the electrons go in a circle, here, right? From A to B via route 1, and B to A via route 2?
Very good idea, looks much clear if we move the probing electron as you say.
Let's drag our probing electron with the flow. From A to B via route 1, and B to A via route 2. Our electron will gain some energy on route 1, then will gain some more energy on route 2. After circling a full loop, from A to A, we end up with some extra energy in our probing electron. That energy is the voltage around the loop. So, the sum of voltages around the loop is NOT zero, as Kirchhoff Voltage Law predicted.
This is the contradiction that makes the professor saying "Kirchhoff is for the birds" here.

so hmm. it this a close analogy?
A mobius strip doesn't have a front and a back.... So therefore all the dummies using the term front and back are really talking about a special case (which is pretty much everything except a contrived thought experiment). So it is therefore an OUTRAGE for textbooks to be incorrectly stating that things have fronts and backs when it is not universally the case?

so hmm. it this a close analogy?
A mobius strip doesn't have a front and a back.... So therefore all the dummies using the term front and back are really talking about a special case (which is pretty much everything except a contrived thought experiment). So it is therefore an OUTRAGE for textbooks to be incorrectly stating that things have fronts and backs when it is not universally the case?
You're pushing it a little too far, but that was quite fun. :DD

Ok, trying to be serious, and sticking my neck out. Is this close at all?
Kirchoff's law is not valid in a changing magnetic field. This is given fact. It's accepted. But this is only because of what we define as a closed circuit. We can add "invisible strings" in the form of magnetic flux, and by convention, the circuit is still closed. Which would be sorta like doing a momentum analysis between two colliding steel balls without figuring the effect of a magnet under the table. But by convention, this is the case, and thus Kirchoff's Law is considered invalid in a magnetic flux.
The good Doc has chosen a strange example to make this point, when a must better example would have been to show one loop in a transformer (well that's not a closed circuit!) another example where you could include in the effect of magnetic flux to show how that make Kirchoffs law correct. In fact, the example/experiment is obfuscating to the actual point, and further weirded by completely ignoring the magnet under the table. But it does make you go ooh, and want to watch lectures 8, 5, 7, 11, and 15.
If he makes more of it that this, then he knows something the rest of the world doesn't? Or he is making a mobius strip out of a molehill? (Hmm, maybe that should be "mountain out of a mobius strip?")

oh for christs sake how hard is it to see that voltage is also induced into the probe wires that were being ignored as part of the circuity are. In magnetic's any length of wire cannot be ignored like we do in DC, in AC it can start to be a problem and in magnetic's well tin foil hat time and don't breath the wrong way.

[Kirchhoff's Voltages Law (KVL) failure] would be sorta like doing a momentum analysis between two colliding steel balls without figuring the effect of a magnet under the table.
:+
That's exactly our kind of problem.
Of course, we were trained to identify and deal with it. But it was not so obvious that, in fact, we are "patching" the KVL by adding imaginary batteries to our circuit loop, isn't it? If it were so obvious, we wouldn't bother to talk about it. We are doing that in order to include the external influences of a variable flux. KVL was not meant to include the external influences. Kirchhoff derived the KVL for circuits with batteries and no external fields.
The other Kirchhoff's law, Kirchhoff's Currents Law (KCL) still works just fine no matter the externally magnetic fields. Only KVL doesn't hold, and only in a variable magnetic flux. KVL in a constant flux, again no problem.
Now, is the professor correct, or not? Does Kirchhoff derived his KVL before, or after adding the virtual sources representing induced voltages caused by a variable flux? All the clues indicates that Kirchhoff was not concerned about induced voltages from external fields. He was not even looking for KVL. Kirchhoff was trying to find a way to calculate all the currents in a mesh of linear wires, so he was looking for KCL, not KVL. If I understood it correctly, Kirchhoff was thinking about telegraph wires when he derived KCL and, unintendly, KVL too. (see https://www.jstor.org/stable/20021539 (https://www.jstor.org/stable/20021539) starting from the last paragraph)
Before taking his degree, Kirchhoff had begun his work in original
research, and published a remarkable paper on electrical conduction in
a thin plate, especially a circular one. His problem was to find the
current in any branch of a network of linear conductors. Starting
from Ohm's familiar law, he derived two results long recognized in
electrical science as Kirchhoff 's laws.
I couldn't find the original papers with the KCL and KVL published by Kirchhoff. All I could find is a followup of the KCL and KVL paper, (which, by the way, seems to be the first analysis of a transmission line: https://www.ifi.unicamp.br/~assis/ApeironV19p1925(1994).pdf (https://www.ifi.unicamp.br/~assis/ApeironV19p1925(1994).pdf) ). In this followup paper, Kirchhoff started from a real problem of those times: What happens in underwater telegraph wires. Again, the influence caused by an external variable magnetic flux was not a concern for the problem of submarine telegraph cables. All clues indicates that KCL and KVL were originally meant to be used for normal circuits, with batteries, and without considering external induced voltages.
I'll say the professor was correct when he said we can not always apply KVL. Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.

Come to rethink of it, and as he's clearly not an idiot, I was then willing to believe that he actually did that on purpose, just to make young students aware of the question: using simplistic models while thinking they hold true in the real world, which is a very common pitfall. This would be all good if he made it clear in the end that it was his intent instead of making it even more confusing, to the point that he even managed to confuse some very experienced engineers, using his position of authority.
Now if he was genuinely trying to instill advanced physics notions in young heads, I think this was a very bad way of doing it from a pedagogical standpoint.
Precisely.
The attitude of some professors to initially troll up some drama then later express the correct explanation in their lecturers but newer really make it clear is just crap mentality and bad pedagogics just causing confusion on everyone else expense. I have seen Prof Leonard Susskind do the same in some of his quantum physics lectures.

I'll say the professor was correct when he said we can not always apply KVL. Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.
We engineers do that all the time. We tend to reduce a complicated problem to a simpler one for practical purposes. What Professor Lewin is probably trying to do is to call the attention to the fact that you'll have a hard time if you always think that way.
You see, FaradayMaxwell is not easy. It involves vector calculus and a bunch of non intuitive concepts. That kind of study takes several semesters of an engineering course. Many consider that theory impenetrable.
For those who have Kirchhoff as second nature, this is an additional difficulty. Since Kirchhoff is simpler and easier to apply, FaradayMaxwell seems unnecessarily complicated and a pain to reconcile.
He probably noticed that in his students and decided to demonstrate with an experiment what kind of confusion this may lead to. But as someone has pointed out, it ended up causing more confusion than convergence.

I'll say the professor was correct when he said we can not always apply KVL. Of course, if we first transform the real circuit into a lumped circuit, where we add the externally induced voltages as voltage sources internal to our circuit, then we obtain a new circuit that obeys KVL.
They are always just going to be two mathematical models of the same circuit, the real circuit is in the lab.
It would be necessary to have the formal definition of the law in front of us to see if it is disproved. If anyone can track that down it would be very informative.
Short of that we can use Wikipedia due to it being the most common interpretation of the law. https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws (https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws)
No one has yet produced a demonstration that disproves KVL in a dynamic magnetic field.
I would like to see it.
As others have stated if you model the system correctly you can predict results using KVL and reproduce them in a lab. If there is an exception to this I would like to have it demonstrated.
Also I think the way some people are interpreting MaxwellFaraday is wrong.
They are thinking the sum of voltages around a closed loop which is short circuited will be equal to the rate of change of the magnetic field. I doubt this is the case. Think of a single loop of copper. How would you even measure the two different voltages at the same point.
I am fairly sure MaxwellFaraday describes a case where the loop is magnetically closed but electrically open circuit.

Wow. I was not even aware that there is such a controversy over Kirchhoff's law.
I though Kirchhoff's laws were derivable from Faraday's law and Maxwell equations in general. But quick search shows that it is not very easy.
KVL is only derivable from maxwells equations when dB/dt = 0. It is basically a statement that the force on an electric charge is representable by a conservative field. That means that the energy to more a particle between two locations is path independent, or in particular that moving a charge in a loop requires zero net work regardless of path. You can mathematically show that a conservative field can be integrated to create a scalar potential field, which in the case of electric circuits is just the voltage.
You can't do that with changing magnetic fields. CurlE = dB/dt, so there is no scalar potential that describes electron motion. That is what Walter Lewin was showing. Everything else is just noise.

Dr. Lewin is discussing two apparent problems with Kirchoff's voltage law when a changing magnetic field cuts through the surface of the loop:
1. The voltage between two points depends on the path you take.
2. The voltages around the loop don't add up to zero.
He is strictly defining voltage as the integral of E dot dl. (This is the definition of electrostatic potential so obviously there is a problem here with a changing magnetic field.)
So he goes from point A to point B on one side and adds up the integral of E dot dl. It's just IR_{1}. Then he goes from point A to point B on the other side and adds up the integral of E dot dl. Its just IR_{2}. OMG! They are not equal! They are not even the same sign! This demonstrates point number 1.
So add up the voltages all the way around the loop. He says this is IR_{1} + IR_{2} and it doesn't equal zero! So KVL is for the birds. In fact it equals the inducted EMF around the loop. So it agrees with Faraday's law:
IR_{1} + IR_{2} = EMF
This demonstrates point 2.
He then does his SUPER demo and blows your mind. End of lecture.
Now people see the YouTube video and start saying:
"As for your demo, you are measuring things wrong. Your test leads are forming a loop around the magnetic field and that is giving you a false measurement.
KVL still works! The EMF appears across the ends of the wires connecting the resistors! It's just like a transformer. If you add up the voltages,
IR_{1} + IR_{2}  EMF = 0
The voltages around the loop sum to zero."
Dr. Lewin's response to this is: You can't do that! You can't just move the EMF from one side of the equation to the other! That's dead wrong! That's criminal. (https://bit.ly/2qzwkh0 (https://bit.ly/2qzwkh0))
This is the reasoning you are arguing against.

Dr. Lewin's response to this is: You can't do that! You can't just move the EMF from one side of the equation to the other! That's dead wrong! That's criminal. (https://bit.ly/2qzwkh0 (https://bit.ly/2qzwkh0))
Wait, one of the top comments on that video is from Mehdi, with responses from Lewin from A YEAR ago. Then three days ago, Lewin added a new response with the same bunch of links he was putting all over the lecture video comments. Wow. He really does get worked up about where you put that EMF, doesn't he?

You can't do that with changing magnetic fields. CurlE = dB/dt, so there is no scalar potential that describes electron motion. That is what Walter Lewin was showing. Everything else is just noise.
Yeah, but that "noise" is a very big claim that two points on the same circuit measure differently, he states that as a fact and uses a flawed demonstration to try and prove it. This is why many people have a big problem with this.

... is a very big claim that two points on the same circuit measure differently... This is why many people have a big problem with this.
Yes, two points can measure differently.
Why do you think this is not OK? What rule does it violates?

The prof might be right in theory, but in this case Mehdi is right.
Loops can cancel or add to themselves in a electromagnetic situation, and (as I understand it) Mehdi points that this was not considered properly.
It’s not because something appears on a oscilloscope screen and you have Einstein’s hairdresser that it automatically sustains your postulate.
I have worked in a electromotor maintenance factory and I think i would be laughed out if i tried to sense a coil with so sloppily and diagnose the motor with the result.
That said, I cannot fault his other stuff, and he might be right in theory for specific situations.

He posted a teaser video, sounds familiar:
https://youtu.be/qAtqgSaEU4Y (https://youtu.be/qAtqgSaEU4Y)

https://www.youtube.com/embed/oXZa89Hv8Bo?start=79&end=81 (https://www.youtube.com/embed/oXZa89Hv8Bo?start=79&end=81)

Let me hazard some thoughts.
The figure below shows a voltage source and two voltmeters. One is connected as closely as possible to the source and another one at a distance very, very far from it. The switch is open, so the second voltmeter reads 0 volts. All conductors are ideal, i.e., resistance is 0 ohms.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=568870;image)
Now we close the switch and see the electric field propagating towards the second voltmeter, which still indicates 0V. We can see that, during this transient, Kirchhoff doesn't hold. Because if you add up all the voltages in the loop they will not result 0.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=568876;image)
But, and there's always a but, you can REDUCE the long line of conductors to a series of inductors and capacitors, and now Kirchhoff holds. You can explain why the faraway voltmeter is indicating 0V by the fact that, along the line, some capacitor is still uncharged, while some inductor is reacting to the change of its current with an EMF equal to the source voltage.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=568882;image)
However, there are no such inductors or capacitors. If we consider their existence, they must be infinitesimal. There are infinite infinitely tiny inductors and capacitors, and for Kirchhoff to hold you will have to apply it to infinite meshes.
This is just a simple example, but we can see that Kirchhoff is not adequate to model situations like that.
For a finite number of lumped components where space and time can be disconsidered, Kirchhoff is fine.
But add space and time and you'd be better off with a theory that takes that into consideration, and that is FaradayMaxwell.

There may be an infinite number of ways to model this to show what you want to prove and this is my take. The circuit above isn't like the original problem at all partly because the left part of the circuit isn't switched the same way as the right half. The two halves are two different problems.
I'm lumping the induced voltage producer to one area, a transformer secondary instead of a distributed magnetic field, which is one part of the loop that includes a left an a right resistor of equal value. A very astute instructor I had once said: "Things that are in series are in series with each other." This means that the right resistor can be moved anywhere along the entire length of the wire connecting the left resistor and the transformer and it will always read the same voltage.
The video with the leads being moved from left to right to 'prove' there is a difference is the same as placing another induced A.C. voltage (or transformer secondary) in series with the test points either aiding or opposing the induced voltage in the coil. Phasing is important.

However, there are no such inductors or capacitors. If we consider their existence, they must be infinitesimal. There are infinite infinitely tiny inductors and capacitors, and for Kirchhoff to hold you will have to apply it to infinite meshes.
This is just a simple example, but we can see that Kirchhoff is not adequate to model situations like that.
For a finite number of lumped components where space and time can be disconsidered, Kirchhoff is fine.
But add space and time and you'd be better off with a theory that takes that into consideration, and that is FaradayMaxwell.
Correct. As I noted at the start of this thread, you must integrate over space to apply KVL and KCL for the general  wave mechanical  case. For the 1D case, this effectively gives the differential RLC transmission line element used above, and when solved, gives the Telegrapher's equations. For the 3D case, you get field solutions of course.
We apply Kirchhoff's laws on coarser elements (e.g., whole circuit loops), when it is justifiable to do so, for example when the signals of interest are slower than the physical scale of the system (so that we need not consider wave mechanics as such). In that case, a netlist (an abstract schematic drawing) and finitely many L and C can be used. At lower and lower frequencies, the number of L and C required drops, until at DC, L and C go away completely and we need only consider the network of resistances.
We can likewise consider wave mechanics alone, when it is justifiable to do so. For example, building active circuitry in as small a form factor as possible, then interconnecting the circuits with transmission lines. KVL and KCL are broken between the ends of the transmission line, but we can still consider them locally, i.e. at each port of the line.
This is a very powerful design approach, allowing the designer to greatly simplify the circuit: one need not consider every possible coupling between elements in the circuit, but only those close enough together (including selfcoupling, i.e., LFequivalent stray L and C).
Tim

However, there are no such inductors or capacitors. If we consider their existence, they must be infinitesimal. There are infinite infinitely tiny inductors and capacitors, and for Kirchhoff to hold you will have to apply it to infinite meshes.
This is just a simple example, but we can see that Kirchhoff is not adequate to model situations like that.
For a finite number of lumped components where space and time can be disconsidered, Kirchhoff is fine.
But add space and time and you'd be better off with a theory that takes that into consideration, and that is FaradayMaxwell.
And this is exactly why we lump together these stray inductance and capacitance into lumped form that approximates the behavior of an infinitely large mesh as close as possible. Makes math a whole lot easier.
Its not only a problem of a wire. The resistors also have physical dimensions and as such have parasitics. To perfectly accurately model the resistor we would need to have a infinitely large mesh of resistors capacitors indusctors just to model the internal construction of say a metal film type troughhole resistor. Can you simplify this infinite mesh down to a single RLC circuit and still have it perform close enough to give us near perfect results once we do math to it? Yep we sure can so we do it, because doing math to 3 components is easier than to an infinite number of components.
If we tried to calculate the behavior of perfect non simplified models of a circuit we would need a computer that is much much larger than the largest supercomputers we have since we would basically need to simulate every single electron and every single atom of of the circuit. Yet using lumped component models we can get nearly the same result using the computing power of a PC from the 90s.

OK, well take the original demo, but instead of two resistors, make the whole loop one big resistor. That is, a loop made out of resistive material:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=569548;image)
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)

Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
No in this case you will end up with 0v if you measure it.
You're misinterpreting FaradayMaxwell.

Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
No in this case you will end up with 0v if you measure it.
You're misinterpreting FaradayMaxwell.
I am fairly sure MaxwellFaraday describes a case where the loop is magnetically closed but electrically open circuit.
I'm fairly sure you are misinterpreting it.
But maybe I wasn't clear. Say you have the resistive loop. If you could measure say a section 1/10th of the way around. (I admit it is not easy to accurately measure in the presence of the magnetic field.) So that section has resistance 1/10th of an ohm and has current 1A flowing. You should measure 0.1V. So there are 10 pieces, and if you add them up, you get 1V, not 0V. You could divide it up in other numbers of sections with the same result.
How do you get it to add up to 0V?

But maybe I wasn't clear. Say you have the resistive loop. If you could measure say a section 1/10th of the way around. (I admit it is not easy to accurately measure in the presence of the magnetic field.) So that section has resistance 1/10th of an ohm and has current 1A flowing. You should measure 0.1V. So there are 10 pieces, and if you add them up, you get 1V, not 0V. You could divide it up in other numbers of sections with the same result.
In your example you are measuring just one section of the loop. In the thought experiment, you are measuring the voltage across two points which are connected by two half loops of wire.
So in your example, if you measured a 1/10th section, you should measure [0.8V]. 0.9V in one direction, 0.1V in the other direction. It's a closed circuit with two parallel branches. But Lewin very clearly states that is possible for the voltmeter to have two different readings. And he suggests that it would read either [0.1V] or [0.9V] in the other direction, but he doesn't explicitly state this would be due to inductance in the probe wires. In this example you made, I think it would be reasonable to assume a voltmeter that is connected properly would read [0.8V], which is part of what Mehdin seems to have shown, but maybe I am completely wrong. A conundrum in this example is what happens are you move your two points closer together until they approach zero distance apart? Will you essentially measure [1.0V] with the probes essentially touching? That would be cool. Lewin would say the voltage is undefined in the ideal experiment in all these cases. But clearly Medhin can get meaningful voltage measurements in the real world experiment using real copper wire and regular resistors.
In the actual thought experiment, it's not the resistance of the wire that is causing drop in the wire, it's the inductance. The wire has negligible resistance, at least in comparison with the two resistors that were put in the loop. Now the inductance apparently can't even exist if the wire were an actual ideal superconductor, according to Lewin's teaser video.
I'm sure I'm completely wrong and look forward to the corrections. But more or less that's the way I tend to think about it, right now.

OK, well take the original demo, but instead of two resistors, make the whole loop one big resistor. That is, a loop made out of resistive material:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=569548;image)
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
Interestingly yes you would get zero volts in this case!
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=569761;image)
It turns out you can poke any two points in this circle and have the points sit at 0V despite there being 0.8mA peak of current flowing in this simulation. This happens because the voltages on each inductor and resistor pair balance out. Spice follows Kirchhoffs rule so you need the voltages to add up. Since the current is the same means the voltage drop on all resistor is the same, the rest of the drop is in the inductors and since they are the same it distributes equally. This makes the voltage on the resistor chunks the same as on the inductor chunks so each one of these lumped inductive resistor models has 0V across itself all around. But there is voltage within the model across the resistor or inductor alone.
This effect is broken as soon as your ring is not completely even around its radius. If you ware to make the resistive material thicker at some point this upsets the balance and you see a voltage across the thinnest part of the ring.
And yes the inductive probing leads again would mess things up, but again you could fix the probing problem by simply averaging what the left and the right scope sees.
EDIT: Updated the test leads to 2.5uH to reflect them being the same as 1/4 of the loop.

Oh and i want to add that the same thing would happen in the physical demonstration with 2 resistors if you made the resistors say both 100 Ohm rather than one being 100 and other 900. This makes the demonstration a bit less exiting because then both scopes see the same shape and magnitude except that one scope is seeing the inverted waveform.
As long as the circuit is symmetrical around the two points you measure this is always the result. The same current flows around it so an identical circuit will produce the same voltage drop on both symmetrical sides, but since one of the halves is having the current running the opposite way it also generates an opposite voltage. So once summed up around the loop you basically are subtracting two voltages of the same size so you get 0V.

@RoGeorge, just to let you know that you are not alone.
The only critic I would move to Lewin is in its use of the word "potential" even when the quantity is not defined because it is multivalued. I wonder if his demo would have had a better reception had he used the word "glorp" or "multivalued potential" to describe it.
In his followup video titled "Believing and Science are Very Different" (youtube code watch?v=wz_GqOUrk4) he also shows a conceptual diagram (I am not calling it a schematic on purpose) demonstrating how the equations give exactly that result: the 'multivalued potential' at the very same pair of points to have two different distinct values at the same time.
It is also possible to push that diagram even further by dragging a voltmeter (and its probes) inside the loop and seeing how the 'multivalued potential' between those two points varies with continuity from +0.9V to 0.1V, as the fraction of the area of the loop containing the voltmeter path goes from 0% to 100% of the area of the loop with both resistors (and the changing magnetic field). And there is also a video made by a detractor (sorry, maybe this is not the right term, opponent might be better) of Lewin that shows just this [note1]... actually confirming Lewin's modeling of the system.
I cannot but wonder what causes this resistance... pun intended... to accept the consequence of the loss of irrotationality (is this even a word?)
I guess one reason is that we place too much faith in our instruments and we tend to believe the numbers they show have a meaning no matter what.
Another might be the difficulty in realizing that the resistor are INSIDE the secondary of the imaginary transformer. So, goodbye lumped component model...
Or probably engineering courses have to cram too much material and leave out too much of the basics, concentrating on the more pragmatic parts.
EDIT: corrected some of my lousy grammar and syntax, but not all.
Also, I would like to add that as long as the probes are outside of the loop (more specifically outside of the region at varying B field) there is no probing problem at all (you might have to worry about capacitive coupling with the mains, and RFI from RadioBoomBoom, but not about the field that is confined inside the loop. Also self inductance is negligible, as shown by Lewin in the aforementioned video.
[note1] Ironically, when we take the measurement path inside the loop, that's where we can interpret the results (changing from +0.9V to 0.1V) as the effect of 'bad probing' (now I have to take into account the intercepted flux). I guess that's the reason Lewin is staying outside, to avoid confusion.
Finally, maybe getting rid of the voltmeters and their probes, resorting to some other way to measure the 'voltage' across each resistor (placing an ammeter in the loop and using ohm's law?, using calorimetric measurements to infer the dissipated power? substituting the resistors with a voltage dependent light source and measuring the light output?) could help in removing the confusion).
Personally I like to think tiny angels are pushing electrons in the loop, producing a 1mA (oscillating) current. That would cause a 0.1V drop on the 100 ohm resistor and a 0.9V drop on the 900 ohm one. The fact that it's angels and not a generator allows the loop to be closed without anything between the resistors, and that show exactly why KVL is no longer valid. You have to mend it somehow by adding a distributed emf, but that does not remove the fact that KVL is broken.
If you do not believe in tiny angels, well you could use a varying magnetic field that stays all within the loop. A toroidal transformer, maybe?

OK, well take the original demo, but instead of two resistors, make the whole loop one big resistor. That is, a loop made out of resistive material:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=569548;image)
Say the EMF induced in the loop is 1V. Say the total resistance is 1 ohm, so you have 1 amp flowing around the loop. Take any point in the loop and go around the loop adding up the IR drop. Go all the way around the loop. You always end up with 1V, not zero.
So how are you going to model this to make Kirchoff's law work? An infinite number of resistors dR and an infinite number of voltage sources dV? (I don't think so.)
Interestingly yes you would get zero volts in this case!
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=569761;image)
It turns out you can poke any two points in this circle and have the points sit at 0V...
That is wrong. Your model is wrong. It led you to the wrong conclusion.
I realize I went down a dark path when I said the word "voltage". As has been pointed out, "voltage" and "potential" are words that are not defined well in this situation. The E field is defined. The E field in this case forms circular loops. The integral of E dot dl is also defined here. As RoGeorge said, charge moving around the loop experiences a force from E over the distance moved, dl. That involves energy. That is defined also. It is not coming from imaginary coils. It's coming from the E field which is coming from the changing magnetic field.
Like a lot of people, I have a tendency to say that "the magnetic field induces a voltage between the ends of the wires". This resistive loop is an example of what happens when there are no wires.
Now I'm not opposed to making this kind of model. It may be appropriate in some situations. The model of just an ideal transformer with a single lumped R would be appropriate in some situations. It depends on what you are trying to model.
As for actually measuring with a voltmeter, if you kept your measurement leads twisted tightly together and arranged the ends tight next to the 0.1 ohm section that you are trying to measure, then you have no magnetic field passing through your measurement loop. You would measure 0.1V, not zero volts. That's just Faraday's law.

@Sredni
Indeed, mathematically speaking it doesn't make sense to talk about Potential in a nonconservative field.
Another big confusion is created because in some modern books the definition of Voltage is considered
1) Voltage1 = Potential in point A  Potential in point B
2) Voltage2 = The energy required to move a unit of charge between A and B
For conservative fields (e.g. in Electrostatic, or in DC circuits) the two definitions are equivalent, and Voltage1 is the same thing as Voltage2. The path does not matter.
In nonconservative fields (e.g. Electrodynamics, or in AC circuits) Voltage1 is undefined. Potential is undefined. Only Voltage2 makes sense, but beware of the path! Different paths will give us different Voltage2 values.
NOTE: Our most beloved voltmeters and oscilloscopes measure the Voltage2 type of voltage. They measures the energy to move the unit charge. They do NOT measure the Voltage1 type of voltage, they do not measure a potential difference.
Mathematically speaking, the notion of Electric Potential doesn't make sense for e.g. AC circuits.
Go figure, Electric Potential doesn't exist for AC!
P.S. Never say that at a job interview. ;D

It turns out you can poke any two points in this circle and have the points sit at 0V...
That is wrong. Your model is wrong. It led you to the wrong conclusion.
Do you find following model as matching your "whole loop one big 1 Ohm resistor" ?
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570035;image)

Do you find following model as matching your "whole loop one big 1 Ohm resistor" ?
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570035;image)
No, that still would have each voltage source + resistor pair cancelling out to 0V.
I'm not sure how to make a model with lumped components that violates KVL.

I do have some resistance wire around here that i could weld into a continuous loop and do the experiment.
Just not quite sure how to keep the probe wires from picking up the magnetic field since we are interested in the actual voltage at the test point. My average out the reading for going left and right only works when probing exact opposite points on the circle.
Using something like a lamp or LED as the 'probe' sounds like a good idea at first but then you realize you still need some wire to connect it to the two points and thus has the same problem. Running it along the ring would give similar results that you get a different voltage depending on the path the wire takes. This essentially makes the magnetically induced voltage disappear and you get to see the voltage drops on sections of resistance again. But what happens if we instead remove the restive ring but leave the probe wires connecting to the same two points in space connected to nothing? Do we measure nothing?

But what happens if we instead remove the restive ring but leave the probe wires connecting to the same two points in space connected to nothing? Do we measure nothing?
I'm thinking you have no current path through the meter, so you you measure nothing.

No, that still would have each voltage source + resistor pair cancelling out to 0V.
Yes, it cancels to 0V. In every test point labelled "A, B, C, D..." voltage against ground is 0V. That's exactly what I am showing.
Your original "model" contains single 1V EMF source in form of single, rounded 1 Ohm resistor dissipating/cancelling that 1V of EMF  that's OK, but model with 10 sources and 10 resistors in series is not ok anymore?  Apply integral to my 10x0.1V EMF sources and 10x0.1 Ohm resistors to get your single loop back. Do you see what I mean now?
[edit] For those who did not pay attention whole thread, it is advised to read this post (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945138/#msg1945138), especially to sentence "KVL/KCL reduce to a single point only: they are a differential relation, which must be integrated over the space of interest".
I'm not sure how to make a model with lumped components that violates KVL.
LOL. You basically said: "you are wrong, but I cannot prove it" :DD

I'm not sure how to make a model with lumped components that violates KVL.
LOL. You basically said: "you are wrong, but I cannot prove it" :DD
KVL holds for lumped circuits. This isn't a lumped circuit.
I can prove those models are wrong because the voltage around the loop in the model adds up to zero.
Using Faraday's law on the resistive loop, integrating E dot dl around the loop doesn't equal zero.

Using Faraday's law on the resistive loop, integrating E dot dl around the loop doesn't equal zero.
Yes. Nonzero current flows in case of electrically short loop. Note that ideal conductor have zero resistance, so in case of short superconductive loop there will be zero volts no matter how, where and using how many scopes you measure. Kirchhoff's Law Holds in this case BTW ;)
KVL holds for lumped circuits. This isn't a lumped circuit.
Why not? If you cut 0resistance loop open and connect 1 Ohm resistor in the opening, then in our 1 Ohm & 1 A example case there will be 1V drop on the resistor and 1V EMF voltage generated in the loop. Loop is voltage source and resistor is load  what's the problem with Kirchhoff's Law in this lumped circuit?
[edit] The same considerations apply to two 0.5 Ohm resistors and two halves of the loop.

Pls keep the thread polite and leave out the emoticons as they can distract.
Back to the thread title.
Does Kirchhoff's Law Hold?
My belief is if you can model something and if you can verify this with measurements then your model holds.
Every model has limitations but what are the limitations of KVL?
So AFAICT it will hold in Time varying magnetic fields.
People use it in steady state analysis all the time.
But not so easy in Transmission lines.
Teslacoil suggested you can use it at either end.
So to dispprove KVL within Time varying magnetic fields I suggest you need to prove it in the lab.
IMO I don't think Dr Lewin did this.

So to dispprove KVL within Time varying magnetic fields I suggest you need to prove it in the lab.
IMO I don't think Dr Lewin did this.
Agreed. Rfeecs already mentioned paper explaining "Super Demo" experiment and it's results:
We've discussed this many times in previous threads. Dr. Lewin gave his world famous SUPER DEMO as he refers to it in 2002, I guess. But he didn't invent it. It is an exact recreation of the experiment in this 1982 paper:
http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)
In the paper, everything is explained very simply without drama. It's no mystery. The meter wires are part of the circuit and the orientation of the wires determines the results.

Using Faraday's law on the resistive loop, integrating E dot dl around the loop doesn't equal zero.
It doesn't. However, every infinitesimal gain of energy represented by E · dl is lost as heat in the infinitesimal resistor dR.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570248;image)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570254;image)

[edit]Apparently this is the setup Faraday used.
Not sure, but wouldn't this be a better setup to what ElectroBoom's/Lewins experiment should be using? [/edit]
(https://upload.wikimedia.org/wikipedia/commons/2/2a/Faraday_emf_experiment.svg)
The torroid would capture most of the stray flux.
So instead of worry about bad probing, you know what flux is linked.

couldn't link image

But what happens if we instead remove the restive ring but leave the probe wires connecting to the same two points in space connected to nothing? Do we measure nothing?
I'm thinking you have no current path through the meter, so you you measure nothing.
Well if you have both meters connected simultaneously just like in Dr. Lewins experiment you actually get the same voltage pulse on both meters no matter if the resistive ring is connected or not (At least inside LtSpice). This clearly points to a problem with the experimental setup since we shouldn't be measuring voltage in a circuit with 0 components. Yes if you leave only one meter connected you will indeed read 0V because the probe wires are floating. Both meters connected provides a return path trough each meter so they can measure something. This shows that the meters are not correctly showing the voltage at points A and B but a voltage somewhere else (Like across the meters terminals)
And that makes sense since the ring is supposed to have 0V across any two points on it. Connecting to nothing also produces 0V so the readings on the meters are the same in both cases.
I do want to do this continuous resistive ring as a physical experiment, but i first need to figure out the correct way to probe this.

I do want to do this continuous resistive ring as a physical experiment, but i first need to figure out the correct way to probe this.
Toroidal iron core AC mains transformer will greatly help to contain magnetic flux. AC mains seems to be good enough "test signal" source as well. All you need to do  add test winding and have a fun. Beauty of using AC voltage here  you don't even need scope. Any multimeter is good enough.

"Well if you have both meters connected simultaneously just like in Dr. Lewins experiment you actually get the same voltage pulse on both meters no matter if the resistive ring is connected or not"
This is a good point. You will have a loop with the meters' internal resistances taking the place of the resistors. With 10 meg input impedance and a 1V emf, the current in the loop would be 1/20 of a microamp. If the internal impedances are the same, the voltmeters will measure the same voltage (edit: the problem with a sinusoidal stimulus is that we lose the sign, but this adds drama). But what happens if the internal resistance are different, say 10 meg, 1 meg? Would they not measure different voltages, despite being connected to the same points?
EDIT
To get the same voltage ratio as in Lewin's experiment the internal impedances (at the test signal frequency) should be 9meg, 1meg.
Probably this is where we reach the language barrier between physics and engineering. An engineer that has different readings from instruments connected to the very same poiints will try to interpret this as a measurement error (load effects) or as wrong probing (in this case using the emf to make the trusted KVL to balance again). A physicist, on the other hand, knows that there is no problem at all, it's just that the so called 'voltage' is no longer positional: it does not depend only on the points where you place the probes, it also depends on the path followed by the probes.
The engineer will say: "see? KVL checks out: one instrument measures 0.1V, the other 0.9V, and then there's the emf of 1V, when I take all signs into account, the result is zero. KVL rulez!". A physicist will say: "see? the voltage is path dependent! If I sum the voltages around this loop I get 1V. That's the emf. KVL is for the birds!"
You might think both are right, but... the engineer is getting his balance check still assuming voltage is positional  and that's not true. The physicist gets his balance check and has the satisfaction to add his impression of Walter Kronkite saying "...and that's the way it is".

I do want to do this continuous resistive ring as a physical experiment, but i first need to figure out the correct way to probe this.
Lemme give it a burl using what I think I know about Maxwell.
Let's suppose we have a changing magnetic field B confined to the area Σ, and we connect a voltmeter like in the picture below. This can be achieved for example when you have a ferromagnetic core that manages to concentrate most of the lines of B in its transversal area. So the very few lines of magnetic field in the area Σ' can be considered negligible.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570917;image)
Now let's remove the right hand side of the loop between the voltmeter probes. We end up with a new loop with an area Σ+Σ'.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570923;image)
FaradayMaxwell says that the emf generated by this loop will be the derivative relative to time of the integral of the scalar product of B and dA on the surface Σ+Σ`. dA is the infinitesimal vector element of surface perpendicular to the surface Σ+Σ`. However B is zero over Σ'. So the scalar product over Σ' will be zero. This means that the voltage measured by the voltmeter will be that as if the loop covered only the area Σ.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570929;image)
Now let's remove the left arc and replace the right arc of the loop.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570935;image)
We can see that B is totally outside of this new loop and, according to FaradayMaxwell, will not induce a voltage. So the voltmeter is going to show 0V.
Now that we know what is going on, we can REDUCE the problem to Kirchhoff and put everything together.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570941;image)
In relation to the voltmeter, the left arc is a generator in series with half of the total resistance of the loop. The right arc is the other half and is just a load. It doesn't contribute to the emf the voltmeter sees.
If you move the voltmeter to the left side of the loop, the left arc is now the load and the right side is voltage source in series with an internal resistance. Notice that source is inverted.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570947;image)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570953;image)
But, of course, we are smart people. We place a voltmeter immune to a magnetic field in the center of the loop. And we have the equivalent Kirchhoff reduction.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570959;image)
And bingo! We have our 0V.
However, if we change the position of the voltmeter and of the leads we are going to have whatever voltages we want between 0 and 1V, in absolute terms.
So what do we take from that? Kirchhoff doesn't always hold. Kirchhoff does not expect that the readings of your voltmeter varies depending on the position of your test gear in relation to your device under test. You need to inspect what you have under FaradayMaxwell and then reduce it to Kirchhoff, i.e., you have to define things that are not predicted by Kirchhoff before you apply it.
We are accustomed to measuring the opencircuit voltage of secondary of transformers and we do not care about FaradayMaxwell, but what we are really doing is an implicit reduction to Kirchhoff because we always have the configuration shown in the second picture of this post.

To be honest, I don't understand what all the fuss is about. What Dr. Lewin is pointing out with his experiment is, as he has repeated often by now, basic physics. The most basic definition of a voltage between two points is expressed as the line integral of the electric field from point A to point B. It is obvious that this only works properly as long as the line integral is _independent_ of the path chosen. If it becomes, for whatever reason, dependend on the path chosen you can no longer define a potential function for that electric field. You don't even need physics for that, thats just basic math at this point. With no potential function the term "voltage" becomes imprecise, because it does not take into account the path of measurement.
Now, if you design an experiment to include a changing magnetic field you get curl E != 0 at some area of the experiment making the very definition of voltages and potentials meaningless. There is this very nice paper [1], that has been shared on this forum multiple times, explaining to the last detail how it is that even with perfect measuring tools you will get two different voltage readings between two points. Note that in this paper bad probing is not a problem. The area where the probes are have no magnetic field, meaning there is _no_ voltage induced into the probes. I think this very fact of voltage not beeing defined is what Dr. Lewin wants to bring across, and I can understand him getting frustrated when people continue to disagree with him there. I was scared of this paper at first, but believe me there is no complicated math involved.
Now to the part of KVL not holding any more: it seems people have different understandings of what KVL means. If you know it as "summed up voltages across a loop in a circuit are zero" then _yes_ it does not hold in this case. Because in the experiment shown by Dr. Lewing the voltages do not sum up to zero. And I will trust him when he says that at MIT they did the experiment with superconductors _which cannot have an electric field inside them_ so there is no voltage across the "ring" that magically makes KVL hold.
If you interpret KVL to say "summed up voltages across a loop in a circuit sum up to the magnetically induced voltage" then this version of KVL holds. It is not nearly as practical as the first one though. You can, for example, not use it in a schematic. Because a schematic does not define the physical location of a component  and therefore, you don't know where the wires are and you don't know what the induced EMF of the loop will be.
Now if you are an engineer, most often you will not deal with "real physical devices" but you will _model_ them to make a equivalent circuit. That is where the voltage source, that many people want to add to the circuit, comes into play. Yes, as long as you are careful with your circuit you can model the effects of EMF into a voltage source. But the very fact people start to talk about "bad probing" all the time shows why this is now only a model of the real experiment. If this were a voltage source it wouldn't matter how I place my probes. They will always read the same voltage. With an EMF they do not. The concept of "bad probing" is that the measurements depend on the way you place your probes. Hence, the voltage you get is *path dependent*
It is of course a common problem, that a model of reality will fail at some point. So to still work with your model, you need to _know how and why_ it can fail. So, as long as you know what you do you can use KVL, but you need to keep in mind that it will only work as long as your actual physical device is carefully designed to match your model (or the other way around).
[1] http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf)

However, if we change the position of the voltmeter and of the leads we are going to have whatever voltages we want between 0 and 1V, in absolute terms.
No. We can't measure whatever voltage we want between 0 and 1V. You shall check model of ring split ring into 10 parts or 4 parts each having 1/4V and 1/4R accordingly. BTW we talked about such case in this thread already.
So what do we take from that?
That you shall doublecheck your theory.
Kirchhoff doesn't always hold.
I'm afraid that you did not prove that.

No. We can't measure whatever voltage we want between 0 and 1V.
Almost right. If the emf is 1V, with equal resistances in the loop you can measure any voltage you want between 0.5V and +0.5V.
This goes from intercepting the whole flux in one sense to intercepting the whole flux in the opposite sense.
You shall check model of ring split ring into 10 parts or 4 parts each having 1/4V and 1/4R accordingly. BTW we talked about such case in this thread already.
Trying to localize in lumped components an inherently distributed phenomena will lead you to contradictions. Trust me, I know because I too did it, before seeing the light. :)

Now to the part of KVL not holding any more: it seems people have different understandings of what KVL means. If you know it as "summed up voltages across a loop in a circuit are zero" then _yes_ it does not hold in this case. Because in the experiment shown by Dr. Lewing the voltages do not sum up to zero.
Experiment of the Dr.Lewin does not show it (voltages do not sum up to zero). It is explained in the paper you BTW refer to: http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf).
And I will trust him when he says that at MIT they did the experiment with superconductors _which cannot have an electric field inside them_ so there is no voltage across the "ring" that magically makes KVL hold.
We are doing experiment with superconductor loop and single, lets' say 100 Ohm resistor. What will be EMF voltage on particular resistor during experiment?

Almost right. If the emf is 1V, with equal resistances in the loop you can measure any voltage you want between 0.5V and +0.5V.
:palm:
Prove it. Download spice (LTspice) and try to model it with more than few lumped elements.
Trying to localize in lumped components an inherently distributed phenomena will lead you to contradictions. Trust me, I know because I too did it, before seeing the light. :)
Try me. Please explain why your model of two batteries and two resistors is OK to show that you read 0V, but mine with 10x0.1V batteries and 10x0.1R resistors (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1960373/#msg1960373) is not?

Yes, he did show exactly that. Open up a physics book of your choice and it should tell you the KVL in presence of magnetic fields is that the sum of all voltages equals the induced EMF. At least from what I can tell that is also what any professor at university taught me.
If you take a ring of superconducting material and connect it to a resistor at one side, the voltage across the resistor will read whatever is appropriate according to faraday. If, however, you measure across the superconducting ring you will read 0 Volts.

If you take a ring of superconducting material and connect it to a resistor at one side, the voltage across the resistor will read whatever is appropriate according to faraday. If, however, you measure across the superconducting ring you will read 0 Volts.
Wait... Please explain. Im afraid that I do not follow you here. Are you saying that if I route my test leads on resistor side, I will read voltage whatever is appropriate according to Faraday, but when I place my test leads on superconducting ring side, I read 0V?

Yes.
Edit: Now I'm sorry, this is not a chat but a forum so i should probably explain myself a little. What you get from faraday is the voltage *across the closed loop*. So thats Superconducting Ring + Resistor. From the resistance of the total loop (which is 0R for super conductor + resistance of resistor) you calculate the the current. Now take the resistance of the super condcutor, which is 0, and multiply it with the current. You will get 0V across the super conductor.

"Prove it"
That's what Lewin did. See his video "Science and believing are different things" and follow his mesh analysis.
He is doing it with two voltmeters outside the main loop where B is changing. As long as you are outside you can always see two meshes with one of the voltmeter inside: one that do not contain the B field, and another one that contains it. As far as the Bencircling mesh go, in one case you have a positive orientation passing trought the small resistor, in the other one a negative orientation passing trough the big resistor. And this gives rise to the different voltages shown by the two external voltmeters.
But you can expand on that and bring the voltmeter inside the Bencircling loop. In this case for the inner voltmeter you will see two meshes that are both inside the B field: one positively oriented passing through the small resistor and the other negatively oriented passing through the big resistor. Depending on what fraction of the area is intercepted in the small or big R mesh, you end up with a different voltage reading.
You should interpret the square mesh as conceptual diagram, the actual area intercepted depends on the path of the probes in the real wold, but still goes from intercepting all the Bvarying region in one sense, to intercepting all the Bvarying region in the other. In between you get all the values of voltage comprised between the reading of the voltmeter on the left and the reading of the voltmeter on the right. All of this from the same two points!
Do the math, solve the circuit and you will see the light.
Now, I understand the urge to choose, among all these values the one that makes you feel better, namely the one from a path the equally splits the area (I should say the normal flux to be precise) between the two meshes, but that's just an arbitrary decision.
EDIT to answer the question posted below: removed another extra space at the bottom.
Also to clarify: I have zero batteries in my circuit, just the emf. And the two resistors are lumped component part of the physical circuit, not a tentative to model a distributed component.
As for your attempt to model a distributed circuit (where voltage is non singlevalued) with a lumped circuit (where voltage is singlevalued) to show that voltage is not multivalued, I guess it's logically flawed.
Solve the mesh circuit with the emf, do the math. You will see the light.

Yes.
Edit: Now I'm sorry, this is not a chat but a forum so i should probably explain myself a little. What you get from faraday is the voltage *across the closed loop*. So thats Superconducting Ring + Resistor. From the resistance of the total loop (which is 0R for super conductor + resistance of resistor) you calculate the the current. Now take the resistance of the super condcutor, which is 0, and multiply it with the current. You will get 0V across the super conductor.
Oh, really? When it is convenient, you just forget about EMF.
We take 1.0V battery with 0.001 Ohm internal resistance, connect it to 1 Ohm resistor. 1A current will flow. Now take the resistance of the battery which is 0.001, and multiply it with the current. Result is 0.001V. So battery miraculously is not 1V anymore but 0.001V? :palm:

"Prove it"
That's what Lewin did.
TL;DR. I did not find answer to my very simple question I asked:
Please explain why your model of two batteries and two resistors is OK to show that you read 0V, but mine with 10x0.1V batteries and 10x0.1R resistors is not?
[edit] Dr. Lewin just recreated experiment http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf). Unformtunately for fanboys of Dr. Lewin, that experiment does not disprove KVL.

Yes.
Edit: Now I'm sorry, this is not a chat but a forum so i should probably explain myself a little. What you get from faraday is the voltage *across the closed loop*. So thats Superconducting Ring + Resistor. From the resistance of the total loop (which is 0R for super conductor + resistance of resistor) you calculate the the current. Now take the resistance of the super condcutor, which is 0, and multiply it with the current. You will get 0V across the super conductor.
Oh, really? When it is convenient, you just forget about EMF.
We take 1.0V battery with 0.001 Ohm internal resistance, connect it to 1 Ohm resistor. 1A current will flow. Now take the resistance of the battery which is 0.001, and multiply it with the current. Result is 0.001V. So battery miraculously is not 1V anymore but 0.001V? :palm:
No, the result of 0.001V is the voltage across the internal resistance of the battery, not the internal voltage source. Which is why the voltage across the terminals of the battery will have dropped by 0.001V, what are you trying to get at now?
I did not forget about EMF, how do you come to that conclusion? Faraday gives us the voltage across the closed loop. You have a loop consisting of 2 components, one is superconducting and will not have any voltage across it. The other is a resistor, which can have a voltage across it if there is current flowing through it. So, naturally, all voltage in the circuit will be across the resistor.
Think of the way this voltage is created: the change of magnetic field puts a force on the charges in the ring+resistor. Now inside a superconductor it doesn't take energy to move a charge (hence resistance of 0R) so your electric field is 0. Inside the resistor it does tage energy to move the charges across, so you will have an electric field of nonzero, therefore a voltage across the resistor.

I did not forget about EMF, how do you come to that conclusion? Faraday gives us the voltage across the closed loop. You have a loop consisting of 2 components, one is superconducting and will not have any voltage across it. The other is a resistor, which can have a voltage across it if there is current flowing through it. So, naturally, all voltage in the circuit will be across the resistor.
"all voltage in the circuit will be across the resistor" .. where superconductor loop terminals are connected meaning same voltage will be present on the both ends of the loop as well. So you do not measure different voltages by manipulating with test leads, this is dumb. Actual effect of test lead placement is explained in the document (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf) linked here so many times already.

I did not forget about EMF, how do you come to that conclusion? Faraday gives us the voltage across the closed loop. You have a loop consisting of 2 components, one is superconducting and will not have any voltage across it. The other is a resistor, which can have a voltage across it if there is current flowing through it. So, naturally, all voltage in the circuit will be across the resistor.
"all voltage in the circuit will be across the resistor" .. where superconductor loop terminals are connected meaning same voltage will be present on the both ends of the loop as well. So you do not measure different voltages by manipulating with test leads, this is dumb. Actual effect of test lead placement is explained in the document linked here so many times already.
No, this is precisely what this is all about. If you measure at the same two points of a circuit you can get different readings on a voltmeter in the presence of an EMF. The reason this is the case and is *not dumb* is that in the presence of EMF the electric field is not a conservative vector field. Your voltage will vary depending on which path you take.
You want to know the voltage across the superinductor, you integrate along a line through the superconductor. Your voltage will be zero, because inside an ideal conductor the electric field is always zero.
You want to know the voltage across the resistor, you integrate along a line through the resistor. Your voltage will not be zero.
I hope we agree, that the voltage induced by the changing magnetic field will be across the resistor. Take any textbook, look up the introdcution to magnetic indcution. You will find an "almost closed loop" split up at some point and a resistor attached to that "split". Every textbook will tell you the voltage across the resistor is the closedloopvoltage as dictated by faraday.
Now assuming for a second that the same voltage is also present across the superinductor. In that case the "closedloop" voltage will be zero. That directly contradicts faradays law.

You can't do that with changing magnetic fields. CurlE = dB/dt, so there is no scalar potential that describes electron motion. That is what Walter Lewin was showing. Everything else is just noise.
Yeah, but that "noise" is a very big claim that two points on the same circuit measure differently, he states that as a fact and uses a flawed demonstration to try and prove it. This is why many people have a big problem with this.
There is no way to fix the demonstration that keeps the character because the whole point is that "voltage" is undefined in the circuit in question. So there is no consistent way to define a measurement of it. I don't get why this is hard to understand.
Yes, there are always good and bad measurement techniques and you always have to worry about measurement technique causing errors. But you always assume there is some underlying "true" value you are trying to get at. Here, the "flawed" measurement is actually intrinsic to the problem.

First I want to point out that SPICE is for simulating, not for proving.
Second, SPICE is not aware of the electric and magnetic fields. SPICE is for solving circuits using Kirchhoff, and it can work only after you, the SPICE user, converts the geometry of a real circuit into a lumped circuit, with equivalent coils and capacitors. You, the user, have the responsibility to take the real circuit where Kirchhoff might fail, and convert it into an equivalent lumped circuit with all kinds of coils and capacitors and transformers, and transmission lines, so SPICE can crunch the numbers using only Kirchhoff and no Maxwell. It is the SPICE user who must take into considerations not only the geometric size and shapes, but also the permeability and the dielectric properties of the surrounding materials. That is a lot left outside SPICE, and even more, the topology of the lumped circuit needs to be changed when the external conditions change.
A lumped circuit is an equivalent circuit, where you, the user, are responsible for finding the correct topology of coils and capacitors and their values in such a way that Kirchhoff's law can be applied.
https://en.wikipedia.org/wiki/Lumped_element_model
Spice is solving its I/V matrix equations based on Kirchhoff and lumped circuits. That is why in SPICE you won't find any circuit that does not obey Kirchhoff.
In real circuits, any piece of wire is a capacitor, a coil and a resistor in the same time. This is crazy, and makes it almost impossible to calculate a lumped equivalent that holds with the real world. We have some dedicated shapes for capacitors and coils where the formulas for L and C are well known, but that's all. For a random piece of wire there is no clear formula without fields and material constants, and Maxwell. If we go into transmission lines or antennas, things goes even more complicated. There are no antennas in SPICE. There is no causality in SPICE. Propagation in lumped circuits is considered instantaneous, which in the real world is not true.
If we go further, let's say to calculate the beam of a particles accelerator, SPICE can not help. Spice does not know Maxwell, and does not know relative speeds and Special Relativity, SPICE knows only Kirchhoff.
If we go even further, for satellites working in different gravitational fields, SPICE is again unaware of General Relativity. It is us who need to take Special or General Relativity into consideration, and invent a lumped circuit in such a way that we capture all these effects into our imaginary lumped circuit.
Maxwell's equations stand no matter what. That is why they are so praised. Maxwell's equations does not need inductors and capacitors. Kirchhoff does. Again, Kirchhoff is great for static fields (AKA conservative), but can not be applied for nonconservative fields. It was not meant for such nonconservative fields.
In order to use Kirchhoff for nonconservative (loosely speaking "variable" fields), we found a workaround, a trick. We stuff the real circuit with all kinds of imaginary parts, and not only we add those imaginary parts, but the values and the topology of the lumped circuit keeps changing based on external fields and external surrounding of the real circuit, yet our real circuit never changed during this, only the surroundings changed. We call this stuffed imaginary circuit a lumped equivalent circuit of the real thing.
This fake stuffing we do in order to obtain a lumped circuit is very, very fake and unnatural thing to do, yet we considered it NORMAL, because we are used to it, and because it makes our calculations easier.
In fact, we did it so often that the lumped circuit became to us a second nature, while the real circuit is looked rather as a fussy oddity that needs a lot of care (like electric and magnetic shielding) for it in order to work as expected. We got so used with our imaginary fake lumped circuits that we now consider reality an anomaly. We call reality parasitic hum, parasitic inductance coupling, parasitic capacitive coupling, parasitic ground loops, parasitic antennas, parasitic transmission lines, parasitic everything.
Suddenly, reality become for us just a parasitic effect, and we like to consider it that way just to accommodate our distorted lumped circuits with the cruel reality. That has a lot to do with how human mind works, and from here we are in the realm of human psychology and philosophy.
"A fake repeated over and over becomes reality" < just an old saying.
Peace!

To confirm what RoGeorge said:
Once you get to the point you can't make a sufficiently accurate lumped element circuit model, you have to resort to field solvers such as Sonnet, ADS/Momentum, HFSS, or COMSOL. Those model what is actually going on in a geometrical model of your circuit. You can't extract a voltage from those. I actually tried this once indirectly  I was trying to make a nice heat map of a crosstalk simulation result. When it had weird discontinuities I looked at what I was doing and realized it made no sense.

I did not forget about EMF, how do you come to that conclusion? Faraday gives us the voltage across the closed loop. You have a loop consisting of 2 components, one is superconducting and will not have any voltage across it. The other is a resistor, which can have a voltage across it if there is current flowing through it. So, naturally, all voltage in the circuit will be across the resistor.
"all voltage in the circuit will be across the resistor" .. where superconductor loop terminals are connected meaning same voltage will be present on the both ends of the loop as well. So you do not measure different voltages by manipulating with test leads, this is dumb. Actual effect of test lead placement is explained in the document linked here so many times already.
No, this is precisely what this is all about. If you measure at the same two points of a circuit you can get different readings on a voltmeter in the presence of an EMF. The reason this is the case and is *not dumb* is that in the presence of EMF the electric field is not a conservative vector field. Your voltage will vary depending on which path you take.
You want to know the voltage across the superinductor, you integrate along a line through the superconductor. Your voltage will be zero, because inside an ideal conductor the electric field is always zero.
You want to know the voltage across the resistor, you integrate along a line through the resistor. Your voltage will not be zero.
Ok. I am still trying to connect theory to my realworld knowledge of transformers. Dr. Lewin do not use superconductor in his transformer. So we can take transformer w/o superconductor as well  AC mains transformer. So you say that my AC mains transformer with 0.1 Ohms secondary winding does not actually output 12VAC that I measure with my (10MOhm input) RMS multimeter? ://

ogden, first I want to point out that SPICE is for simulating, not for proving.
Second, SPICE is not aware of the electric and magnetic fields.
I did not ask to prove Maxwell's equations using SPICE :palm: Before you even consider to spread your wizdom, you really shall read what we actually were talking about.

There is another way of looking at it. Circuits analysis calls things like this a overdefined circuit. In the real world these circuits don't happen but can happen in diagrams with ideal components.
You don't even need magnetic fields to create such a circuit. Lets go break Kirchhoffs law again! :box:
For example this is an overdefined circuit:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571382;image)
What is the voltage across A and B? Well looking from one side its 1V, looking from the other side is 2V. And look Kirchhoffs voltage law is wrong again! The voltages don't add up anymore.
What happens if you do this in real life? You just get lots of current and the 1V that Kirchhoffs is missing to make it work is in the internal resistances of the voltage sources and wires. This is essentially a battery charger circuit.
Okay okay everyone knows you can't just parallel together voltage sources or series together current sources. That's like dividing by zero in math. So lets take a different circuit then:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571388;image)
When the switch is open its pretty easy to solve the voltages everywhere. A to B is 1V and C to D is 0V (Assuming the capacitor was not given any energy upon its creation in the universe). But then lets close the switch and ask what are the voltages at that moment.
So lets look at it from the left side first:
Voltage source is putting 1V there so A to B must be 1V. And switch is closed so A=C and B=D. So in that case the voltage between C and D is also 1V. Solved
Now lets try solving it from the right side:
If we know the voltage across the capacitor then we can know the voltage between C and D. We do have a formula for the voltage on a capacitor:
(https://wikimedia.org/api/rest_v1/media/math/render/svg/bbfc2bb45579b0a0c8e1604bd898ca18871c6909)
So the 1/C part is simple, we know its 1uF so that works out to 1e6. We also know V(t_{0}) is 0V. All we need is the integral of the current. Since the switch has been closed for 0 seconds means the integral is also 0 so from this we conclude the voltage on C and D is 0V....wait didn't we say it was 1V before?Aha! Dr. Lewin is on to something, it does matter from what direction you look at it!
Alright fine the switch basically didn't do anything because no time has passed. Lets fix out question a bit then "What is the average voltage on the nodes in the span of 1ms of the switch closing". Okay now we are integrating from t=0 to t=0.001 .This time we do need to calculate the current, since this is one loop this is easy. We just sum up all the voltages and resistances and use Ohms law. So we get I = 1V / 0 Ohm ... yeah we can't divide by zero so the current is undefined. So the integral is undefined. So the voltage on C and D is also undefined. Okay fine we could say the current is infinite since approaching division by zero limits towards infinity. Well then the integral is also infinite and we find C and D have infinitely large voltage. But as soon as we introduce a resistance of not 0 in there we can calculate it just fine and it becomes a mathematically valid circuit.
This is the same as trying to solve:
x^{2} = 3
x = ?
Yes i know this has a complex number answer, but when doing DC circuit analysis what does a current of 2+j3 Amps look like in DC?
Circuit analysis methods break when you introduce these overdefined circuits, its not just SPICE that will throw a angry error message at you for trying to simulate one. Analyzing it by hand simply gives you weird results like 0, undefined or infinity in places where there should be a sensible number, or you get multiple results for the same voltage or current depending on what path you calculate.
Dr. Lewins circuit is also such a circuit because he is forcing a current around while the resistors try to define there own current. Its not only Kirchhoffs law that breaks in such circuits, you can break many other laws since the math simply does not come together.

ogden, first I want to point out that SPICE is for simulating, not for proving.
Second, SPICE is not aware of the electric and magnetic fields.
I did not ask to prove Maxwell's equations using SPICE :palm: Before you even consider to spread your wizdom, you really shall read what we actually were talking about.
I think SPICE was used in the previous pages to prove Kirchhoff holds, you used it in page 4, but maybe I misunderstood why you used it there. My apologies if it was so.
Anyway, I shouldn't have started a 2AM rambling speech with a name, in the first place. Name removed.

@ogden
you probably missed my answer because I added it to my previous post to keep the number of posts down.
Here it is again:
As for your attempt to model a distributed circuit (where voltage is non singlevalued) with a lumped circuit (where voltage is singlevalued) to show that voltage is not multivalued, I guess it's logically flawed.
Solve the mesh circuit with the emf, do the math. You will see the light.
So to avoid wasting this post space with just a repetition, let me add this
Forget the circuit with two resistors and the voltmeter. That appears to be too complex.
Think of just two voltmeters hooked up to form a loop. Place the coil inside the loop. The instruments will measure voltage in opposition of phase with amplitudes partitioned according to the ratio of their internal impedance (suppose one with 9 Mohm impedance, the other with 1 Mohm impedance at the frequency of the test signal  ok to have decent reading with homelab created magnetic field we'd probably need far lower impedences, but consider this to be a thought experiment).
So, which one is probing 'the right way'? (please don't say "the right one" :) )
Are they both wrong? And yet it checks out: the sum of the voltages around the loop is not zero, it's the emf.
Engineers like to think that to be a 'generalized' KVL. The sum of voltages and emfs around a loop gives zero, but somehow some of them freak out when they see two voltmeters, attached to the very same two endpoints, reading two different values (that add up exactly to what they expect!!!) and call that 'bad probing'. Go figure.

This is a good thread to ask. Does anyone know the original publication of these two Kirchoff laws 1st and 2nd, not voltage and current laws as usually wrongly tittled.
There is probably also pointed out that this our typical "ideal" circuit analysis way of drawing circuits is also ideal and centralized model that brakes down miserably when you go smaller in time domain, or go further in component size (ie. cross continent powerlines).

As for your attempt to model a distributed circuit (where voltage is non singlevalued) with a lumped circuit (where voltage is singlevalued) to show that voltage is not multivalued, I guess it's logically flawed.
Solve the mesh circuit with the emf, do the math. You will see the light.
As you disagree with my model where between any two points of 1Ohm ring where 1A current is running, there's always is 0V, you shall demonstrate mesh circuit with emf, do the math to prove that I am wrong and prove that you are right:
Almost right. If the emf is 1V, with equal resistances in the loop you can measure any voltage you want between 0.5V and +0.5V.
Show me the light you so often refer to.  If you can.

Yes the voltmeters would read different values in a 9 to 1 ratio because the EMF voltage is in the wires used to connect them.
But along the way i found another fun way to break Kirchhoffs law without using any magnetic field:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571631;image)
Here the orange wire is made out of constantan(55% Cu, 45% Ni) while other wires are made out of copper. This creates a thermocouple joint at both ends of the constantan wire. If we now heat the indicated corner to 100°C while leaving all other parts of the circuit at ambient temperature we get the shown readings on both voltmeters.
3.03mV + 0.34mV = 3.37mV
And Kirchhoffs voltage law is broken again because we should be getting 0V when we sum the voltages in the loop. We could again fix it by adding a lumped thermocouple model in the corners where the missing hidden voltage source is located, but if we are not adding any lumped elements to the circuit to describe the magnetic properties of the wire then i suppose we also wouldn't add lumped elements to describe thermocouple effects. The thermoelectic effect after all does not need electric fields to push electrons around, just like the magnetic field does not (But magnetic fields do sort of create 'virtual electric fields' trough the effects of special relativity).

Current induced in the measuring wires.
it would be interesting to try this with untrimmed surface mounted film resistors
Those thruhole resistors are most likely spiral cut ( which forms inductors by itself ... )

Yes, current induced in the measuring wires. But the point is that now we read two different values from the same points.
This is not a measurement issue, it is exactly what is predicted by the theory. And in fact, the values confirm that the sum of the voltage read around the loop do not give zero. They give the value of the emf.
Even with the original Lewin circuit you had current induced in the measuring wires. It was deemed negligible because the resistances in the circuit were much lower than the multimeter's impedances. But still, despite the probes not linking the flux there was always a mesh that enclosed the whole area with variable field. In one case with a positive orientation and containing a high valued R, in the other with a negative orientation and containing a low valued R. This is what gives rise to the different reading.
When you take the probes path inside the variable flux area, you end up partitioning it and now both meshes are linking the flux with opposite orientation and variable proportion (determined by how you place the probes). You can then get a reading of all voltage values included between the extreme values of 0.9V and 0.1V depending on which of the two meshes cuts more flux. From the same two endpoints!
Now, it seems that someone would like to single out, among the infinite values of V, the one where the contribution from the two meshes cancel out, put it on a pedestal and worship it as the "true voltage". I have no problems with that. You can find that same value from the same two endpoints for an infinite number of other probe path configurations, no need to twist and shield: just jerrymander the cables so that you get the value you want.
But the point is that voltage is no longer defined in this context.
And that's exactly what the math predicted: if the integral of the E field across any closed path is not zero, then V is not determined by the endpoints only, but also by the shape of the path.
This is not even basic physics. It's basic mathematics.

Yes, current induced in the measuring wires.
:palm:

@ogden
Thou doth facepalm too much.
Solve the circuit shown in Lewin's "Science and believing are different things", do the math.
Now I am no longer convinced you will see the light, but it's still worth a shot.
EDIT to answer the post below: I am not your tutor. Lewin has already solved it in his video, I did check it on my own but I am not wasting my time translating and formatting (I even tried to upload a pic two days ago, but gave up on tinypic and its enter code here and there) it for someone who does not even want to watch a video.
Maybe next week I will tell you a fairytale about an island with a hill and an instrument to measure the energy per unit mass required to move a mass from bottom to top, with and without a curly wind. You might understand what potential really is.
edit: correct mispelled name

Solve the circuit shown in Lewin's "Science and believing are different things", do the math.
Now I am no longer convinced you will see the light, but it's still worth a shot.
Trying to shift discussion offsubject? :DD
I already did show simulation using lumped elements (10x0.1V EMF sources and 10x0.1R resistance). You disagreed. So now you shall solve the mesh circuit with the emf, do the math  to disprove my approach.
[edit] I remind that all I ask you  prove following words not using :bullshit: :blah: but solving the mesh circuit with the emf, doing the math:
No. We can't measure whatever voltage we want between 0 and 1V.
Almost right. If the emf is 1V, with equal resistances in the loop you can measure any voltage you want between 0.5V and +0.5V.

This is a good thread to ask. Does anyone know the original publication of these two Kirchoff laws 1st and 2nd, not voltage and current laws as usually wrongly tittled.
From here:
https://books.google.com/books?id=a434DAAAQBAJ&pg=PA3&lpg=PA3&dq=translation+of+%E2%80%9CUeber+den+Durchgang+eines+elektrischen+Stromes+durch+eine+Ebene,+insbesonere+durch+eine+kreisf%C3%B6rmige&source=bl&ots=JSjEAnl4cu&sig=REI3wpeFihBgq4PaU6gCX_VTeac&hl=en&sa=X&ved=2ahUKEwjFhOK_0NTeAhXEwMQHHWYkC90Q6AEwAnoECAgQAQ#v=onepage&q&f=false (https://books.google.com/books?id=a434DAAAQBAJ&pg=PA3&lpg=PA3&dq=translation+of+%E2%80%9CUeber+den+Durchgang+eines+elektrischen+Stromes+durch+eine+Ebene,+insbesonere+durch+eine+kreisf%C3%B6rmige&source=bl&ots=JSjEAnl4cu&sig=REI3wpeFihBgq4PaU6gCX_VTeac&hl=en&sa=X&ved=2ahUKEwjFhOK_0NTeAhXEwMQHHWYkC90Q6AEwAnoECAgQAQ#v=onepage&q&f=false)
The citation is note 4:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571763;image)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571781;image)

EDIT to answer the post below: I am not your tutor. Lewin has already solved it in his video
I can't find video where he solves 1 Ohm ring loop problem where as you say  you can read any voltage between 0.5V to + 0.5V. It is not about tutoring. It's about proving that your words are not BS.

You should have read my post more carefully
"EDIT to answer the question posted below: removed another extra space at the bottom.
Also to clarify: I have zero batteries in my circuit, just the emf. And the two resistors are lumped component part of the physical circuit, not a tentative to model a distributed component. "
This is what I was talking about: Lewin's so much debated setup.
Your problem is even worse from the standpoint of spice simulation, because everything is distributed but still, off the top of my head, the voltage between two points forming an angle alpha with the center will be different when you measure it from one side out of the loop V = (alpha/2pi) * emf and from the other side of the loop V = (2pi  alpha)/2pi * emf (you need to fix the signs).
If you go inside you will end up will all values comprised between these two values (with adjusted signs). It all depends on how you cut the varying flux area.
EDIT
Added formulae, corrected one of the seventyfour typos and also to add:
So, your spice model shows one out of those infinite values, and that should prove what?

Yep you can get any of the infinitely many values by rearranging the wires. But then the model should capture that so that you can then solve the circuit for that particular one.
The arrangement of wires i am interested in is the one where both probing wires summed together produce a EMF voltage of 0V. This means that the end where the voltmeter is at is at the same voltage as the two points we are trying to measure since this way the probes are not affecting the measurement. This collapses the circuit down to a single solution for the voltage.

@Berni
Yep, and that's totally fine with me. I know that's what some called "correct probing", but you should know that you are just deceving yourself if you think that voltage has a physical meaning outside the context of the particular path you have found. As I wrote before there is no need to twist and shield your cables  just jerrymander them until the instrument shows the value you like (which for the symmetric setup of Lewin's circuit will be the average of the values, considering the signs, so... 0.4V IIRC).
The fact that that is not the only voltage is not only a matter of definition. In my fairytale about the hill, there are Conservatives and SUPERDEMOcrats that have to ship medicine to their relatives at the top of the hill. Conservatives laugh at SUPERDEMOcrats, thinking that they believe the height of the hill changes with wind, but they end up all dead because their conservative "true value" of the energy required to shoot the package up is either too high or too low to safely reach the destination when there is net wind along the path.
PS
no politics please, it's just that the names were so fitting...

Your problem is even worse from the standpoint of spice simulation, because everything is distributed but still, off the top of my head, the voltage between two points forming an angle alpha with the center will be different when you measure it from one side out of the loop V = (alpha/2pi) * emf and from the other side of the loop V = (2pi  alpha)/2pi * emf (you need to fix the signs).
Where did you lost 1 Ohm distributed resistance? You also forgot that loop we are talking about is electrically short!
Let's view at obvious case where alpha equals PI. As two identical halves of the loop we have one +0.5V and one 0.5V EMF source and two 0.5 ohm resistors connected in parallel series to each of them. How do we measure any voltage here between those two points?
 By "scientifically" manipulating voltmeter leads? ;)

Where did I lose the resistance? I didn't. If the emf is 1V, the current is 1V/1ohm = 1amp.
Why do you think the measured voltage should depend on the value of the resistance? Is it not a uniform resistance loop?
What do you expect by raising the total resistance to 2 ohms?
EDIT
also with 1V emf, and the measure points on a diameter, you will measure 0.5V on one side, from outside the loop, + 0.5V from the other side, still outside the loop, and any value you wish in between when you go inside the loop, depending on how much of the flux you cut in the two parts you are partitioning the area.
If you want to read the 0V you like so much, you place your inner voltmeter along a diameter. Or, you can go yinyang.
EMF is still 1V, why should that change?

Where did I lose the resistance? I didn't. If the emf is 1V, the current is 1V/1ohm = 1amp.
Why do you think the measured voltage should depend on the value of the resistance? Is it not a uniform resistance loop?
What do you expect by raising the total resistance to 2 ohms?
Just realized mistake in a hurry in previous post, corrected.  Each half of the loop is 0.5V EMF generator having 0.5 Ohm internal resistance, so obviously 0.5 Ohms is connected in series to 0.5V EMF source.
also with 1V emf, and the measure points on a diameter, you will measure 0.5V on one side, from outside the loop, + 0.5V from the other side
Only if loop is not shorted. We talk about shorted loop!

"Each half of the loop is 0.5V EMF generator"
EMF on half loop?
What's next? Magnetic monopoles?
I am sorry, I can't help you fill those gaps.
Continue facepalming.
EDIT after your following post: my last remark, I'll leave you to emoticons after this.
When your endpoints are on a diameter you have +0.5V measuring outside on the left (whatever); 0.5 V measuring on the other side, still with voltmeter outside the loop. Total, following the signs +0.5  (0.5) = 1V. That's the emf. It does not show up as a lumped generator, it's distributed. Your error is trying to localize it and compute fractions of it when you consider only part of the circuit.

"Each half of the loop is 0.5V EMF generator"
EMF on half loop?
What's next? Magnetic monopoles?
I am sorry, I can't help you fill those gaps.
Continue facepalming.
LOL. Nice try. When it's convenient, you just pretend that you do not understand what I am talking about  partition (half) of the closed loop. Now suddenly your formula "V = (alpha/2pi) * emf" giving 0.5V with alpha=PI and emf=1V is not true anymore as well. [edit] In same post I say "we talk about closed loop".

Just watched "Science and believing are different things", did the math. Left meter reads 900mV, right 100mV. In both  calculation and "lumped simulation". Funny that LTspice does not scream at me ;)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571904;image)
[Edit] agrees to paper http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf (http://www.phy.pmf.unizg.hr/~npoljak/files/clanci/guias.pdf) as well.

Just watched "Science and believing are different things", did the math. Left meter reads 900mV, right 100mV. In both  calculation and "lumped simulation". Funny that LTspice does not scream at me ;)
That's amazing! I did not know Spice could do that!
Can you please highlight on the circuit the two (2) nodes that give two different values of voltage between them?
Maybe one is GND, so what is the other node?

The explanation video promised by Prof. Walter Lewin.
https://www.youtube.com/watch?v=AQqYs6O2MPw (https://www.youtube.com/watch?v=AQqYs6O2MPw)

So... Dr. Lewin just discovered impedance.
And he dropped his two scope, mobius strip with induction battery and improper probing experiment.
What a waste of time.
I still don't get why he says Kirchoffs works when the voltmeter is attached. Unless he is saying that the voltmeter has a resistance (conductance), and thus the voltmeter is what is dropping the voltage. At T approaches zero and the inductor's impedance is higher, yeah, that could be true and you could say that the voltemeter is part of the circuit; but between T= 0 and T= Tsaturation, most of the current is through the inductor and the voltage is dropped across the inductor, and the voltmeter will be pretty much not significant part of the circuit. I don't get the point he was making with that.

Just watched all three videos.
These are all abstraction tools. Some tools you pick for some jobs. Some tools you pick for others.
One thing you do is pick the right tool for the job. KVL works fine for the use cases we use.
Two things you don't do are claim people are religious and fuck up your test environment and then wiggle out of it.

Can you please highlight on the circuit the two (2) nodes that give two different values of voltage between them?
So you are believer.
These are all abstraction tools. Some tools you pick for some jobs. Some tools you pick for others.
Well said. He integrate over time to disprove Kirchhoff's Law but to show special case when Kirchhoff's Law holds, he uses voltmeter with high time resolution :)
What a waste of time indeed.

Kirchoff reduced his observations empirically and mathematically to produce kirchoffs laws. Later, someone studied a curious thing dubbed impedance/reactance, and Faraday was able to correlate impedance with magnetic flux, mathematically, using integrals.
Dr. Lewin used these equations of giants to rediscover impedance and has amazed several college students.

That's basically it.
Let's look at the insignficance of the entire point too....
Avoiding worrying about this is the most powerful tool in your arsenal. Avoiding any problem is.
Extrapolating my point earlier, now I have a few minutes, the whole point of the "tree of knowledge" is that you pick a branch which allows you to solve your problem without having to understand the underlying abstractions if you can help it. Your objective is to solve the problem and move on. How many people in the modern world require knowledge of simple things like integrals, derivatives and logarithms? Not many. When it comes to applied knowledge, we almost never need to care about Maxwell's Equations or vector calculus. And thank goodness for that. They're horrid. I spent a good while scratching my head over these going through Feynman's books.
An example. Just last week I was building an opamp integrator. I couldn't be bothered to work it out as an integral (it was late and I'd had way too little coffee that day and the magic integral button on my calculator didn't work) so I picked a higher level abstraction which is a current source (input resistor to noninverting input) and ideal behaviour of an opamp (lifts output to keep non inverting at zero here). Thus you can solve it using I = C * dv/dt ... I knew I wanted to go 1v/second and had a 1uF cap sitting there staring at me waiting to be used so I knew I. I know input voltage (saturated near rail) so picked an R for that using ohms law. Did maths in head, picked closest value, job done.
Not once did I look at integrals, maxwell, even kirchoff here. Just a rule of thumb which was dervied from this entire stack of knowledge.
At university, many hours did I spend sitting there doing page after page of kirchoff, solving simultanous equations to the point I wrote a linear equation solver on my calculator so I didn't have to do it any more because my arms were so heavy that the thought of doing more made me want to just quit and go and do a BA in arts or something.
And to make a mockery of it all, two points: I never used it. Not even once. TAOE dedicates about 1/3 of a page to it because that's all the attention it needs in the real world.
So this is an hour+ of my life I have wasted on people arguing about technicalities which change nothing, unless you're a research physicist, which I'm not and most of us aren't.
Lewin: Look my abstraction is more right than yours!
Who gives a shit?

The explanation video promised by Prof. Walter Lewin.
https://www.youtube.com/watch?v=AQqYs6O2MPw (https://www.youtube.com/watch?v=AQqYs6O2MPw)
Case closed.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=572381;image)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=572399;image)

Well duh :DD
(which is the whole point here)

Duh, indeed.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=572420;image)

Can you please highlight on the circuit the two (2) nodes that give two different values of voltage between them?
So you are believer.
I am sorry, it seems you do not have sarcasm in Latvia.
Let me rephrase it:
Show the id of the two nodes (not three or four, two) whose potential difference gives both 0.1V AND 0.9V.
If you can't, because you need at least 3 nodes, or more likely 4, it's because Spice can only give you an answer with a singlevalued potential.
And if your aim was to find an equivalent lumped circuit where you could see 0.1V and 0.9V you should have not bothered to add all those inductances. Just uses a lumped secondary coil giving you 1V and put the two resistor sin series. There you go: in this case you need three nodes to show two voltages.
Please repost your schematics indicating with TWO arrows the TWO nodes (not two pairs of nodes, just two nodes) that give you two separate potential differences at the same time.
My bet is that you cannot.
What a waste of time indeed.
You simply did not understand it.
It's not a crime, after all this is very counterintuitive stuff, like everything that has its roots in relativity.
Do not give up, study a bit more and you will see that Lewin is indeed right.
PS
Wanna see something nice: put two batteries with different voltage in parallel in spice. You will find that spice will give a singlevalued voltage, namely the average of their voltages. Why? Because it cannot handle multivalued potentials. So it assumes a finite internal resistance to avoid impossible systems of equations.
I guess it's written in the manual.
But nowadays, who read the... fine manual anymore?

And if your aim was to find an equivalent lumped circuit where you could see 0.1V and 0.9V you should have not bothered to add all those inductances.
My aim was to show opposite. That miraculous reading of two voltages in single point is just bad probing and it can be explained using simplified model of EMF sources and loads. BTW Berni showed more detailed model (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312) of what actually happens. Where do you see inductances? You think R1 and R2 in Dr.Lewin's circuit (picture attached) are inductances as well?
Honestly I do not see any reason to continue this forum chat with you. I agree to disagree and stop internet ink waste.

ogden, the "miraculous reading" of two voltages in single point is NOT about bad probing.
Please look at this picture made by bsfeechannel.
bsfeechannel perfectly summarizes the whole debate:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=572381;image)
The first equation is Kirchhoff's KVL law. In words, "the sum of all voltages in a closed loop = zero".
In the second equation, the term on the right side of the "=" is the induced EMF. In words, "the sum of all voltages in a closed loop = induced EMF"
Kirchhoff says the sum of voltages in a loop is zero.
Faraday says the sum of voltages in a loop is EMF.
Contradiction. Why?
When there is no induced voltages, Kirchhoff is true.
If you have induced voltages in your circuit, Kirchhoff is false.
Q: So, Kirchhoff was stupid, and the Physics is broken?
A: No. Kirchhoff was a genius, but when he made those laws of him, Kirchhoff was talking only about circuits with NO induced voltages.

@odgen It was a lapsus. Change inductances with resistances and the gist does not change: the lumped circuits you can model in Spice cannot give you two different voltage readings from the very same two points (edit: and that's why Spice did not scream at you). BUT the system in the real world CAN.
As for your model to show two readings, yes, I sent you there just to show where those readings came from: the different flux linkage. Where did you guys think this multivalued potential came from? An alternate universe?
It is written clearly in Faraday's law.
What you call 'bad probing' is an inherent and irremovable characteristic of the physical system. Voltage is no longer 'positional' so if your aim is to create a map of 'voltage' values on the ring, you should know you can have any kind of mapping you want depending on how you place your probes.
(Edit: If your definition of 'true voltage' is what you read when the probe paths partition the area of the loop in order to give cancelling contributes...) ...what happens when the flux is not spatially uniform? You have to follow strange paths in the ortogonal section of the loop area. And if the loop is not circular symmetric, same thing. And if the flux change is relative not only to the module of the B field but also to its spatial distribution? You have to make your probes dance with the field to cancel the contribute of the flux linked by the two inner meshes.
Oh well, I guess you have the right to remain ignorant.
And I start to see why Lewin is giving those copypasted comments on youtube. (edit, posted after reading a post below) He was literally drag to post video after video and now people are saying "he's just repeating himself".
edit: typos and additions, as shown
further edit: typos typos typos. They're coming out of the effing walls!

So in this latest video, Dr. Lewin again says that almost all the textbooks are wrong. One he specifically calls out is Halliday and Resnick. So just for fun, what does it say about inductors? From Halliday and Resnick "Fundamentals of Physics" 9th edition, section 308:
In Section 306 we saw that we cannot define an electric potential for an
electric field (and thus for an emf) that is induced by a changing magnetic flux.
This means that when a selfinduced emf is produced in the inductor of Fig. 3013,
we cannot define an electric potential within the inductor itself, where the flux
is changing. However, potentials can still be defined at points of the circuit that
are not within the inductorpoints where the electric fields are due to charge
distributions and their associated electric potentials.
Moreover, we can define a selfinduced potential difference V_{L} across an
inductor (between its terminals, which we assume to be outside the region of
changing flux). For an ideal inductor (its wire has negligible resistance), the magnitude
of V_{L} is equal to the magnitude of the selfinduced emf E_{L}.
If, instead, the wire in the inductor has resistance r, we mentally separate the
inductor into a resistance r (which we take to be outside the region of changing
flux) and an ideal inductor of selfinduced emf E_{L}. As with a real battery of emf
E and internal resistance r, the potential difference across the terminals of a real
inductor then differs from the emf. Unless otherwise indicated, we assume here
that inductors are ideal.
So it doesn't attribute anything to Kirchoff's law. It specifically says we can't define a potential from the E field produced by the inductor's changing magnetic flux. It says we can still define a voltage outside the changing magnetic field of the inductor and use this as the potential difference across the inductor. And we can make a "mental" lumped model of the inductor with internal resistance as an EMF in series with a resistor.
None of that sounds criminal.
He's made his point several times over in four or five videos. At this point he's just repeating himself.

After watching the response video I do have to apologies that I missed the point. Yes I agree that Kirchhoffs voltage law is not describing the actual underlying physics. If you need to describe that go and use maxwells equations, I'm sure they work great. The video explains the difference nicely. :+
However I still don't agree with the demo experiment. But I do agree with some of it. There is indeed 0.9V and 0.1V on those resistors, it's Ohms law after all. Where I stop agreeing is the claim that the mid point of the circle is both at 0.9V and 0.1V at the same time. It's only at those voltages at the ends of the wire where it touches the resistors, but the voltage gradualy changes between the two as you move the measurement point along the wire. So i thing the experiment is misleading in the way it is explained.
The magnetic field is pushing those electrons down the wire because the two are moving in relation to each other. However the electrons want to equalize along the wire so they push back. At some point the two forces balance out and you end up with a certain number of extra electrons towards one end of the wire. More electrons means more charge so the voltage is higher there (actually lower since they are negative charges, but you get the point). If you provide another path for the electrons to equalize towards, such as placing a voltmeter between the two nodes in question they will happily flow towards it, the meter simply senses how eager those electrons are to equalize. Where the tricky part comes is that wires need to carry the electrons to the meter and electrons in these wires are also susceptible to being pushed around by that magnetic field, this creates the extra voltage we measure. The voltage between the two probing points is defined by the difference in charge density and can only be one number. This is the voltage that I refer to as the true voltage between the nodes. Since the probe wires are not supposed to be part of the circuit (but are a nececerry evil to be able to connect the meter) this means they should be used in a way that does not produce extra voltages. These are the voltages that push electrical current trough circuits (even if they are not the direct fault of a electric field)
SPICE is showing these voltages in its results and yes it will throw an over defined circuit error if you parallel two voltage sources due to there being no way for standard circuit analysis methods to resolve that. If it does simulate it fine then the simulator added a parasitic resistance to the voltage source. Often simulators apply some default (but overridable) parasitic values because it makes circuits act closer to what we expect in real life.
Kirchhoffs voltage and current laws are still incredibly useful tools for circuit analysis and they always work for that. It's a matter of the right tool for the job. These circuit analysts methods do a very good job of predicting what would happen in a real circuit. This is what science is about, making theories and then rigorously testing them to the limit with experiments. The ones that match experimental results are considered to be more valid and can then be of incredible use to engineers from all fields to help them predict the performance of there designs before they are built. You don't want to build a bridge just to test if it will collapse or not. Abstractions are great and all but they don't always give the whole picture even if the math works out so nicely (And yes Kirchhoffs laws ride on top of quite a few stacked up abstraction layers, it also relies on these layers to work in a certain way)

There is indeed 0.9V and 0.1V on those resistors, it's Ohms law after all.
Well, yes and no.
There is 0.9V if you measure with the voltmeter on one side, and there is 0.1 V if you measure with the voltmeter on the other side of the loop. Even if you place the probe across THE SAME resistor.
Look at the meshes, can you see that in one case you are linking the flux with one orientation inside the mesh with the big resistor, and in the other case you link the flux with the opposite orientation inside the mesh with the small resistor?
Where I stop agreeing is the claim that the mid point of the circle is both at 0.9V and 0.1V at the same time.
Ay, there's the rub. You still think voltage is a property of the points on the circuit. It is not. Not anymore, it's not!
It depends on the points A and B AND on the PATH.
So you can have both readings at the same time, there is no 'quantum superposition of voltage states' so to speak.
It's only at those voltages at the ends of the wire where it touches the resistors, but the voltage gradualy changes between the two as you move the measurement point along the wire. So i thing the experiment is misleading in the way it is explained.
You are still under the spell of the positional voltage.
But you are this close to see the light.
Come to the bright side!!!
We literally own the light! [note]
[note] as a matter of fact, when the magnetic flux changes it concatenates a circulating electric field  you do not even need electrons or any kind of matter. And that varying electric field concatenates a variable magnetic field, and... well, it's the bright side, no?

In a world of spherical cows, the path does not exist. What then?
The only reason the measurement is different is because the path is different.

The first equation is Kirchhoff's KVL law. In words, "the sum of all voltages in a closed loop = zero".
It is attempt to apply Kirchhoff's KVL law to superconductive loop placed in the changing magnetic flux. Kirchoff's law does not hold for such. Do not recall anybody arguing that. Interesting stuff (https://en.wikipedia.org/wiki/Flux_pumping). Excerpt: "An electric current flowing in a loop of superconducting wire can persist indefinitely with no power source."
Debate was about flawed experiment which had cut loop as EMF source and resistor(s) as load. On resistor terminals you can measure voltage and there are no two different values. Also kinda obvious that nobody tries to apply Kirchoff's law to circuit with single element, not to mention shorted battery!

However I still don't agree with the demo experiment. But I do agree with some of it. There is indeed 0.9V and 0.1V on those resistors, it's Ohms law after all. Where I stop agreeing is the claim that the mid point of the circle is both at 0.9V and 0.1V at the same time. It's only at those voltages at the ends of the wire where it touches the resistors, but the voltage gradualy changes between the two as you move the measurement point along the wire. So i thing the experiment is misleading in the way it is explained.
Maybe consider that potential or voltage is a mathematically calculated quantity that doesn't necessarily correspond to something physically real. In this case, it is not defined at all unless you define a path over which to do the calculation.
So consider real quantities instead:
The current is real. The current has to be the same everywhere around the loop because of the continuity equation.
The magnetic field is real. The only magnetic field is in the middle of the loop. There is no magnetic field anywhere else in this simple two dimensional scenario. So there is no magnetic field in the wires or in the resistors.
The electric field is real. The electric field is caused by the changing magnetic field. There is no field inside the perfect (or near perfect) conducting wires. The only field is present in the resistors. As you said, there is a charge distribution that maintains zero field in the wires and enhances the field in the resistors.
Energy is real. So consider the charge that moves around the loop due to the current. When it goes through the wires it doesn't gain or lose energy because there is no field inside the wire. Where it passes through the resistors, it loses energy due to heat, and this energy is provided by the electric field.
So how could the voltage in the wire gradually change from one end to the other? Wouldn't that require the charge to gain or lose energy as it moved from one end to the other?
There's no contradiction here. All the real quantities are consistent, energy is conserved, charge is conserved.
But voltage is not a real quantity in this case.
The experiment is not saying that the midpoint of the loop is both at 0.9V and 0.1V at the same time. It is saying one meter is reading 0.9V and the other is reading 0.1V. This is because the meter leads follow different paths. Simple as that.

Sorry for the long post, but it is worth a read since i think it finds a good middle ground between Lewin and ElectroBoom
My explanations leans on this:
https://en.wikipedia.org/wiki/Electromotive_force#Formal_definitions
Inside a source of emf that is opencircuited, the conservative electrostatic field created by separation of charge exactly cancels the forces producing the emf. Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in opencircuit condition
If you have a open circuit length of wire in a moving field (Or vice versa) you do get a different amount of charge density on each of the ends that corresponds to the EMF voltage. The longer the wire is the more electrons there are for the magnetic field to tug along so as you go along the wire they cumulatively get pushed more and more. Much like a vertical column of water getting pulled on by gravity, the bottom ends up with more pressure than the top (Yes i know water is not the same as electricity but the idea is similar). Here this effect is called charge separation.
This works even in superconductors. At first it sounds wrong because more electrons at one end would create a electric field inside of a superconductor, but the magnetic field that shoved the electrons over to the end did so using its 'virtual electric field' (Well it is a real electric field, but its not caused by a charged object). So the two fields put together are again zero. Once you connect it into a loop they are free to move so the field disappears and the current they cause opposes the outside field so then you have no electric field induced by charge separation and the field caused by the magnetic fields cancel out to zero too. The current and field sustain each other so the current flows forever and the field stays forever. Very useful for making incredibly strong magnets and is used extensively for this in things like MRI machines and particle accelerators.
If we instead close the loop by putting a resistor in series then we get a case of both. We need an electric field to push electrons trough that stubborn resistance inside the resistor so this effect of open loop charge separation on the wire puts extra electrons on one side of the resistor so they can force themselves trough using there own electric field. But because now electrons are flowing trough the resistor we have a current in the loop so the loop makes its own opposing magnetic field. So far it looks like a closed loop superconductor again, but the resistors don't allow the electrons to flow freely so they can't make it around the loop fast enough to fill the 'electron void' on the other side of the resistor. As a result some electrons are left behind on one end of the resistor and continue to experience charge separation, thus making the wire look like it has voltage and this voltage appears as a smooth gradient across the length of the superconductor. Due to the resistor limiting the amount of current the magnetic field it creates around the loop is smaller than the outside magnetic field and so the 'virtual electric field' it creates in the loop does not fully subtract out the one caused by the outside field. The field that steps in to fill the missing part is the electric field caused by charge separation and gets the sum of fields inside the superconductor back to zero as it should be.
This means that if we connect a wire between two points on the superconductor and route it in a way that generates no EMF on the wire we get current flow that is proportional to the voltage on the two points and the wire resistance.(But only if this superconductors loop is closed with a resistor in series). This gives the two points a set voltage between them that is a single value.
So lets see the definition of voltage then:
https://en.wikipedia.org/wiki/Voltage
Voltage is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points.
Wait... ??? Yeah this is what throws the wrench in the works.
So if you integrate the total electrical fields around the path you get zero volts inside the superconductor and all the rest of the voltage on the resistor. Since the path goes trough a different resistor depending on what way around you go you also get a different voltage. So by definition of voltage it checks out. This is why this is such a big argument, Dr. Lewin is not saying anything wrong.
So where is the problem then?
We don't have a voltmeter that drags an electron around and logs the work needed to do so. Tho if someone did make one id love to see it cause it sounds really cool. So because of this we can't measure the voltage in the exact way it is defined. What we have to do instead is tap off the voltage with extra wires and bring that voltage to the voltmeters input port. When the wires are run in such a way that they don't get affected by the magnetic field only get the charge separation effect pushing electrons trough the voltmeter so the voltmeter ends up measuring electron charge density between the points. The voltmeter becomes part of the circuit and the voltage drop on the 10MOhm resistor inside the voltmeter is this voltage we see. (Doing this adds a third possible solution to the node)
TLDR starts here:
Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.
The whole thing is explained with a schematic and using some basic circuit analysis tools. Any voltmeters in the schematics are assumed to tap off the electric field integral of the loop you want to see and ignore others. It would have been much better to explain it on the level of electric fields and electrons moving around if the goal was to show the underlying physics. Using a schematic and then simply using the ideal wire model out of circuit analysis methods and then talking about the fields inside a wire is confusing. You ether don't use the abstraction of circuit node analysts methods at all and focus on electrons in a wire (so you can interact your magnetic fields with them), or you go all the way with circuit analysis and create an equivalent circuit that shows the magnetic effects as inductors. One or the other ways of explaining it makes sense and works great! Kirchhoffs law is a circuit analysis tool and it works (for circuit analysis), its not a law that governs how the universe works.
So why does circuit analysis not agree with physical electrons moving in wires? Because that's not the point of this abstraction. The goal of circuit analysis methods is to make it as easy as possible to predict the behavior of a circuit with as little math as possible. So to not complicate something as simple as a wire it simply cuts the concept of voltage down to the effect the voltage has on components (including the effect the voltage has on a voltmeter). In this simplified world Kirchhoffs law works perfectly and because the abstraction uses voltages that we can observe in real life means that the results of these circuits analysis methods also work in real circuits with electrons running trough them.
Many simple equations you have been taught in your first few years of physics are actually set inside an abstracted world where for example the speed of light is infinite and our atmosphere is a perfect vacuum. So are they wrong? Well... in theory yes they are wrong, but they work just fine in the abstracted world. The math is much easier and faster in this abstracted world, yet when done carefully still gives results that are very close to real ones you would get in the real world.
Please use a hammer for hammering nails rather than screws.

You are defining a "true" measurement as one where the fields don't interfere with the meter leads. We are taught that the leads are not supposed to be part of the measurement. If there is a voltage drop in the leads, that is an error. So you have to eliminate or account for the error to make an accurate measurement.
Fair enough.
So to measure from A to B, arrange your leads vertically so they are parallel to the magnetic field and perpendicular to the E field. Or in some other way shield the leads from the fields. So now apply Faraday's law. First integrate the flux over the surface of your measurement loop. There is no net flux through the area surrounded by the measurement leads and the line from A to B, because of the way the wires are arranged or shielded. So you can pick either surface in the current loop going from A to B. You are splitting the loop in half, so they each have the same flux which is half the total flux. So either way you pick, there is an EMF of 0.5V. Then integrate around the path of the measurement leads and either half of the loop. If you go one way, you get 0.5V0.1V=0.4V. If you go the other way, 0.9V0.5V=0.4V. OK. So the true voltage is is 0.4V.
And yes, if you move the test points toward one of the resistors, you would "slice the pie" of the surface of the current loop differently, and the voltage you measured would continuously change and end up just the voltage across the resistor.
So your model, using lumped coupled coils or transformers, works. It gives you the "true" answer. I get it. It agrees with Electroboom and it agrees with Faraday's law. There's nothing wrong with it.
This is basically the same thing bsfeechannel did in his analysis back in reply #106. Some of the reactions were "you are just picking a path that gives you the answer you want".
But based on the standard way that electrical engineers look at measurements, this is the correct path. Again, fair enough.
edit: And yes, if you choose this path, the resistive ring always measures 0V.

So to measure from A to B, arrange your leads vertically so they are parallel to the magnetic field and perpendicular to the E field. Or in some other way shield the leads from the fields.
So now apply Faraday's law. First integrate the flux over the surface of your measurement loop. There is no net flux through the area surrounded by the measurement leads and the line from A to B, because of the way the wires are arranged or shielded.
I am not sure to understand this.
You do know that the flux depends on the area orthogonal to the field that is enclosed by the contour, right?
How on earth do you plan to place or shield your leads to avoid intercepting the flux when you are partitioning a disk? You should shield the area, but then forget connecting to a circuit immersed in the field.
But let's say we have find a probe placing such that...
You are splitting the loop in half, so they each have the same flux which is half the total flux. So either way you pick, there is an EMF of 0.5V. Then integrate around the path of the measurement leads and either half of the loop. If you go one way, you get 0.5V0.1V=0.4V. If you go the other way, 0.9V0.5V=0.4V. OK. So the true voltage is is 0.4V.
Ok, let's call 'true' the voltage measured along paths that split the area in equal parts. This is not the only possibile logic choice but let's go with this.
And yes, if you move the test points toward one of the resistors, you would "slice the pie" of the surface of the current loop differently, and the voltage you measured would continuously change and end up just the voltage across the resistor.
If you call true potential the one along paths that split the area in equal parts, no. You have to gerrymander the probe to give two identical areas when your endpoints are not on a diameter.
So your model, using lumped coupled coils or transformers, works. It gives you the "true" answer. I get it. It agrees with Electroboom and it agrees with Faraday's law. There's nothing wrong with it.
Ahem, but let's suppose that we have agreed to use a certain class of possible paths (they are not unique for the same measurement  for example a measure with endpoints on a diameter can be done using the diameter as a path, or the yinyang path, but let's brush this aside for the moment)
This is basically the same thing bsfeechannel did in his analysis back in reply #106. Some of the reactions were "you are just picking a path that gives you the answer you want".
But based on the standard way that electrical engineers look at measurements, this is the correct path. Again, fair enough.
I beg to differ. And here's another reason why.
The standard way that engineers look at measurements, voltage is addittive. If you want to find VAB you can find it by summing VAC and VCB.
Also, you might like the property VAB = VBA.
Well, with path dependent measurements you have to give up both of these properties.
The latter one can easily be amended. If we agree to use the same path, only reversed, for BA and AB, then we gave to change
VAB + VBA = 0 (KVL)
in
VAB + VBA = EMF (Faraday, or as engineers sometime call it, generalized KVL)
What happens when you want to sum two voltages? Each of them might require a different path to give the "true" potential reading. In general the three paths connecting the points A, B and C will enclose a portion of space that non necessarily encloses ALL of the flux. You you'll end up with
VAB+VBC+VCA = a fraction of emf corresponding to the varying flux linked by that area.
And what area is that? There is more than one path that can give you the 'true' potential (remember? diameter and yin yang). So, your sum of 'true potentials' is... whatever you want it to be.
edit: And yes, if you choose this path, the resistive ring always measures 0V.
This is right. :)
PS
I wrote this after having slept nine hours in three days. So, check it.

Hey guys, I've solved it for ya:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=573734;image)
Vab = I*R = I*9R
Are these resistors in series, in parallel, or both?

https://www.youtube.com/watch?v=ototTU5NUNA (https://www.youtube.com/watch?v=ototTU5NUNA)
Dr. Lewin just uploaded another video.

So to measure from A to B, arrange your leads vertically so they are parallel to the magnetic field and perpendicular to the E field. Or in some other way shield the leads from the fields.
So now apply Faraday's law. First integrate the flux over the surface of your measurement loop. There is no net flux through the area surrounded by the measurement leads and the line from A to B, because of the way the wires are arranged or shielded.
I am not sure to understand this.
You do know that the flux depends on the area orthogonal to the field that is enclosed by the contour, right?
How on earth do you plan to place or shield your leads to avoid intercepting the flux when you are partitioning a disk? You should shield the area, but then forget connecting to a circuit immersed in the field.
I'm thinking 3 dimensionally. The contour is bent 90 degrees along the line from A to B. The idea was to try to keep the test leads parallel to the magnetic field and perpendicular to the electric field as I said. But yes, it is probably not physically possible. For shielding, I was thinking more like coaxial shields around the test leads.
The other way is to account for the "error" introduced by the EMF induced in the loop of the test leads. Measure the EMF separately in a calibration step, and then subtract it out the measurement. The result is the same.
I was trying to rationalize the lumped element circuit that people are automatically coming up with as a valid interpretation of a "correct" measurement.
Personally, I think this demo is a fairly simple demonstration of Faraday's law, and trying to come up with the lumped circuit just adds unnecessary complications.
Electronics people automatically react strongly because of Dr. Lewin's use of a schematic in a confusing way and his lack of detailed explanation of what is really happening.I'm sure it was covered in more detail for his students in discussion sections and lecture supplements. And then there's his provocative "Kirchoff's law is for the birds."
I haven't watched the latest video he just posted, yet. We'll see.

For shielding, I was thinking more like coaxial shields around the test leads.
Just put whole experiment into transformer core like this:
(http://www.edn.com/ContentEETimes/Images/01Steve%20T/LivAnaPotCores140/Pot%20Cores%201.jpg)

For shielding, I was thinking more like coaxial shields around the test leads.
Just put whole experiment into transformer core like this:
(http://www.edn.com/ContentEETimes/Images/01Steve%20T/LivAnaPotCores140/Pot%20Cores%201.jpg)
Yes, put the current loop where the "windings" are, and route the wires connected to points A and B outside and measure. Now you can move the meter from one side to the other and measure the same value. Or two meters, one on each side, both connected to A and B would both measure the same.

Dr. Lewin just uploaded another video.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=574943;image)
He's got the current wrong :)

Ah yeah i did think that current was pretty high for 140 Ohms but never went to check it. Yeah the decimal place is in the wrong spot and should be 0.064 A. Ah well can happen to anyone.

In the last video 1) He's totally avoiding the crux of the matter with electroboom: that the voltmeter wires are part of the circuit, and when considered properly, explain the (seemingly bizarre) results he gets.
And 2) Kirchoff's KVL says "the sum of the emfs in any closed loop is equivalent to the sum of the potential drops in that loop", he leaves the induced EMF of the loop out of the equation to prove that KVL is wrong? Well, yeah, right.

Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.
Most simply don't care ;D

Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.
Most simply don't care ;D
But they should to be honest. I mean, you should at least *know whats going on* and why voltage as a concept can break down in the presence of an induced EMF. You may practicaly never encounter it or have ways do deal with it, which surely is the case for most. But at least know the basic physics of your job and know the limits of the models you use in your daily work. I mean, you people have gone through university and have a masters degree, at least show some respect to your field of education.
You behave like a general practitioner not knowing how to perform a tracheotomy or what it even is. Yeah, he may never have to do one. But when he does, I want him to have at least a general idea of how to go on.

Okay our voltmeters suck... so really what is the problem?
The experiment is never explained how the voltmeter 'selects' what voltage it can see. There is no mention given to the importance of the path that the voltmeters probe wires take and why they are routed in that exact way. It just leaves you head scratching how is it possible to see two different voltages at the same point. It demolishes your intuitive notion of voltage in circuits. Many electronics engineers after university are likely still confused as to how it works.
Most simply don't care ;D
Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.
It takes lots of enthusiasm for electronics to really get yourself to understand the field.

Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.
It takes lots of enthusiasm for electronics to really get yourself to understand the field.
Yeah, and those are probably the ones jerking off the most about how they are STEM educated and making fun of any nonSTEM students during university. Which is funny, because if you just leave all the complicated stuff out of EE you can break it down to get pretty simple in practice.

Well to be honest i wouldn't be surprised. Most people in university just memorise things to pass the test and are not even interested in understanding it.
It takes lots of enthusiasm for electronics to really get yourself to understand the field.
Yeah, and those are probably the ones jerking off the most about how they are STEM educated and making fun of any nonSTEM students during university. Which is funny, because if you just leave all the complicated stuff out of EE you can break it down to get pretty simple in practice.
...And then they become walkers searching lost beans in some corporation, ruining everyones work with their idiocy.

I still don't think Lewin uses the right way to make his point nor quite the right examples, but I must admit he at least opened our eyes on something we tend to use without actually really *caring* about all the underlying theory, as Dave said. When we do our work properly, it still doesn't change anything much, but now we know we don't use KVL the way it was intended, and that our definition of "voltage" is in all aspects more practical than theoretical.

Yet another short video. He mentions Electroboom this time.
https://youtu.be/d_XqrZo5_7Y (https://youtu.be/d_XqrZo5_7Y)

Summary:
1. Title is "my sincere apologies"
2. 90% of video is arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct. Take great glee in squashing this strawman by repeating the same thing he has stated like a broken record for the past week.
3. State that anyone with a masters in electronics who suggests that the different readings are only* due to placement of the probing leads is an idiot.
4. Clarifies that the "sincere apology" is for being too blunt in laying out his 100% correct argument against the fairy tale strawman while completely brushing off the actual point of contention.
*but let's forget that I was the one to apply real oscilloscpes and their readings to a real test circuit. If we applied these real oscilloscopes to my theoretical model, we would apparently learn that [start broken record]
Super shorter summary:
"I can see the sailboat, and you can't."
Next up:
"Newton's laws are just a special case of relativity. It's a crime that we call these things laws, when it is really Newton's Loopholes."

Take two square clocks and put them side by side so that they have a common side. Paint it red to make it stand out.
Do you find it suprising that that same red side is seeing the hand of the left clock going down and the hand of the right clock going up?
Would you call that a measurement error? Or bad glancing?

Maybe a bad analogy?

https://www.youtube.com/watch?v=vZYAHGwS3mA (https://www.youtube.com/watch?v=vZYAHGwS3mA)

I still don't think Lewin uses the right way to make his point nor quite the right examples
I think the same. Lewin's not wrong, but his experiment to explain his point is poor IMO.
Because he's not a practical engineer, I think he's incapable of seeing it from that aspect. He lives in the world of physical theory and knows it so intimately it's all he can see. And there is nothing wrong with that of course, it's important stuff in it's own right, and he's right to point it out.
, but I must admit he at least opened our eyes on something we tend to use without actually really *caring* about all the underlying theory, as Dave said. When we do our work properly, it still doesn't change anything much, but now we know we don't use KVL the way it was intended, and that our definition of "voltage" is in all aspects more practical than theoretical.
How many of us have ever really thought about it? I doubt there is a single one of us. KVL is a practical theory that works and holds for all but the most obscure aspects of the entire EE field.
It's like trying to argue that Newtons laws are "for the birds" and are just a special case of general relativity. You aren't wrong by saying that, but geeze, try going into NASA and telling all the space probe engineers that Newtons laws are "for the birds", you'd get laughed out of the room.

Maybe a bad analogy?
Do you really not see any relevance of the two clocks example with electromagnetism?
It exemplifies the convention used to define positive oriented areas in vector integral calculus.
The orientation of the path defines the orientation of the area.
Now, that is instrumental in computing the flux of a vector field. And the flux of a function of said field, like its time derivative.
Even the flux of the rotor of a vector field.
And what is the definition of rotor? Basically, it's the circulation around a tiny closed path around a point. So the flux of the rotor can be computed by summing, integrating, all those tiny contributions.
And what happens to the contours? Well, thanks to that 'bad' clock analogy they all cancel out except for those on the external border (look at figure 3.9 here http://www.feynmanlectures.caltech.edu/II_03.html (http://www.feynmanlectures.caltech.edu/II_03.html)). That's what Stokes theorem tells you: the surface integral of the rotor of a field on an oriented area is the circulation of that field along the closed contour encircling it, with the convention of the right hand rule. Like the hand of a clock.
Add in FaradayMaxwell equation that tells you that the rotor of E is the time derivative of B (ok, there's a sign but that does not change anything since it's always the same) and you should now see the relevance of that analogy.
In fact, if you split a finite area in two parts with a common side, just like those two clocks, you will find that despite the orientation of the areas be the same, the orientation of the common path will come out reversed. Namely, if we assume the same flux configuration, you will get opposite contributes to the circulation along that path depending on which loop it is considered to be part of.
This 'reversal' of the integral of E dot dl (which in an electrostatic situation we would call "the" potential) is not because of bad probing or a measurement error, it is just a consequence of that inversion you see along the common side of two adjacent clocks.
I doubt anyone would find it surprising, just as they would find perfectly normal that the hand of the right clock is seen going up along the common side, while the hand of the left clock is seen as going down.
And there is no escape from this, no matter how small you choose the adjacent contours.
And when you consider finite contours, you can still divide them in two with a common side: the result is the same: if the same flux is intercepted by both partial areas (edit: actually this is not even required, what it counts is that the E field is the same along the common side and well, it has to be since it's the same set of points), the contribute to the emf on the common path will be reversed.
Would you call that measurement error, or probing error?
I would call that "that's just the way it is", Kronkite style.
This is the same inversion that comes out with Lewin's experiment when both resistor are the same.
Would you call that probing error?
To me, that's just how EM works. And the roots of this behavior go down to both that orientation behavior and the fact the circulation of one quantity is related to (a function of) the flux of another one.
No, I would not call that a bad analogy. But that's just me.
(of course, if you remove the link with the flux because the function of B is always zero you get a very special situation where this weird shit does not happen)
EDIT: changed "convention" with "behavior", because its the correlation between area orientation and path orientation that makes all this happen (clockwisecountclockwise vs up and down in this case)
EDIT: changed "infinitesimal" with "tiny" for not riling up mathematicians. Added link to picture. Corrected some minor typos.
EDIT: changed path with contour where relevant to avoid ambiguities.

It's like trying to argue that Newtons laws are "for the birds" and are just a special case of general relativity. You aren't wrong by saying that, but geeze, try going into NASA and telling all the space probe engineers that Newtons laws are "for the birds", you'd get laughed out of the room.
I'm sorry Dave, but it's not like that.
Faraday's law is not a refinement of the theory used in the 'generalized KVL' engineers use to analyze circuits with inductances, transformers and motors. It is the very same theory.
The only reason the 'generalized KVL' works, giving 'singlevalued potentials' is because we are not allowed to cut through the fluxes that make inductances, transformers and motors work. All the weird stuff happens inside, and since our physical circuit cannot repartition the area where the variable flux is linked in the device, nor can it go around it the other way (think of a toroidal transformer, you can go around it any way you want, but you cannot cut through the flux since it is all contained inside  same happens with normal iron core transformers, yes, there may be leakage, but you can't cut through the core) [edit]... we get single valued potentials, like when we measure Lewin circuit from one side OR from the other.
If we avoid that repartitioning and cutting through, we're fine. We can still delude ourselves into believing that our voltages are uniquely determined by endpoints only. But that's just an illusion that helps in making circuit analysis more streamlined. Nothing more than that.
But if we are presented with a circuit that cuts through or allows for encircling with opposite orientation a varying flux region, then we can no longer indulge in that illusion and we must fall back to the reality of electromagnetism, where that linking between fluxes and circulations is deeply rooted down to the bone.
Saying that the multivalued potential we are witnessing can be ascribed to a 'probing error' is denying what Maxwell's equations and basic vector calculus are telling you.
Edit: added "and basic vector calculus".
Edit: added conclusion to sentence after very long parentheses. I had forgot to finish it.
I also wanted to add the voice of Hal saying "I'm sorry, Dave. I can't let you do that, Dave" but did not find a way to do that.

Calm down a bit. Nobody is claiming that Maxwell equations are wrong or that KVL describes the underlying physics.
Maxwells equations describe the underlying physics perfectly fine. And yes KVL is indeed in theory wrong.
But this does not mean that KVL is "for the birds" as these feathery creatures have no use for it, while in contrast engineers use it all the time, sometimes even daily. Try to find an engineer who claims to have used Maxwells equations in the last 12 months (And i don't mean use the idea behind it, but actually calculated something with it). So why are we all using the clearly inferior KVL when we could all be using proper Maxwells stuff? Well... turns out KVL is simply more useful for everyday use.
Maxwells equations involve fields and geometry that needs to know the exact dimensions and locations of everything in 3D space. This brings about a lot of extra complicated math that just slows you down when you are trying to get actual work done and drastically increases the potential for human error. The way engineering has solved this problem is to introduce an abstraction called circuit schematics. For the case of magnetic components we can simplify all of this geometry and fields down to a single inductance number in units of Henry. We have prebaked equations (That do eventually involve Maxwell if you drill deep enough) that quickly turn common geometrical segments of wire into inductance values, or the same inductance value of a real life circuit can be measured quicker and more accurately than its geometry. This single number is then inserted in the equivalent inductor model and is used for all further calculation. An extra benefit of doing this is that it not only abstracts the magnetic effects but it even abstracts voltage in to a sort of "effective voltage" that always has 1 defined value. An even better bonus is that now KVL works for all cases, but as a consequence the voltage it operates with and gives as a result are these "effective voltages" rather than the real definition of voltage(Intergal of fields around a path). Getting a result of "the voltage here is 1.4 V" is more useful than the result being multiple values and you need to use the correct one depending on what you are doing with the voltage. In order to give a single number it is not simply throwing away the other values and cherry picking this one. The math deep down works out in a way where the positive and negative signs of all the numbers line up in a way that gives the same result regardless of the path. The results of these abstracted calculations can be verified with experiments and they match up with measured results. This is the same kind of thing as using Complex numbers in calculations, we could have 4+j3 Volts across two points. So when a voltmeter in real life shows 5V is it wrong? No its not, its just that our math was using imaginary numbers as an abstraction of phase to make math much easier, we still need to know how to interpret the abstraction.
KVL is not a special case of Faradays law even if it looks similar. Instead it is a tool used in analysis of abstracted schematic circuits. If you are to unravel all of these mathematical circuit modeling tools far enough you would eventually get to Maxwells equations, but its not as simple as sticking an extra voltage into KVL, you would end up with multiple pages of math before you get there. Our circuit schematics are the equivalent of "spherical cows in vacuum" in physics, its an abstraction that optimizes and simplifies the math for quick and easy computation. In physics the well known F=m*a equation(Often called Newtons 2nd law) is also wrong in certain cases (Rockets and mass–energy equivalence) and we still use it with its limitations in mind rather than saying its for the birds.
So is it bad probing? I think we need a definition of what that is first. Its hard to find a formal definition of it but lets say we use something like this:
Bad probing is the result of performing a measurement of a desired quantity in such a way that the resulting measured value differs from the actual value of the quantity by more than than our defined error margin allows for.
So by this definition Dr. Lewin is not doing bad probing since he is indeed measuring the voltage he is after within tolerances required by the particular demonstration. The one who is doing bad probing is ElectroBoom since he is after the "apparent voltage" on the two points but is doing so in a way that cause the probes to significantly affect the reading. He should likely have used the setup suggested by this post: https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1972940/#msg1972940 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1972940/#msg1972940) .This would cause the inductive coupling coefficient to the probe wires to become negligibly low, giving the voltage that he is after and so solving the bad probing error. Solving the same circuit setup using Maxwells equations would return a similar result, except that the two values it gives for each path would be nearly identical (Keep in mind we are solving for voltage across the voltmeter terminals, not the voltage inside the ferrite shield).
So who is wrong about what?
ElectroBoom is wrong about using a oscilloscope to measure voltage as formally defined in literature. He needed to use that elusive voltmeter that drags an electron around and measures the mechanical work taken to do so, it would have given him the result Dr. Lewin predicted. But he is using Kirchhoffs law correctly by using it for circuit analysis and not to describe electric fields. He is also using it correctly to determine the voltage across the oscilloscope terminals by correctly interpreting the "apparent voltage" result of the abstracted circuit analysis math.
Dr. Lewin is wrong about using Kirchoffs law for describing what happens to electric fields. Kirchhoffs laws actually describe the behavior of ideal electrical circuits (That are merely an simplified but accurate abstraction of what happens in real circuits with actual fields and electrons). If you look up KVL on wikipedia it explicitly calls them in the title "Kirchhoffs's cirucit laws" ( https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws (https://en.wikipedia.org/wiki/Kirchhoff%27s_circuit_laws) ). He is however correct in using Faradays law to determine the voltage as per formal definition on the two points, but he never includes the oscilloscope and its connections into his calculation and does not explain why the voltage seen on the terminals of the oscilloscope is equal to the voltage at the two nodes of interest.
Its all a case of comparing apples to oranges. They are simply not the same thing even if they seam to fit in the same basket. Part of it is because Kirchhoffs circuit laws predate Maxwells equations and its likely that his laws ware used to describe the physics until Maxwell came around with his more elegant and physically accurate way simply because that's the best theory they had at the time. This is just how science works.

Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...

He still doesn;t undestand the mistake he is making.

Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...
When you do that, what are you supposed to read? Because there's two different resistors in parallel that are in series too, with the same current going through both... I*R1? I*R2?

Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...
When you do that, what are you supposed to read? Because there's two different resistors in parallel that are in series too, with the same current going through both... I*R1? I*R2?
If two meters that are part of super experiment circuit shows 0.1V and 0.9V accordingly, then such "halfway" meter shall read 0.4V. It is discussed/explained in this thread many times by the way

KVL is not a special case of Faradays law even if it looks similar. Instead it is a tool used in analysis of abstracted schematic circuits. If you are to unravel all of these mathematical circuit modeling tools far enough you would eventually get to Maxwells equations, but its not as simple as sticking an extra voltage into KVL, you would end up with multiple pages of math before you get there. Our circuit schematics are the equivalent of "spherical cows in vacuum" in physics, its an abstraction that optimizes and simplifies the math for quick and easy computation. In physics the well known F=m*a equation(Often called Newtons 2nd law) is also wrong in certain cases (Rockets and mass–energy equivalence) and we still use it with its limitations in mind rather than saying its for the birds.
It's kinda similar with that "current flowing through a capacitor" video. Electrons don't actually flow through the capacitor, but that interpretation along with AC impedance is the practical and easiest way to design and analyse circuits and that's why it's used and is a perfectly valid way of thinking. Ironically, it's Maxwell's displacement current theory that helps validate the concept here. So the deeper into the theory you go, the more it backs up the "incorrect" current flow viewpoint.
So is it bad probing? I think we need a definition of what that is first. Its hard to find a formal definition of it but lets say we use something like this:
Bad probing is the result of performing a measurement of a desired quantity in such a way that the resulting measured value differs from the actual value of the quantity by more than than our defined error margin allows for.
So by this definition Dr. Lewin is not doing bad probing since he is indeed measuring the voltage he is after within tolerances required by the particular demonstration.
I'd call it "deceptive" probing ;D

It's kinda similar with that "current flowing through a capacitor" video. Electrons don't actually flow through the capacitor, but that interpretation along with AC impedance is the practical and easiest way to design and analyse circuits and that's why it's used and is a perfectly valid way of thinking. Ironically, it's Maxwell's displacement current theory that helps validate the concept here. So the deeper into the theory you go, the more it backs up the "incorrect" current flow viewpoint.
Yes, not only is KVL for the birds, but KCL is too!
Here's a rough derivation of Kirchoff's laws from Maxwell's equations: KVL from Faraday's law, KCL from Ampere's law:
https://bit.ly/2Fy2svN (https://bit.ly/2Fy2svN)
Let’s look at when are Kirchoff’s Laws would be violated. Notice that both laws assume the
time rate of change of something is approximately 0. This means they are true in the ‘static’
or ‘low frequency’ limit. The circuits that you will deal with in this course work under this
limit. However, it’s interesting to note that KCL is violated inside the capacitor because
charge can build up on the capacitor plates, so if part of your closed surface passes between
the plates the net charge changes significantly with time. However if you consider the
capacitor as a whole ‘lumped element’ and include both plates inside the closed surface, the
charges on opposite plates cancel out and KCL will still work. Similarly, KVL is violated
inside the inductor because a significant magnetic flux passes through the coil, so if your
closed path runs along the coil’s wiring a voltage drop occurs even across the perfect metal
wire. However if you consider the inductor as a whole ‘lumped element’ and recognize its
total voltage as the induced electromotive force due to Lenz’s Law, KVL will still work.

Seems to me it's simple to resolve, put the meter HALFWAY and see what you read...
When you do that, what are you supposed to read? Because there's two different resistors in parallel that are in series too, with the same current going through both... I*R1? I*R2?
If two meters that are part of super experiment circuit shows 0.1V and 0.9V accordingly, then such "halfway" meter shall read 0.4V.
It's 0.1V and 0.9V.
It is discussed/explained in this thread many times by the way
Oh, oh, ok. This, but with only one voltmeter in the center:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=571904;image)
Thanks.

It's 0.1V and 0.9V.
Yes. I omitted signs, sorry
Oh, oh, ok. This, but with only one voltmeter in the center:
Yes. You can refer to more detailed model shown in this post (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312) as well.

Yes, not only is KVL for the birds, but KCL is too!
Somebody finally said it.

Yep capacitors also break Kirchhoffs current law when you think about what electrons are actually doing.
But we are not in arguing about it because like Kirchhoffs voltage law we know it applies to circuit analysis where the capacitor is regarded as a black box with a large capacitance across the terminals. The reason we are arguing about KVL is that Dr. Lewin is trying to apply KVL to electric fields rather than circuits and is then blaming KVL for being wrong just because he is using it wrong.
There is a similar theoretical electrical circuit paradox involving two capacitors:
https://en.wikipedia.org/wiki/Two_capacitor_paradox
(https://upload.wikimedia.org/wikipedia/commons/thumb/8/86/Two_capacitor_paradox.svg/220pxTwo_capacitor_paradox.svg.png)
Just throwing circuit analysis math at it and analyzing what happens in the circuit when the two differently charged capacitors are shorted together seams to cause capacitors to violate themodynamics by violating the law of conservation of energy. Go read trough it, its pretty interesting.
So of course the reason why this happens is that this is a circuit that can't exist in our universe. Same thing as Dr. Lewins circuit with two resistors and a mysterious current forced trough it without having a circuit component doing the actual current pushing. It breaks the circuit abstraction by doing things that are not supposed to happen and as a result breaks the math used to analyze circuits (Like KVL). In this circuit with two capacitors we simply need to add the parasitic inductance and resistance of the wires and suddenly the circuit acts like it would in real life. It would oscillate back and forth trough the stray inductance while gradually reducing in amplitude as the energy (that we seamed to miss before) got turned into heat on the resistance.
I can see how Dr. Lewin would throw Maxwells equations and Kirchhoffs laws into the same basket. He is a physicist and has likely not done enough circuit analysis and modeling to see that KVL is not just Faradays law with a missing voltage.
I do have to admit he did make me look at voltage is a bit of a different light. I think should continue to do this lecture and demonstration as it is quite dramatic. BUT he should not go to a conclusion of "Kirchhoff is for the birds". Instead he should explain inside the same lecture that Kirchhoffs laws are a circuit analysis tool rather than a physics equation that describes the working of the universe. Briefly explain the importance of correct circuit modeling and understanding how the math you use works. Leave it there and continue on with whatever other physics you have to teach.

The reason we are arguing about KVL is that Dr. Lewin is trying to apply KVL to electric fields rather than circuits and is then blaming KVL for being wrong just because he is using it wrong.
He is not using it wrong. And you say so, too:
Dr. Lewins circuit with two resistors and a mysterious current forced trough it without having a circuit component doing the actual current pushing. It breaks the circuit abstraction by doing things that are not supposed to happen and as a result breaks the math used to analyze circuits (Like KVL).
Yes, KVL works for lumped circuit abstraction only. When the premises for lumped circuit analysis are missing, KVL is for the birds.
He is a physicist and has likely not done enough circuit analysis and modeling to see that KVL is not just Faradays law with a missing voltage.
No. In order to see KVL as Faraday's law with a missing voltage, lumped circuit assumptions need to be met. All fluxes should be confined inside the lumped components and you should not be allowed to run circles around them. It's as easy as that. No refinement of the theory (the concept of inductance used in the 'extended KVL' you mention is based on Faraday's law), no need to add parasitics, no nothing.
An engineer should know the limits of their tools and theories.
KVL is lumped circuits stuff. Circuit not lumped > KVL for the birds.
Edit: changed highlighted part, able>allowed

Dr.Lewin's demo in lecture #16 is bird trap for parrots, not KVL.

He is not using it wrong. And you say so, too:
Can you show me a source that claims that KVL is allowed to be used outside of lumped cirucit schematics? And if it does use it as a simplified version of Faradays law does it ever say its valid in a non DC scenario?
Yes, KVL works for lumped circuit abstraction only. When the premises for lumped circuit analysis are missing, KVL is for the birds.
Yep exactly. Without lumped circuits KVL does not exist as it contains a summa operator (∑) that operates on voltages across components. Without lumped circuits there are no components to put inside the equation (You can't strictly define down to the atom level a point in space where a resistor begins and where it ends). If you are operating on real life components made out of actual atoms you need the integral operator found inside Faradays law because real components have physical size. When you see an integral inside what looks like KVL, that is just a unfinished derivation from a special case of Faradays law, this is not KVL.
In the same way Faradays law does not exist in lumped circuits as the integral takes in physical dimensions that do not exist in lumped circuits, trying to apply it there would also make it appear broken, much like KVL appears broken in the real world. That would be a case of using Faradays law wrong.
No. In order to see KVL as Faraday's law with a missing voltage, lumped circuit assumptions need to be met. All fluxes should be confined inside the lumped components and you should not be allowed to run circles around them. It's as easy as that. No refinement of the theory (the concept of inductance used in the 'extended KVL' you mention is based on Faraday's law), no need to add parasitics, no nothing.
An engineer should know the limits of their tools and theories.
KVL is lumped circuits stuff. Circuit not lumped > KVL for the birds.
Edit: changed highlighted part, able>allowed
There are are other laws that are made for use inside lumped circuits and this includes Ohms law in the form we use! We are not extending KVL by adding inductance. The inductance is simply how the math behind circuit analysis takes in account the electrical effects of a wire having non zero length. The calculation of this inductance value involves Faradays law deep down, this calculation condenses the potentially incredibly complex geometry of a wire down to a single number that can simply be plugged into the other math rather than dragging whole Faradays law along for the ride and causing all further math to grow exponentially more complex. If you used Faradays law directly you would still be adding the effects of the wire as a extra piece of area in the loop, if you don't add it in then the wire appears to have zero length just like in the lumped circuit without the inductor added in. The only difference being that circuit modeling gives it a name of "parasitic inductance" (Because its usually undesired in circuit design) while Faradays law adds it in just the same but does not give it a specific name, instead just assuming it as extra loop area.
Can you explain why using a lumped circuit is bad?

And what can electroboom say in reply, now?

And what can electroboom say in reply, now?
He could say he was looking for a particular set of potential differences among the infinitely many you can find inside a varying flux region. If you look at the symmetry of the problem, a uniformly variable flux directed along the z axis will generate a non conservative induced E field tangential to concentric circumferences. If you choose radial paths to reach any couple of points A and B on the circuit circumference, the contribute of the induced field will be non zero only on the arc. This will give you a nice set of potentials that end up being additive and (possibly) uniquely defined. This is essentially what Cyriel Mabilde has done.
EDIT: actually I have yet to check the E field goes around in concentric circles, but seems reasonable.
(note, that this is not equivalent to intercept equal and opposite fluxes in both the meshes the disk has been partitioned into  it's quite the opposite: intercepting different fluxes so as to give a nice set of values in a way to give VAC = VAB+VBC).
BUT, and it's a big butt I mean but, you can measure them only by specifying a particular class of paths. Confirming what Faraday has always said: the voltage depends on the path.
(I suppose that by offsetting the circuit with R1 and R2 with respect to the main coil you should make your probes exit the circle not from the center of the circuit but from the center of the coil).
Edit: specified addittivity, made dependance on area explicit

Can you show me a source that claims that KVL is allowed to be used outside of lumped cirucit schematics? And if it does use it as a simplified version of Faradays law does it ever say its valid in a non DC scenario?
Lewin is not using KVL wrong, because he is not using it. He is using Faraday. Watch his video "Science and believing..." and follow the mesh analysis. You might have been confused by the fact that he drew what appears to be a circuit with lumped elements (and in fact, many posts ago, I said "I am not calling it schematics on purpose") but that curly arrow magnetic field representation inside the central mesh is telling it all. He is using Faraday.
And, in fact, he is getting path depending voltages.
No incongruences whatsoever.
And why is he using Faraday and not KVL?
Because he is analyzing a circuit that is NOT LUMPED. He is INSIDE the frigging coil!!!
If you insist in using KVL, for example at the mesh with the two voltemeters, you find and impossible result.
Impossible for Kirchhoff, but not for Faraday.
As for the rest of your post, I sense confusion. I don't know how to say it. KVL works only in the lumped component assumption. Real world components like inductors, coupled coils and transformers can be modeled with lumped components AS LONG AS YOU DO NOT MESS WITH THEIR FLUXES. In this case you can mend KVL in 'generalized KVL'.
If in your circuit you are able to mess with the flux, say goodbye to KVL and 'generalized KVL'. You need to apply Faraday, or you will find inconsistent results.
Why?
Because the voltage depends on the path.
Also, you seem to mixing togheter external and internal inductance. You might want to have a look at "Fields and Waves in Communication Electronics", by Ramo, Whinnery and Van Duzer.
Edit: IIRC, Lewin used the magnetic field representation with little crosses or dots, and not the curly arrow. Either way, that's not lumped circuits language.

Because he is analyzing a circuit that is NOT LUMPED. He is INSIDE the frigging coil!!!
Right. Those two resistors put inside that frigging coil does not count. Dr.Lewin can ignore internal resistance of EMF source in his equations just because Dr.Lewin is always right.
https://www.youtube.com/watch?v=uAXtO5dMqEI
(https://www.youtube.com/watch?v=uAXtO5dMqEI)

He is not using it wrong. And you say so, too:
Can you show me a source that claims that KVL is allowed to be used outside of lumped cirucit schematics? And if it does use it as a simplified version of Faradays law does it ever say its valid in a non DC scenario?
I think these two were answered in the original 'quote' of Kirchoff work some trillion posts ago. ::)

An engineer should know the limits of their tools and theories.
KVL is lumped circuits stuff. Circuit not lumped > KVL for the birds.
And that is the entire reason why Dr Lewin's experiment is flawed. He's trying to use a practical lumped circuit to show how his nonlumped "inside the inductor" Faraday thinking is right.
And that's wrong, or at best misleading, even though what's he's saying and explaining is not wrong.

In real life if two voltmeters connected to the same two points are reading different values, what to do then?
0) check if was not a mistake to use two instruments to perform the same measure
1) check if one of the two is broken or need calibration (or need some new fresh battery ;))
2) check if there is an induced emf to the leads going to the DVMs, by moving the leads you should see a change in the readings
Can you tell me what I forgot? Thanks!
PS: Yes, I believe in God!

An engineer should know the limits of their tools and theories.
KVL is lumped circuits stuff. Circuit not lumped > KVL for the birds.
And that is the entire reason why Dr Lewin's experiment is flawed. He's trying to use a practical lumped circuit to show how his nonlumped "inside the inductor" Faraday thinking is right.
And that's wrong, or at best misleading, even though what's he's saying and explaining is not wrong.
I think what Prof. Lewin is trying to convey is that no circuit is really lumped.
The "lumpiness" comes only after you make certain assumptions, which most of the time we do implicitly and unconsciously.
If I could translate "Kirchhoff is for the birds", I would say, "Please, put Kirchhoff circuital laws aside for a moment, while I introduce you to a more fundamental theory that not only will explain a lot of phenomena that Kirchhoff can't, but will explain Kirchhoff itself".
I think that, if he came up otherwise so politely with a soothing voice, people wouldn't pay attention to his advice and would try to derive Faraday from Kirchhoff, which is a mistake, instead of the other way around.
So I think that's why he decided to add some hyperbole to his rhetoric. Not sure if it worked though.

I had seen Dr Lewin's demonstration a few years ago but he did not do a good job showing his setup and I always assumed he had made a mistake. I later saw another MIT lecture with a slight twist to the demonstration but again, I felt a bit letdown by the lack of details surrounding his setup. I don't have a problem with what he presents on the board, well except the miss on ohms law. lol. Figured I would watch them all again as it had been so long. Rare I watch EBs channel but after about 8 minutes in, I thought he did a good job with it.
I really don't have much to add. I repeated the test using some coax. Braid terminated at one side, core at the other. Then made both sections symmetrical. My mind wasn't blown. It behaves as I would expect. As someone else said, take into account all the loops.
There are a few things to note. I didn't take a lot of care to try and get good numbers as I didn't think that was important. Where both Dr Lewin and EB use a mechanical switch, I am driving the coil and you can see both halves of the cycle.
***************
I finished Romer's paper. Had I been aware of it at the time I had first seen Dr Lewin's demonstration, I would have understood what he was trying to show. I am now watching Dr Lewin's latest videos where he is going over Romer's paper. Still he misses the opportunity to discuss the various ways the circuit could be arranged as Romer's paper covers. I feel as if I an being expertly trolled by an 80 year old! :DD

An engineer should know the limits of their tools and theories.
KVL is lumped circuits stuff. Circuit not lumped > KVL for the birds.
And that is the entire reason why Dr Lewin's experiment is flawed. He's trying to use a practical lumped circuit to show how his nonlumped "inside the inductor" Faraday thinking is right.
And that's wrong, or at best misleading, even though what's he's saying and explaining is not wrong.
I'm not sure I'm understanding this.
Where did Lewin used a "practical lumped circuit"?
In the demo at the end of the famous lecture 16
he used a physical system constituted by two resistors connected in a loop of metal wire. The resistors themselves are inside the loop, or as engineers like to call it, the coil. That alone should have alerted the student and made him think: "Oh, wait a minute... I have always seen coils made of wire only, and then the rest of the circuit attached to its terminals. This is something different".
Then he used two oscilloscopes as 'voltmeters', still in the physical world to show that they gave different readings despite being connected to the very same two points.
That should be mind blowing for a second year university student used to probe circuits that do not mess with the flux. Now, the student should have started to use the matter between the ears and ask himself "how is this possible?" and should have started questioning the assumptions made.
And that is the purpose of the demo. Stimulate thinking. Lewin did many similar thoughtprovoking demos in his lectures. He never gave an explanation on purpose, not to spoonfeed the students.
That's good teaching, I see no flaws here. (but that's me) [note1]
In the explanation and subsequent videos
He explained why the instruments in the real world gave that apparently impossible result. Because that circuit, for the fact of having resistors inside the coil and the instruments linking opposite flux depending on how they encircled the coil (you can't do otherwise when they are part of the coil itself EDIT: unless you want to cross the flux, which is bad as Venkman would tell you) could not be considered a lumped circuit where KVL works.
And in fact he solved it using Faraday. If you look at his 'schematic' there are symbols representing the magnetic field in the middle of the main mesh representing the metallic loop with the resistors. There is no such thing in lumped circuit theory: you draw that wiggly symbol that represents an inductance or the secondary of a transformer and you are sure the magic fluxvoodoo happens inside and do not draw the crosses or dots that represents the direction of the magnetic field.
EDIT: Also, the equations he penned are Faraday's, and yes they obviously look like 'generalized KVL' but the source of emf is no longer localized in a lumped element (if you do that, you end up with single valued potentials). (end EDIT)
There is, therefore, no 'practical lumped circuit'. Neither in the real world, nor on the blackboard (or whiteboard).
If the student does not understand it, how should it be Lewin's fault?
But even if we agree Lewin should have spoonfed his students (which are MIT students, so I guess he had somewhat higher than average expectations), the 'he did not explain it well enough' excuse could work for about 1015 minutes. After that, well, it's no longer Lewin's fault.
And this thing has been going on for much longer than that.
(There is a silver lining, though: many people have been learning about Faraday better than ever)
(Note0: when I said 'inside the coil' I meant the loop with the two resistors. As for the primary coil  the one generating the field  it could have been substituted by a falling magnet, or a nuclear explosion...)
[Note1: I found this comment by Lewin in one of his videos
>>>asks me to find a mistake on my own>>
that is by far the best way to teach Trust me I have been teaching Physics for 58 years. If present a student on a silver plate what (s)he did wrong they will quickly forget. But if they have to put in the effort to find their mistake (after I have sent them my lectures which address their topic) they will never forget.
Edit: typos (some of them) and added part on equations on board.
Edit: added silver lining and Lewin teaching advice

So nobody posted the proper pounding yet?
edit.. already posted.
“Sincere Apology” nice one. Sorry you’re wrong! :D

Lewin is not using KVL wrong, because he is not using it. He is using Faraday. Watch his video "Science and believing..." and follow the mesh analysis. You might have been confused by the fact that he drew what appears to be a circuit with lumped elements (and in fact, many posts ago, I said "I am not calling it schematics on purpose") but that curly arrow magnetic field representation inside the central mesh is telling it all. He is using Faraday.
And, in fact, he is getting path depending voltages.
No incongruences whatsoever.
And why is he using Faraday and not KVL?
Because he is analyzing a circuit that is NOT LUMPED. He is INSIDE the frigging coil!!!
If you insist in using KVL, for example at the mesh with the two voltemeters, you find and impossible result.
Impossible for Kirchhoff, but not for Faraday.
Well at some point in the video he does add up all the voltages according to KVL and points out you don't get zero. This is his reasoning for saying "its for the birds". So one of the flowing cases is happening:
a) Assuming a circuit is lumped: He is claiming the circuit drawn is an lumped equivalent circuit of the real circuit so KVL should work inside it but it does not.
b) KVL in non lumped circuit: He is wrongfully applying KVL to a non lumped circuit so it does not work because its not meant to work
c) Inaccurate lumped circuit: His lumped lumped circuit model is describing a physical circuit consisting of zero length wires that can't exist in real life
Mesh analysis is a big part of the circuit analysis toolkit and is used on lumped circuits. This is another reason why i get the feeling he is mixing lumped and real circuits as if they are the same thing. As soon as you draw a resistor symbol you are creating a lumped model of a resistor. This resistor has a physical size of zero, acts perfectly according to Ohms law and has exactly 2 strictly defined connection terminals. A real resistor has a physical size larger than zero, stops following Ohms law when taken outside of operating limits and has a volume of material representing the connection terminals rather than a infinitely small point in space.
Lumped circuits are not ignoring Maxwell. They are fully embracing it and using Maxwell in a way that hides it away under abstraction in order to make math easier because 3d space integrals are hard. Its a math shortcut.
So rather than saying KVL is wrong he should have said ether "KVL can't be applied here because this is not a lumped cirucit" or "Here is a lumped equivalent circuit that is required to apply KVL"
As for the rest of your post, I sense confusion. I don't know how to say it. KVL works only in the lumped component assumption. Real world components like inductors, coupled coils and transformers can be modeled with lumped components AS LONG AS YOU DO NOT MESS WITH THEIR FLUXES. In this case you can mend KVL in 'generalized KVL'.
If in your circuit you are able to mess with the flux, say goodbye to KVL and 'generalized KVL'. You need to apply Faraday, or you will find inconsistent results.
Yes that is the main point of using a lumped circuit. You don't have to mess with the fluxes. All the flux interaction are calculated using Maxwell into a inductance and coupling coefficient number. Giving you inductors that act like the real one by simply multiplying its values with the correct things rather than having to calculate flux in 3d space every time. All of the flux interactions are modeled in that single coupling coefficient.
The only case where i can see lumped models of wires being a bad idea is when the wires are physically moving during the circuits operation. This would make you need to recalculate the inductance and coupling coefficients as well as the induced EMF according to Maxwell for every timestep of the calculation. Since you are calculating Maxwells equations in 3D space every time it makes sense to just use Maxwells equations directly, because the lumped circuit equivalent of that wire is no longer a math shortcut if you can only reuse the values once. So if you are calculating what happens inside a electric motor its better use Maxwell directly.
Additionally all off the shelf passive electronic components are specified in Ohms, Farads or Henrys. The manufacturer has calculated Maxwell for you (Tho more likely measured with an instrument) and created a equivalent model of the component. You can no longer stick this component in a non lumped circuit. You would need to disassemble the inductor and accurately measure the path the wire takes inside and then use that in your non lumped circuit model.
Nobody is stopping you from only analyzing circuits with non lumped models, but don't expect anyone else to do so. Most people enjoy calculating the result in a few lines of math rather than a few pages (And still get the same result).

There is, therefore, no 'practical lumped circuit'. Neither in the real world, nor on the blackboard (or whiteboard).
So wrong. Indeed there is practical lumped circuit (for coil loop with resistors)  consisting of as many fragments of the coil as needed for purpose and two resistors. Actually kind of lumped approach is used in Romer's paper stating that 1/2 of the coil have 1/2 of the EMF induced. Dr.Lewin forgot about Faradays law in lecture about Faradays law :) It is obvious that he had "ups, I fracked up" because in the apology "To Agree or Not to Agree with the Master" video circuit he did not use superconductive wire anymore to further smear things up and make his error(s) less obvious for those (parrots and cultists) who learn physics just by memorizing it.

Summary:
1. Title is "my sincere apologies"
2. 90% of video is arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct. Take great glee in squashing this strawman by repeating the same thing he has stated like a broken record for the past week.
3. State that anyone with a masters in electronics who suggests that the different readings are only* due to placement of the probing leads is an idiot.
4. Clarifies that the "sincere apology" is for being too blunt in laying out his 100% correct argument against the fairy tale strawman while completely brushing off the actual point of contention.
*but let's forget that I was the one to apply real oscilloscpes and their readings to a real test circuit. If we applied these real oscilloscopes to my theoretical model, we would apparently learn that [start broken record]
Super shorter summary:
"I can see the sailboat, and you can't."
Next up:
"Newton's laws are just a special case of relativity. It's a crime that we call these things laws, when it is really Newton's Loopholes."
You have to remember that Electroboom is making a really really bad claim here. Electroboom is claiming that induction in the probe wires is what causes the result.
This is easy to prove incorrect experimentally: You can use shielded grounded coxial cable for the meter probes  the volt meters still show different voltage.
They show different voltages because there is different currents in the left and right loop because of the induction in the centre loop. Lewin explains why this is with actual math and has done detailed videos of 30min+ length about this multiple times.
Mehdi makes motherhood statements, uses napkin diagrams, and refers to analogies about voltage, fields and inductions.
At the end Mehdi shows a circuit which he claims is the 'correct' way. What he actually shows is a circuit of two meter probe loops that DO have induction. So he actually changes the circuit from 3 to two loops, both of which now have induction, and he basically claims that this is the correct way to not have induction. He is totally backwards!
If you look at Mehdis answer, I bet he pulled it from somewhere else, because his solution at the end doesn't follow at all from what he had been blabbing about in the minutes leading up to it, and this is evidence by the fact he says he isn't 100% sure, makes no mention of the magnetic field nor even the position of the probes relative to the soleniod. His solution involves rearranging circuit so there is induction in the meter probe loops, something that he said was causing the incorrect readings. Hence the only reasonable explination is: he is wrong. It it his is 'probing' that is wrong.
Sorry but Mehdi got owned here.... if he is going to do a video like that he should brush up first. As Lewin said, this is embarrassing for him.

You have to remember that Electroboom is making a really really bad claim here. Electroboom is claiming that induction in the probe wires is what causes the result.
What is your explanation then?
Sorry but Mehdi got owned here.... if he is going to do a video like that he should brush up first. As Lewin said, this is embarrassing for him.
You just embarrassed yourself  because induced EMF in the probe wires is actual cause of "surprising" result. Dr.Lewin explains it in the video "Believing and Science are Very Different".

Fine... well I will do a full dissection of the all the mistakes Mehdi makes:
At 5:47 Mehdi claims that in a twisted wire there is induced current inbetween each twist that cancels out the one in the next twist. This is false. The cables cross over for each twist, they do not connect, so there is no induction loop in the 'circle' of each twist. The reason twisting cables stops induction is because as you twist the cable, you are flipping the area of the loop over. So the magnetic field is now effectively passing though the next twist upside down. So the magnetic field through the first twist is in one direction, and the magnetic field through the next twist is in the other direction  when you consider the plain the loop made up by the wire run. So by twisting you can make the net field through the overall loop zero  therefore no induction.
At 8:18 Mehdi measures the current 'across both resistors'. Mehdi then concludes that voltage R1 plus voltage R2 is the same as voltage across the loop. In adding the volt meter across R1 and R2, Mehdi has changed the topology of the circuit. It now has 4 loops instead of 3. Most importantly, the meter is now in the inductive loop, not the resistors. Mehdi is oblivious that he has done this. In this case the voltage around the loop is the voltage shown on the meter. By adding the voltage meter here there is no longer any induction in the smaller loop containing the resistors, as that smaller loop does not enclose any of the magnetic field.
At 9:10 he admits that if the meter is put on the out side, reforming the original induction loop with the resistors in it, that the voltage again goes to zero. He then asks who is correct. Obviously it is Lewin who is correct, as Mehdi is oblivious the he changed the topology of the loops when he measured what he is calling the 'loop voltage'. With the circuit back in its proper arrangement, he measures as per Lewin. Ironically it is Mehdi who is doing 'incorrect probing' here.
At 9:27 his inability to think of the inductive loop is shown further at 9:27, when he claims to be 'measuring across the gap'. Of course he is just completing a loop with his meter.... there is no gap. Once again he is obvious to his own incorrect probing....
At 9:42 he then runs the meter the other way, so there is no loop around the magnetic field, and he reads zero. He later attributes this to 'cancelling out', but there is nothing to cancel out, as he has formed no loop around the magnetic field.
At 9:49 he claims if he makes the sense lines 'a little bit shorter' than the loop, but without crossing (or encircling) the magnetic field in soleniod, and says "I will have voltage jumps". This shouldn't happen of course because he doesn't have any loop around the magnetic field inside the soleniod. The reason he reads a bizzare wave form here is because there is a weak magnetic OUTSIDE the soleniod (imaging it come out the top stretching to infinity as it spills down and comes back in the bottom of the soleniod). The thing he is measuring at this point is actually the magnetic field 'falling' through his loop in the opposite direction as the magnetic field through the solneiod. This is why his wave form is opposite to when he just measures around the soleniod. He incorrectly attributes this to the meter probes no longer 'canceling out' properly. You can see plainly that he has made a fork shape loop, and he puts his loop in the worst possible position: over the end of the soleniod while not enlcosing the magnetic field inside the soleniod. Lewin explains how you need at least a 30cm soleniod with your loop half way down, the point of this is to ensure the magnetic field outside the soleniod is for practical purposes zero. Mehdi has a complete failure of experiment setup here. You can replicate it yourself, if you have any fork shape loop around the soleniod (but not enclosing it) you read zero. Start moving it up to the end of the soleniod and you will start getting induction in the OPPOSITE direction compared to when you enclose the soleniod.
At 10:00 to 10:27 Mehdi makes the extraordinary claim that a nonclosed loop will have half V induction, cancelled out by half V the other way. He never produces a single measurement to show this is true. If his claim was correct, he could measure the Half V by putting meter across left and right sides of the 'semi circle' he shows. This is of course complete garbage. There is no loop formed around the magnetic field, so there is no induction.
At 11:18 Mehdi claims "the same voltage of the loop wire are induced on the sense line". The sense lines are on the left and right side loops, which enclose no magnetic field, so there is no induction involving them. The induction loop is just the inner loop with the resistors. He is 100% wrong about induction 'in' the sense lines.
At 12:02 the proof of Mehdi being wrong is made final when he shows a circuit claiming to show "properly" how to measure the voltage across the loop. Once again this just changes the topology of the circuit. By bringing the probes through the middle he is now creating two induction loops, the left loop and the right loop, each enclosing half the magnetic field. Only this time HIS METER PROBES ARE PART OF THE INDUCTION LOOP. So he has gone from the original Lewin circuit that had no magnetic field through the left and right loops that contain the meter probes, to a circuit with only two loops, both of which form an inductive loop by using the meter probes. Yet he claims it is Lewin who incorrectly probed :DD
He overall main mistake is that for some reason he thinks voltage must exist across the wire portion of the induction loop. This is because he is used to thinking of circuit elements in conservative fields, which have a voltage drop across them. He out right says it himself when he claims Lewin 'forgot' the 'transformer'. He has no idea at all when it comes to non conservative fields, not even the most basic requirement of a closed loop around the magnetic field being required for induction.... Throughout his video he is completely obviously when he creates new induction loops and changes the topology of the circuit.
In all seriousness... has anyone checked this guy even is actually qualified? Is it just a show? His videos are entertaining but his video on this is absurd junk science. What is scary is the amount of people on here, and youtube, and reddit, who are siding with Mehdi...

b) KVL in non lumped circuit: He is wrongfully applying KVL to a non lumped circuit so it does not work because its not meant to work
It's not KVL, it's Faraday.
Mesh analysis is a big part of the circuit analysis toolkit and is used on lumped circuits. This is another reason why i get the feeling he is mixing lumped and real circuits as if they are the same thing.
I called it mesh analysis to make the sentence short. And in fact he is analyzing the meshes, applying Faraday. Where's the big difference with lumped circuit analysis? That the emf is not localized. This is best seen when you bring the voltmeter inside the loop and you probe the points on a diameter. Now, if you use Faraday and the emf is not localized, the emf contribute appears in BOTH submeshes, proportional to the area encircled by the submesh. If you localize it as if it were a lumped circuit, the emf contribute appears only in one submesh, no matter the area.
As soon as you draw a resistor symbol you are creating a lumped model of a resistor.
And where is it written that that lumpiness is contagious?
Come on, what should he have done? Invent a new symbology? I've never seen that in any of the EM books I've read.
You should have enough mental flexibility to understand what is going on.
So rather than saying KVL is wrong he should have said ether "KVL can't be applied here because this is not a lumped cirucit" or "Here is a lumped equivalent circuit that is required to apply KVL"
Good if you want your students to think in a compartmentalized way. Like technicians. But if you are forming scientists, or even engineers, you should teach them to question the limits of the tools (practical and theoretic) they use.
Yes that is the main point of using a lumped circuit. You don't have to mess with the fluxes.
[...]
The only case where i can see lumped models of wires being a bad idea is when the wires are physically moving during the circuits operation.
Lewin's circuit IS A CASE WHERE A LUMPED MODEL IS INAPPROPRIATE.
How can this be so hard to grasp?
Nobody is stopping you from only analyzing circuits with non lumped models, but don't expect anyone else to do so. Most people enjoy calculating the result in a few lines of math rather than a few pages (And still get the same result).
Seriously? After all these umptillion pages of discussion you still have not realized that Lewin's circuit cannot be analyzed with lumped circuit theory?
Nobody is saying that you have analyze all circuits with 'non lumped models' only. You just have to do that only when it is necessary. Such is the case of Lewin's circuit.
Oh, for the love of... Physics! :)

You just embarrassed yourself  because induced EMF in the probe wires is actual cause of "surprising" result. Dr.Lewin explains it in the video "Believing and Science are Very Different".
ogden, I promise I will not interact with you again on this matter (I did it before when you refuse to watch the video, but then you watched it so I turned back on my steps, but now no conditions).
I will leave you with this question.
When the voltmeter is outside the loop, for example measuring 0.9 V, does it matter the area its probes are enclosing in excess of the loop area? I mean, assuming the field is all confined inside the two resistors loop, does it even matter to twist the probes? Will you read, for example, a different voltage when that excess area enclosed by the probes changes from nearly zero (twisted probes) to say, half the area of the loop, equal to the area of the loop, twice the area of the loop, ten times the area of the loop?
That's all.
Now, believe what you wish.
Edit: typos, syntax, grammar, oh Lord! Somebody get me a dictionary and a basic English course!

Sredni, seriously? If you did not watch video, here's screenshot from it. Pay attention to EMF equation of loop4 and what loop4 actually is. And watch the Funny video! Also reading Romer's paper will not hurt BTW.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=578696;image)

He overall main mistake is that for some reason he thinks voltage must exist across the wire portion of the induction loop.
Here we go AGAIN. Groundhog Day (1993) movie. Why don't you read the forum first? Read Romer's paper as well.

In all seriousness... has anyone checked this guy even is actually qualified? Is it just a show? His videos are entertaining but his video on this is absurd junk science. What is scary is the amount of people on here, and youtube, and reddit, who are siding with Mehdi...
I think it's far more alarming that people ridicule the desire to understand and learn, and start talking in "siding with" terms when a younger engineer wants to question a professor and ask for clarification in order to gain and spread understanding, and does it in a completely civil way, with a lot of more thought and actual experiments put into it than what goes to usual lecture question. I would be extremely happy for such wellformed and scientifically sound questioning from someone outside the formal scientific circles.
Even more alarming is that an academic person who has been actually teaching is completely unable to handle this kind of situation, which should be everyday practice when it comes to science and learning.
It's also interesting how new accounts pop up in the EEVblog forum just to write such passiveaggressive "taking side" comments like this.
Thank you for your analysis, though.
If I needed to side with someone, it would definitely be Mehdi, regardless of who is being "right". One is clearly encouraging scientific engineering process (which includes questioning, experimenting, and desire to understand), while the other is actively hurting the process (by scaring, denying proper discussion, generally being a total asshole). I understand there are fanboys for the both "cultures".
Luckily, no one is forcing anyone to "side with" anyone.

It's not KVL, it's Faraday.
Yes he got his results with Faradays law. But to prove that KVL is wrong he shows that the voltages don't add up to zero. Voltages adding up to zero is KVL and he was applying it to a circuit model that is not valid in normal circuit analysis methods where KVL is meant to be used. This is his proof before saying its for the bids.
Just like usual Newtonian kinetic energy equation ( E = (m*v^2) / 2 ) breaks if you are approaching the speed of light since that form of the equation works with the assumption that speed of light is infinite or that Einsteins relativity effects don't exist, yet we don't say that Newton is for the birds. It works when used correctly
I called it mesh analysis to make the sentence short. And in fact he is analyzing the meshes, applying Faraday. Where's the big difference with lumped circuit analysis? That the emf is not localized. This is best seen when you bring the voltmeter inside the loop and you probe the points on a diameter. Now, if you use Faraday and the emf is not localized, the emf contribute appears in BOTH submeshes, proportional to the area encircled by the submesh. If you localize it as if it were a lumped circuit, the emf contribute appears only in one submesh, no matter the area.
Lumped model still works with the voltmeter inside the loop, you simply have to recalculate the values of the inductors that represent wire segments so that they match the crossection contribution and you again get accurate results from a lumped model. You can use an inductor to represent a fractional turn in order to model just one section of wire around the loop. If you want to know whats going on in the middle of that section of wire then simply split it into two half valued inductors and you get a node with the voltage and current at that point in the loop.
The lumped model does not make it necessary to put all the inductance in the loop inside one inductor. This inductance can be split over as many inductors as you want to expose the voltage and current at any point along a wire. It may seam strange to have this fractional turn section of wire since Faradays law requires a loop, but it does work and can be imagined as taking a slice of cake out of the loop and attributing that slice to its accompanying length of wire.
You have the freedom to construct a lumped model in a way that makes the desired measurements easy to access while not changing the behavior of the circuit.
And where is it written that that lumpiness is contagious?
Come on, what should he have done? Invent a new symbology? I've never seen that in any of the EM books I've read.
You should have enough mental flexibility to understand what is going on.
Sorry if that was misunderstood. I was mostly using it as an example of how quickly and often lumped component models sneak up when doing math with electricity. These lumped models have there own set of limitations, just like KVL and all other circuit analysis tools. It makes sense to use a resistor symbol, but you have to realize that it does introduces "lumpynes" into the model.
Lewin's circuit IS A CASE WHERE A LUMPED MODEL IS INAPPROPRIATE.
How can this be so hard to grasp?
I have created a lumped element model that behaves identically to Dr. Lewins experimental circuit on the first page of this thread:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312)
It uses the above described "slice of flux cake" way of determining inductance values for sections of wire. Due to the lumped model it makes KVL work perfectly fine in it and allows any other circuit mesh analysis tool to be applied to it correctly.
Can you explain why a lumped model is inappropriate given that it is required in order to apply KVL to it?
Seriously? After all these umptillion pages of discussion you still have not realized that Lewin's circuit cannot be analyzed with lumped circuit theory?
Nobody is saying that you have analyze all circuits with 'non lumped models' only. You just have to do that only when it is necessary. Such is the case of Lewin's circuit.
Oh, for the love of... Physics! :)
Well that's because so far nobody has shown me what exactly i am doing wrong in my lumped model linked above. It reproduces the same waveform as Dr. Lewins experiment and does not have any cherry picked or tweaked component values in it.
I am not saying you have to analyze everything non lumped. But if you want to use KVL correctly you need to do it lumped.
If someone thinks this model is a lucky fluke i can also show it adjusted to probe other points on the loop or put the voltmeter inside the loop.

I have created a lumped element model that behaves identically to Dr. Lewins experimental circuit on the first page of this thread:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312)
I will answer to this part only, because I cannot repeat the same things over and over again. Forgive the use of capital letters, but at this point I want to emphasize the message.
Your model DOES NOT BEHAVES IDENTICALLY to Dr. Lewins experimental circuit.
In Lewin's circuit you can have two different voltage readings from the VERY SAME TWO NODES.
Your circuit cannot do that. You get two different reading from TWO DIFFERENT COUPLES OF NODES. I do not even have to check it because I know that Spice can not tolerate that kind of ambiguity. I have already written about it, some twelve billions posts ago. And if you want to see 0.1V and 0.9V on those two resistors, you could have placed just one coil, with the two resistors in series. Et voilà, the magic dual reading. Except it isn't referred to the same two nodes.
Also, note that the 'extended KVL' is just Faraday under disguise. The original KVL cannot even account for lumped inductances and trasformers. It is indeed for the birds when you have these kind of components in the circuit. But we can still save the appearances by moving the emfs on the other side and pretend it's a voltage drop or a voltage generator (so to speak) and happily simulate our circuits in Spice  it won't scream at you because in this case you can still have singlevalued potentials.
But that WORKS only if the components are lumped, i.e. you do not mess with their fluxes. When you can mess with the fluxes, you can no longer pretend to have lumped components, so even the extended KVL is for the birds  you need to account for the distributed emf 'manually'. You can simulate a different, similar circuit in Spice to help out in solving the equations, but you won't see that magic trick of the voltage across the very same two points assuming different values at the same time.
Come back when Spice can give TWO different voltages from the very same TWO NODES. Not three, not four. TWO.
I'll be waiting for you in my igloo in Hell.
In any case the key point is: having voltages depending not only on the endpoints but also on the path, is no magic at all. It is basic electromagnetism  it is a behavior that goes down to the bone of EM structure. Starting from the definition of rotor, passing through Stokes theorem and adding in a pinch of experimental result (Faraday's law).
And that is really basic physics.

I was wrong.
Lewin is the fraud.

Your model DOES NOT BEHAVES IDENTICALLY to Dr. Lewins experimental circuit.
My circuit model produces a graph identical to what what Dr. Lewins two oscilloscopes show, so in what way does it behave differently to the real circuit?
In Lewin's circuit you can have two different voltage readings from the VERY SAME TWO NODES.
Your circuit cannot do that. You get two different reading from TWO DIFFERENT COUPLES OF NODES. I do not even have to check it because I know that Spice can not tolerate that kind of ambiguity. I have already written about it, some twelve billions posts ago. And if you want to see 0.1V and 0.9V on those two resistors, you could have placed just one coil, with the two resistors in series. Et voilà, the magic dual reading. Except it isn't referred to the same two nodes.
So how do you get a real life voltmeter to show you two different voltages at the same time? (Without flipping wires around as that effectively connects the voltmeter to a different part of the cirucit)
Also, note that the 'extended KVL' is just Faraday under disguise. The original KVL cannot even account for lumped inductances and trasformers. It is indeed for the birds when you have these kind of components in the circuit. But we can still save the appearances by moving the emfs on the other side and pretend it's a voltage drop or a voltage generator (so to speak) and happily simulate our circuits in Spice  it won't scream at you because in this case you can still have singlevalued potentials.
But that WORKS only if the components are lumped, i.e. you do not mess with their fluxes. When you can mess with the fluxes, you can no longer pretend to have lumped components, so even the extended KVL is for the birds  you need to account for the distributed emf 'manually'. You can simulate a different, similar circuit in Spice to help out in solving the equations, but you won't see that magic trick of the voltage across the very same two points assuming different values at the same time.
I do actually agree to all of that. KVL doesn't have to account for inductance, or even resistance, other circuit analysis tools do it so it doesn't have to. You indeed can't mess with fluxes because they don't exist in lumped models so no worry there. And finally SPICE will indeed always give one voltage, that's why i like it, its always nice to get a concrete answer to a question.
Come back when Spice can give TWO different voltages from the very same TWO NODES. Not three, not four. TWO.
I'll be waiting for you in my igloo in Hell.
In any case the key point is: having voltages depending not only on the endpoints but also on the path, is no magic at all. It is basic electromagnetism  it is a behavior that goes down to the bone of EM structure. Starting from the definition of rotor, passing through Stokes theorem and adding in a pinch of experimental result (Faraday's law).
And that is really basic physics.
I sure hope i don't see SPICE giving two voltages, i don't like bugs in my software.
I completely agree with you that the nodes in Dr. Lewins have two different voltages across it according to the formal definition of voltage. I even explained it in one post how that works on the level of electrons and fields in a wire.
But do try to understand circuit analysis and lumped circuits a bit better. Then you will see how KVL indeed works when applied correctly (And no it still won't give you two voltages because the "effective voltages" used in circuit analysis always have exactly one value unlike "formal definition voltages" that Maxwell operates with).
So when do i get to see a real life voltmeter showing two voltages?

The voltage across the meter reads 0V.
This video at 9:30 shows this experimentally:
Indeed it shall read 0V between A&D points  if both resistors are equal (100 Ohms in this case). BTW thank you for providing video which at 12:30 confirms discussed in this thread behavior of the circuit  that actual voltage between A&D in Dr.Lewin's experiment is 0.4V.

I was wrong.
Lewin is the fraud.

So when do i get to see a real life voltmeter showing two voltages?
I see you excluded going around the flux. Naughty boy! :)
But I can do this with an arm tied behind my back. Bring the voltmeter inside Lewin's two resistors loop, solder its probes on opposite points on the diameter. Wiggle the probes around.
There you go. You can read anything you like from 0.1V to +0.9V (ok, it's either AC or pulsed so the sign is more about phase in the AC case).
Don't tell me you want to see a voltmeter giving two readings from the same two points and the same path.
Am I the only one sensing a shifting goalpost, here?
I am afraid I cannot help you further in solving your confusion. All I can do is suggest you read Ramo, Whinnery, Van Duzer. It will clarify a lot about lumped circuits, distributed circuits and field analysis for waveguides, resonant cavities and antennas. There's a whole world out there, beyond Kirchhoff's columns.

So when do i get to see a real life voltmeter showing two voltages?
:// If you really want to see it in real life, your best bet may be to take a few minutes and set it up yourself. If you lived next door, I could invite you to see my setup in person. Dr Lewin did make a video using volt meters as well as a scope but I can understand wanting to see it for yourself. Some wire, a bolt, battery, couple of resistors and a couple of cheap analog meters.

I'm not sure why sectokia posted a link to this video, then deleted his posts. But I think it's worth watching if you are interested and have half an hour to kill.
Some people will say he found the proper way to make this measurement. Others will say that he is just choosing a measurement path that gives him what he wants:
https://youtu.be/JpVoT101Azg (https://youtu.be/JpVoT101Azg)

Quote from: rfeecs on Today at 13:55:16 (https://www.eevblog.com/forum/index.php?topic=149278.msg1986992#msg1986992)
I'm not sure why sectokia posted a link to this video, then deleted his posts.
Because it kind of proves EB right, contrary to his critique?
Edit: NVM.I was wrong.
Lewin is the fraud.

We can all agree that meter probe when completely off to side reads .1v and when off the other side completely reads 0.9v.
If the meter probe comes down through the magnetic field splitting it exactly in to two halves of equal area it reads 0.4v.
You can get any value you want from 0.1 to 0.9 by changing the ratio of the left and right area formed by the meter probes cutting the magnetic field.
You can attach the meter directly across the left resistor and read anything from 0.1 to 0.4, it depends solely on the ratio of the two areas that the meter probes cut the solenoid field into.
The same is true when putting the Probes across the other resistor in the other side.
The same is true when putting the probes on any point between the resistors to any point between the resistors on the other side.
In all those cases you can arrange the probes to read anything from 0.1 to 0.9V.
I can connect 3 meters across the resistor on the left and have one read 0.1v, one read 0.4V and one read 0.9v.

I'm not sure why sectokia posted a link to this video, then deleted his posts. But I think it's worth watching if you are interested and have half an hour to kill.
Some people will say he found the proper way to make this measurement. Others will say that he is just choosing a measurement path that gives him what he wants:
https://youtu.be/JpVoT101Azg (https://youtu.be/JpVoT101Azg)
Nice try. But why did he take half an hour to measure the voltage of a single loop connected to two resistors? Because he had to go into long considerations about Faraday's law of induction before he measured the voltages the "right" way.
Well, if you have to use another theory to validate yours, it means that your theory is not as fundamental.
Make no mistake. Kirchhoff is cool, but for flux sake, learn the doggone Maxwell. There you gon' understand Kirchhoff and much more.

So when do i get to see a real life voltmeter showing two voltages?
I see you excluded going around the flux. Naughty boy! :)
But I can do this with an arm tied behind my back. Bring the voltmeter inside Lewin's two resistors loop, solder its probes on opposite points on the diameter. Wiggle the probes around.
There you go. You can read anything you like from 0.1V to +0.9V (ok, it's either AC or pulsed so the sign is more about phase in the AC case).
Don't tell me you want to see a voltmeter giving two readings from the same two points and the same path.
Am I the only one sensing a shifting goalpost, here?
I am afraid I cannot help you further in solving your confusion. All I can do is suggest you read Ramo, Whinnery, Van Duzer. It will clarify a lot about lumped circuits, distributed circuits and field analysis for waveguides, resonant cavities and antennas. There's a whole world out there, beyond Kirchhoff's columns.
Sure you can exclude the flux in the lumped model if you want. All you need to do is set the voltmeters wires to have 0 Henrys of inductance.(This makes the circuit impossible to construct in real life tho). I chose to include the flux so that it does behave like Dr. Lewins real circuit.
Nope not a shifting goalpost. You asked to see a lumped model show two voltages different across two points, voltmeters show this same "effective voltage" as used in lumped circuits so to have two voltages in the same point a voltmeter needs to show two different readings simultaneously too.
You make the different voltages show by changing the path of the wires. The model does the same by simply updating its probe wire inductance values to match the new wire path. Both get the same result on the voltmeter. So how are these results different?
I'm not sure why sectokia posted a link to this video, then deleted his posts. But I think it's worth watching if you are interested and have half an hour to kill.
Some people will say he found the proper way to make this measurement. Others will say that he is just choosing a measurement path that gives him what he wants:
<YOUTUBE>
That video does a great job of explaining what is happening. To top it off all of his claims have an accompanying experiment to prove it, rather than just saying "This is how it is, chose to believe it or be wrong"
:// If you really want to see it in real life, your best bet may be to take a few minutes and set it up yourself. If you lived next door, I could invite you to see my setup in person. Dr Lewin did make a video using volt meters as well as a scope but I can understand wanting to see it for yourself. Some wire, a bolt, battery, couple of resistors and a couple of cheap analog meters.
I did the experiment a few days ago just because i thought it would be interesting, but i haven't posted photos since there ware no unusual results, it works the same as Dr. Lewins experiment as expected.

I'm not sure why sectokia posted a link to this video, then deleted his posts. But I think it's worth watching if you are interested and have half an hour to kill.
Some people will say he found the proper way to make this measurement. Others will say that he is just choosing a measurement path that gives him what he wants:
https://youtu.be/JpVoT101Azg (https://youtu.be/JpVoT101Azg)
Great video. Well worth watching.
He uses a much, much better experimentation methodology and gives much better explanation of what is happening than Dr Lewin does.
He also understands how MaxwellFaraday interacts with reality too rather than just seeing it as an equation.
He credits someone called Kirk McDonald for his explanation of the "Lewin paradox".

Here are the photos of my recreation that i did last week but never posted photos. I still had it set up so i just cleared the bench a bit and made some photos and scope captures.
I used a MOSFET driver circuit i had laying around to pulse the current to the coil using a waveform generator so that i had a repeatable waveform with a trigger signal. The recreation of the experiment was mostly done because i thought it was a cool experiment and i don't get to play with such magnetic effects often.
Results are identical to Dr. Lewins experiment and are identical to my lumped circuit model ( https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312) ) that i have put together before even doing the experiment.
So my conclusions stay the same:
1) Faradays law works and does show two different voltages across two points in a circuit. The two voltages appear because we are calculating only one section of the whole loop, what voltage you get depends on what loop section you are going along (The whole voltage is path dependent). There indeed is 0.1V and 0.9V across A and B in Dr. Lewins cirucit, but these are voltages along a incomplete loop (Probe wires complete it into a closed loop to then produce a single result on the voltmeter). Its more of a math technicality and NOT something like Schrodingers cat(Being both dead and alive simultaneously) where both voltages are somehow physically existing in two forms. Its only as real as imaginary numbers.
2) Kirchhoffs voltage law works too. When applied to a lumped circuit mesh representing the real circuit it shows the sum of voltages is zero and makes a prediction that matches Dr. Lewins experiment. Note that the lumped circuit includes the probe wires as part of the circuit (Dr. Lewins application of Faradays law does not include probe wires, hence why it does not fit together)
3) Dr. Lewin is right about everything in his videos except his claims about KVL are wrong. He is applying KVL incorrectly to his circuit. It should instead have been said that KVL is a circuit analysis tool and like all other such tools requires a circuit mesh model to work on (This model includes probe wires). Additionally KVL is defined as being "algebraic sum of all the voltages around any closed loop in a circuit is equal to zero" this is not the same as an integral of the electric field around the loop as he writes it, you require lumped components to be able to apply the summa operator(∑) in the equations of KVL
4) Electroboom is technically wrong about bad probing since Dr. Lewin was measuring the voltage he set out to measure. However he recognizes correctly that the probing method is where the double voltage phenomenon comes from and has shown the underlying reasons for why. There are indeed some minor aspects of his video that could be improved, but he comes to the correct conclusion that KVL always works when used correctly.
4) This is a difficult to explain topic and its very hard to make an explanation that everyone understands.
I would love to see a 3 minute video that carefully condenses the information and explanation from this thread, but i am not a youtube creator.

He also understands how MaxwellFaraday interacts with reality too rather than just seeing it as an equation.
The equation summarizes reality. That's why you, I and everyone in this forum need to study Maxwell.
Maxwell didn't come up with his equations out of an exercise of math. He collected experimental data from Faraday, Ampere and Gauss, tried to figure out what was going on, i.e., what the REALITY was, and proposed the equations that better describe it.
More important, after he grasped the deep meaning of that REALITY, he could predict, among other amazing things, the existence of something that REALITY was not making so obvious in his time: the propagation of radio waves.
Fifteen or so years later Heinrich Hertz proved with an EXPERIMENT that the equations were right.
When you see people treating Maxwell just "as an equation" it is because they understand the solidity of the theory, have proved its efficacy in practice and have absolute confidence in its predictions.

He credits someone called Kirk McDonald for his explanation of the "Lewin paradox".
Good read BTW: http://www.hep.princeton.edu/~mcdonald/examples/lewin.pdf (http://www.hep.princeton.edu/~mcdonald/examples/lewin.pdf)
3) Dr. Lewin is right about everything in his videos except his claims about KVL are wrong.
He is wrong in other claim as well  that 1/2 of the (superconductive) loop has no EMF and potential difference voltage drop between points A1 & A2 at the moment of observation is 0V (video: "Kirchhoff's Loop Rule Is For The Birds", @3:40). This assumption is kinda naīve as properly noted by Dr. Kirk McDonald.

In all seriousness... has anyone checked this guy even is actually qualified? Is it just a show? His videos are entertaining but his video on this is absurd junk science. What is scary is the amount of people on here, and youtube, and reddit, who are siding with Mehdi...
I think it's far more alarming that people ridicule the desire to understand and learn, and start talking in "siding with" terms when a younger engineer wants to question a professor and ask for clarification in order to gain and spread understanding, and does it in a completely civil way, with a lot of more thought and actual experiments put into it than what goes to usual lecture question. I would be extremely happy for such wellformed and scientifically sound questioning from someone outside the formal scientific circles.
Even more alarming is that an academic person who has been actually teaching is completely unable to handle this kind of situation, which should be everyday practice when it comes to science and learning.
I think I understand sectokia's rant. Instead of taking this opportunity to show the limitations of Kirchhoff and encourage people to learn Maxwell, people are transforming the discussion into a libel against the old professor.
This kind of attitude, we've got to admit, is disgusting and will only make halfassed engineers of all of us.

He also understands how MaxwellFaraday interacts with reality too rather than just seeing it as an equation.
The equation summarizes reality. That's why you, I and everyone in this forum need to study Maxwell.
Maxwell didn't come up with his equations out of an exercise of math. He collected experimental data from Faraday, Ampere and Gauss, tried to figure out what was going on, i.e., what the REALITY was, and proposed the equations that better describe it.
More important, after he grasped the deep meaning of that REALITY, he could predict, among other amazing things, the existence of something that REALITY was not making so obvious in his time: the propagation of radio waves.
Fifteen or so years later Heinrich Hertz proved with an EXPERIMENT that the equations were right.
When you see people treating Maxwell just "as an equation" it is because they understand the solidity of the theory, have proved its efficacy in practice and have absolute confidence in its predictions.
I don't think anyone here ever said they doubted MaxwellFaraday.
But from what I can see Dr Lewin has absolute confidence in it's predictions, to the point he thinks he can measure the voltage difference at one set of two points, twice (using a CRO) and get two different answers.
Whereas Cyriel Mabilde shows he only reads two different voltages, because of the different fluxes linked in the leads.
Cyriel Mabilde in doing this shows us how we can measure emf properly. Incidentally he does it using a sinusoid instead of a transient to show the sign of the voltage better.
Then Dr Lewin goes on to conclude KVL is for the birds.
This is sensationalist rubbish. KVL is successfully used everyday.
The proof is you can easily apply KVL to his demonstration with predictable experimental results.
The predictable results shows KVL works in this case too. Quite a few people have.

Instead of taking this opportunity to show the limitations of Kirchhoff and encourage people to learn Maxwell, people are transforming the discussion into a libel against the old professor.
Bullshit. sectokia's comment was directed to Mehdi specifically, in a clearly malicious manner; but Mehdi's not responsible for other "people" transforming the discussion into any "libel". He couldn't have been more appropriate, and to the point.

In Cyriel Mabilde's video, he is claiming that Dr. Lewin says "there is no EMF in the wires". He says this is wrong and that his measurements remove all doubt about the existence of EMF in the wires.
To say there is "EMF in the wires" makes no sense. According to Faraday's law, in this case the EMF is the time rate of change of the magnetic flux through a surface. The surface defines the EMF. It is not located at specific points in the path that defines the surface.
When he makes his wedge shaped measurements, he is defining a surface outlined by the wedge. That determines a quantity of magnetic flux through that surface, and that determines an EMF. Obviously the EMF changes when he moves his wedge sides to different positions around the loop, because he is changing the size of the surface. It doesn't mean the EMF is "in the wires".
I think this confusion happens because of the lumped model we use for induced EMF in inductors and transformers. You have to stick a voltage source that represents the EMF somewhere in series with the wires. You can stick it anywhere that makes sense. We get so used to this model that we think that the EMF is "in the wires" of the inductor or "in the turns" of the transformer. In fact it is just a model to give us the right voltage at the terminals of the transformer, and is not an actual voltage source in series with the wires in a specific location.
That being said, I think his video is a nice demonstration of Faraday's law and this particular setup. It shows the effect of different measurement path choices and explains things fairly clearly.

but Mehdi's not responsible for other "people" transforming the discussion into any "libel".
Thank you for admitting that people are really turning the discussion into a libel against Lewin instead of realizing the limitations of Kirchhoff or being encouraged to learn Maxwell.
Admitting the problem is the first step to the solution.

But I think it's worth watching if you are interested and have half an hour to kill.
This was excellent. Thanks rfeecs, I feel like now I understand everything and the earth is one more time not flat.

To say there is "EMF in the wires" makes no sense. According to Faraday's law, in this case the EMF is the time rate of change of the magnetic flux through a surface. The surface defines the EMF. It is not located at specific points in the path that defines the surface.
Wait... So you say that there is no EMF induced in the straight wire which is located in the changing magnetic field and only complete/closed loop results in EMF?

To say there is "EMF in the wires" makes no sense. According to Faraday's law, in this case the EMF is the time rate of change of the magnetic flux through a surface. The surface defines the EMF. It is not located at specific points in the path that defines the surface.
Wait... So you say that there is no EMF induced in the straight wire which is located in the changing magnetic field and only complete/closed loop results in EMF?
I'm saying this is Faraday's law:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=579944;image)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=579950;image)
The right hand side of the equation is the EMF. It is defined by a surface bounded by a closed contour. The closed contour doesn't have to be a wire. It can be any closed contour.
For the EMF to do work, you need a circuit. So that forms a closed contour. A straight wire by itself is not a closed contour. You can't say it results in an EMF all by itself, or that it contains an EMF.
So what can you say about a straight wire that is located in a changing magnetic field? There will be a defined charge distribution in the wire. There may even be current in the wire as the charge moves back and forth. There will be an electric field around the wire, induced by the magnetic field. The current in the wire may induce it's own magnetic field. You can say lots of things, but not that it contains an EMF.
You can connect a meter across the ends of the wire. Now you may measure a voltage and call that an EMF. Because you created a closed contour with the wires of the meter.

To say there is "EMF in the wires" makes no sense. According to Faraday's law, in this case the EMF is the time rate of change of the magnetic flux through a surface. The surface defines the EMF. It is not located at specific points in the path that defines the surface.
Wait... So you say that there is no EMF induced in the straight wire which is located in the changing magnetic field and only complete/closed loop results in EMF?
That's exactly right.
And this is something Mehdi gets wrong when he measures the emf across the loop with the gap in it. By closing the gap with the meter probes only now does the emf exist.
Those is not just a theoretical thing. It is verifiable. If there was an emf there would be a static build up at each end of the wire that you could measure the e field of. But there isn't. It only becomes measurable when you close the loop. If you close it with a resistor there is a static build up on either side of it that you can measure.

Those is not just a theoretical thing. It is verifiable. If there was an emf there would be a static build up at each end of the wire that you could measure the e field of. But there isn't. It only becomes measurable when you close the loop. If you close it with a resistor there is a static build up on either side of it that you can measure.
I think the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end.

Those is not just a theoretical thing. It is verifiable. If there was an emf there would be a static build up at each end of the wire that you could measure the e field of. But there isn't. It only becomes measurable when you close the loop. If you close it with a resistor there is a static build up on either side of it that you can measure.
I think the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end.
Yes the charges move in a open loop of wire too. Just that they quickly bunch up at the end of the wire, this causes a electric field inside the wire that starts pulling the changes back into a equalized state. At some point the force put on the changes by the magnetic field balances out with the force from the electric field and the charges stop moving. This means the electric field is equal to the magnetic EMF. So there is indeed a electric field inside the wire (Happens even on a superconducting wire), but you can't directly use Faradays law to calculate it as it requires a loop. You have to calculate it using more fundamental math of applying forces to electrons (Faradays law is mostly an application of that fundamental math in a more useful form). It all depends on how you think about voltage. Yes there are more bunched up electrons on one end of the wire and if you generated a few kV of EMF you would even have the electrons fly off into the air and ionise it, but there is also an opposing magnetic EMF present. So if you add up all forms of EMF (electric and magnetic) you indeed get 0V. Electrons feel both types of EMF so the formal definition of voltage across the ends of the wire is 0V. However if you connect the two ends using a wire that travels in such a way that it generates no magnetic EMF you will get current flow proportional to the electric field of those bunched up electrons. This wire would close the loop in such a way that Faradays law would calculate a EMF voltage equal to the voltage of the electric field the bunched up electrons created.
So yes the open piece of wire does push electrons much like a open circuit battery would, but due to the definition of voltage its still 0V because the magnetic EMF is included.
The way definitions are set up we get confusing things when dealing with open loops of wire, but that's kinda okay since a open loop of wire can't do anything useful, it needs to be connected to something on the ends to do something meaningful and at that point the loop got closed anyway.

I think the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end.
And which end will have a plus and which will have a minus?
Imagine your AB segment in a uniformly distributed timevarying B field. It is all the same, spatially.
Which end will get the plus, and which end will get the minus?
Can't decide?
Well, let's create a square loop with AB as its side. Use the right hand rule to find out how the current will flow with that flux varying configuration. Now you can tell me which extreme of AB is plus and which is minus, correct?
Except...
That it all depends which 'side of the loop' AB is on.
Think of two square clocks with a common AB side. Is the seconds hand going up or down? Does it depends on which clock the hand belongs to?

With a strong enough (variable) magnetic field and/or enough loops, you should (in theory) be able to light a LED (for example, to say something) even with the ends of the loop open, simply because there's charge being pushed/moving along into the wire and that's what a current is.

For those that are disappointed to not see Kirrhhoffs laws be broken here is a way to break them.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580238;image)
This is the schematic of the experiment for it. We have a AC signal source that powers a circuit of two resistors. Circuit analysis tells us this is essentially a 50% restive divider. So we expect the blue voltmeter to always read half of what the yellow voltmeter is showing.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580244;image)
Here is the test setup. Voltmeters are again represented by an oscilloscope. The RF signal generator (set to +10dBm) is out of the shot, but you can see the coax cable coming in from it. The red coiled up wire is a 1m crocodile clip lead to serve as the 1m monopole antenna.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580250;image)
Here is the closeup of the test circuit. It is built using SMD resistors to provide better behavior at RF frequencies while trace lengths are kept to a minimum. Active scope probes ( 0.6pF loading) are used to probe the circuit without drastically affecting it. Additionally a 6dB attenuator is used before the signal enters the board to prevent standing wave issues in the long coax cable to the RF synthesizer.
Antenna disconected
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580256;image)
This is what we get once we turn it on.
Acording to cirucit analysis we should be getting
504mV / 2 = 252mV
We measure 259mV so an error of 2.8% .This is well within reason given resistor, probe and scope tolerances.
Antenna connected
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580262;image)
So now we connect the antenna to the midpoint between the resistors and let it hang over the edge of the table so that it is far away from objects it could potentially capacitively couple to. Other end is not connected to anything and is floating in mid air.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580268;image)
This results in the flowing image on the scope. The overall loading caused the input signal to sag a bit so we need to recalculate it:
470mV / 2 = 235mV
We measured it to be 150mV this is an error of 57%. This is certainly not inside a reasonable margin of error! Clearly the currents in the two resistor can't be identical if the voltages across them are so different. Well the solution is easy, the missing current is simply flowing into the antenna.
Okay, but where is that current returning? The antenna has only one connection. All currents flow in loops, so where does this loop return the current back?
The frequency of 76MHz was not just randomly picked. The calculated quarter wavelength for a 1m long monopole is 71MHz. But mine ended up measuring to be 76MHz due to the way its bent, its insulation, evnivorment... etc. This means that 1m piece of wire is very good at radiating energy out as radio waves for that particular frequency. Its sucking energy out of our circuit to be able to do so.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580274;image)
But what if this is just capacitive loading from the wire dragging down the signal? Well capacitors always create a phase shift. If you look at the previous screenshot you can see the two signals are still perfectly in phase with each other. So to prove this is not the case we leave the wire connected to change the frequency to 152MHz. This is double the frequency before and as a result turns out quarter wavelength of wire into a half wavelength of wire. This makes it very difficult for the wire to radiate the energy because all of it is simply bouncing back into it.
So we do the math again for the expected result:
472mV / 2 = 236mV
And we measured it to be 233mV so an error of 1.3%. This is once again well within our margin of error. So the circuit is again acting like circuit analysis tells us. This proves that capacitive loading of the wire was not at fault here. But because it no longer was able to radiate out energy as radio waves means it was no longer stealing energy out of the circuit so it was allowed to operate as usual.
Conclusion:
Kirchhoffs laws indeed stop working when your circuit starts to emit radio waves. This is very difficult to model and is very frequency dependent. This is not caused by parasitic inductance and capacitance so the circuit model can't be fixed by simply adding those in.
This is the reason why a lot of literature states that Kirchhoffs laws only work in low frequency AC circuits. The low frequency here is considered to be one witch has a wavelength significantly shorter than the circuits physical size. This prevents parts of the circuit becoming antennas and radiating away energy. This is a known limitation of his law.
So are you happy now all of you that want to see Kirchhoffs being wrong?

I think the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end.
And which end will have a plus and which will have a minus?
Imagine your AB segment in a uniformly distributed timevarying B field. It is all the same, spatially.
Which end will get the plus, and which end will get the minus?
Can't decide?
Well, let's create a square loop with AB as its side. Use the right hand rule to find out how the current will flow with that flux varying configuration. Now you can tell me which extreme of AB is plus and which is minus, correct?
Except...
That it all depends which 'side of the loop' AB is on.
Think of two square clocks with a common AB side. Is the seconds hand going up or down? Does it depends on which clock the hand belongs to?
Sure you can decide. You follow the usual rules of direction with magnetic fields.
(http://hyperphysics.phyastr.gsu.edu/hbase/magnetic/imgmag/genwir.gif)
This example shows the wire moving trough the magnetic field, but you can just as well keep the wire stationary and move the magnetic field instead.
So i see no issue with determining what end is positive, its the one that has current is flowing towards it.

I think the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end.
And which end will have a plus and which will have a minus?
Imagine your AB segment in a uniformly distributed timevarying B field. It is all the same, spatially.
Which end will get the plus, and which end will get the minus?
Can't decide?
Well, let's create a square loop with AB as its side. Use the right hand rule to find out how the current will flow with that flux varying configuration. Now you can tell me which extreme of AB is plus and which is minus, correct?
Except...
That it all depends which 'side of the loop' AB is on.
Think of two square clocks with a common AB side. Is the seconds hand going up or down? Does it depends on which clock the hand belongs to?
Sure you can decide. You follow the usual rules of direction with magnetic fields.
And you are the one who does not shift goalposts, eh?
There is no motional emf in Lewin's circuit.
In your example, the velocity of the moving bar is breaking the symmetry.
Please answer the question:
How do you decide which extreme of the bar has the plus and which has the minus when your bar is STATIONARY with respect to a SPATIALLY UNIFORM but TIMEVARYING B field?
Are you capable of answering THIS question without changing the problem?
This example shows the wire moving trough the magnetic field, but you can just as well keep the wire stationary and move the magnetic field instead.
Not the same problem. Please answer the question above.
Example, if I ask
"What it 9 divided by 4"
you should not answer
"9 divide by 3 is 3".
How do you decide which side is plus and which is minus in the case of a bar, stationary with a spatially uniform, timevarying magnetic field?
Same question applies to GeorgeoftheJungle, of course. He too did not answer.
EDIT: As for the antenna example, of course that breaks KVL as well, but we are trying to keep things simple here. So our circuit is in the domain of quasistatic electrodynamics, where the d/dt of the field is so small that the concatenation of B and E fields dies off in a very short distance. We are in fact disregarding the displacement current in AmpereMaxwell's equation. So, no radiation.
EDIT: removed emoticon.

And you are the one who does not shift goalposts, eh?
There is no motional emf in Lewin's circuit.
In your example, the velocity of the moving bar is breaking the symmetry.
Please answer the question:
How do you decide which extreme of the bar has the plus and which has the minus when your bar is STATIONARY with respect to a SPATIALLY UNIFORM but TIMEVARYING B field?
Are you capable of answering THIS question without changing the problem?
Sorry, my mistake there. I forgot about the uniform varying field in the original question.
In this case you can simply apply the left hand rule to determine the positive end. Align your thumb with the field and the fingers show the direction of current.
The only case where this is problematic is when a wire is straight since we can't determine if a straight line is bending towards the clockwise or counter clockwise direction. But such a straight wire would not generate any EMF so it doesn't have a direction.
If you prefer to solve this with Faradays law you can also just connect the ends of the wire with a straight line in this case. That straight line will not generate any EMF but will close the loop so that you can take an integral of the field going trough its surface area, so whatever the result of Faradays law is the EMF of that wire segment.(This only works in a uniform field tho as otherwise you can get EMF on a straight wire)
EDIT: Made a mistake here on how open loops work, see this thread for explanation: https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1993139/#msg1993139 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1993139/#msg1993139)
EDIT: As for the antenna example, of course that breaks KVL as well, but we are trying to keep things simple here. So our circuit is in the domain of quasistatic electrodynamics, where the d/dt of the field is so small that the concatenation of B and E fields dies off in a very short distance. We are in fact disregarding the displacement current in AmpereMaxwell's equation. So, no radiation.
I do agree it is a more complex example and is more difficult to reproduce, but it does show a case of something that you can't properly model using lumped circuit meshes. Because you can't produce a lumped circuit that also means you can't use Kirchhoffs laws.
Dr. Lewins example can be easily modeled accurately using lumped circuit meshes. Once you have a lumped circuit you can apply Kirchhoffs laws and they work perfectly fine.
So i suppose RF engineers can indeed say "Kirchhoffs law is for the birds", most other engineers, not so much.

How do you decide which side is plus and which is minus in the case of a bar, stationary with a spatially uniform, timevarying magnetic field?
Same question applies to GeorgeoftheJungle, of course. He too did not answer.
A varying magnetic field pushes q in one direction, that's how you know where q is going to move to. Berni has even drawn it for you. What am I missing?

How do you decide which side is plus and which is minus in the case of a bar, stationary with a spatially uniform, timevarying magnetic field?
Same question applies to GeorgeoftheJungle, of course. He too did not answer.
A varying magnetic field pushes q in one direction, that's how you know where q is going to move to. Berni has even drawn it for you. What am I missing?
Yes but that picture is not very helpful for a varying uniform field. When you have a varying non uniform field you get induction in that straight piece of wire because the field lines appear to be moving in relation to the wire.
When you have a varying uniform field its only the magnitude of the field that changes, the actual field lines stay in the same place. This field will try to push electrons in a circle around the field lines. This can be imagined as every field line trying to get electrons to circle around it at the same time. On a straight wire this makes the electron get pulled in both directions simultaneously since some field lines are on one side and some on the other side of the wire. Once you put a bend in the wire this makes the electrons easier to move in the direction the wire is bending. So as a result the fields on the outside of the bend are mostly pushing the electrons into the side of the wire while the fields on the inside of the curve are pushing electrons more along the direction of the wire. This makes the fields on the inside of the bend win out and start moving electrons along the wire according to the left hand rule.
Sorry if this explanation is not very scientific but i think it makes the concept easier to grasp.
EDIT: Made a mistake here on how open loops work, see this thread for explanation: https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1993139/#msg1993139 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1993139/#msg1993139)

How do you decide which side is plus and which is minus in the case of a bar, stationary with a spatially uniform, timevarying magnetic field?
Same question applies to GeorgeoftheJungle, of course. He too did not answer.
A varying magnetic field pushes q in one direction, that's how you know where q is going to move to. Berni has even drawn it for you. What am I missing?
Yes but that picture is not very helpful for a varying uniform field. When you have a varying non uniform field you get induction in that straight piece of wire because the field lines appear to be moving in relation to the wire.
When you have a varying uniform field its only the magnitude of the field that changes, the actual field lines stay in the same place. This field will try to push electrons in a circle around the field lines. This can be imagined as every field line trying to get electrons to circle around it at the same time. On a straight wire this makes the electron get pulled in both directions simultaneously since some field lines are on one side and some on the other side of the wire. Once you put a bend in the wire this makes the electrons easier to move in the direction the wire is bending. So as a result the fields on the outside of the bend are mostly pushing the electrons into the side of the wire while the fields on the inside of the curve are pushing electrons more along the direction of the wire. This makes the fields on the inside of the bend win out and start moving electrons along the wire according to the left hand rule.
Sorry if this explanation is not very scientific but i think it makes the concept easier to grasp.
Oh, ok, (I think) I get it. Thanks!
When I said "the charge moves in the wire even if it's not a closed loop, if you could measure it you'd see a + q in one end and a minus q in the other end" I was thinking in ElectroBooms' setup @ 9m13s: youtu.be/0TTEFF0D8SA?t=9m13s

You do realize you are making up rules on the fly, do you?
So, let me get this straight (pun intended).
Let's consider a square loop, with AB side perfectly straight. According to your model, there is no 'partial emf' on that side, right? And if you bend it a bit, the sign of the 'partial emf' will change according to the curvature of that side?
Or, let's just consider an AB segment alone: according to your rule: when it is straight there is no charge build up, but if it is bent in one way the charges are + on A and  on B, while if it is bent the other way the charges are  on A and + on B, correct?
Man, am I glad I do not live in the same universe as you. Looks pretty much more complicated than the universe I am in.
Its not the curvature itself that causes voltage, but the overall trend the wire is taking. A square is still bending around to form a loop that creates the usual direction. An example that seams to go both ways is a S shaped line. If you connect the ends of it you get a clockwise and counterclockwise loop so the surface area integrates to zero if both are symmetrical. If you did connect the ends you would also get zero current due to the area being zero. Electrons in the positive side of the S curve can't magically know about the ones in the negative side and not move because of it. The path the wire takes causes fields on the inside of the curves overall trend to overlap causing one side of the wire to start having more effect than the other.
I will admit i don't fully understand the underlying magic that determines why things move in the specific directions inside fields but the overall effects this causes seam to point towards this.
I would love to live in a simpler universe but magnetic and electric effects are linked trough the effects of Einsteins relativity and that stuff does all sorts of weird things.
KVL breaks in the case of radiation, correct. But it also breaks in the case of induction.
It worked just fine for me in the case of Dr. Lewins experiment so do we perhaps need a different experiment to show it not working with induction?
So for the case of open loops still producing charge separation i propose the flowing experiment:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580757;image)
We break a loop by putting a capacitor in series with it. This capacitor can be formed by two metal plates just like the symbol so there is a real air gap between the ends of the wire. No electrons can jump the gap between the plates. The capacitor requires a change in voltage to push electrons onto the plate and off the other plate in order to create the illusion of current flowing trough it.
So what would happen in this circuit when the uniform magnetic field is suddenly turned on?
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=580763;image)
But one could argue that that's just a small gap so we could just ignore it. So lets take it a step further and introduce a 2nd capacitor on the other side to completely cut the loop in half.
Can the 2 completely separated segments of wire generate a voltage on the capacitor to get the current flowing?
By the way this example is also possible to build as a real life experiment. There is even a way to measure the current in this loop without actually connecting any test equipment to the loop. Circuit analysis tells us that this is a LC circuit, if it indeed is one it will hold on to the pulse of energy and use it to oscillate back and forth, generating an AC magnetic field around the loop even after we remove the original field. We can measure this field as proof of current in the loop.

Its not the curvature itself that causes voltage, but the overall trend the wire is taking. A square is still bending around to form a loop that creates the usual direction.
It looks like you are trying to say you can define emf only if you can identify an area to associate to it.
Well, that's progress. That's what Faraday has tried to tell you since the nineteenth century.
I will admit i don't fully understand the underlying magic that determines why things move in the specific directions inside fields but the overall effects this causes seam to point towards this.
Yes, it points towards an area, encircled by a closed (possibly fictional, in the sense it does not have to be all inside real conductors) loop.
As the formula stating Faraday's law has always said.
I would love to live in a simpler universe but magnetic and electric effects are linked trough the effects of Einsteins relativity and that stuff does all sorts of weird things.
Correct, but not as weird as you think.
I suggest to brush up your physics on some good book, like Purcell (Electricity and Magnetism, second volume of the Berkeley physics series), and then look up the practical applications of the basic concepts in books like Ramo, Whinnery, VanDuzer (Fields and Waves in Communication Electronics).
As for the further goalpost shifting at the end of your post, please... Leave caps out  we are trying to keep things simple here. If we are having trouble understanding each other with a simple circuit like that, what do you think would happen if you introduce another paradox generating element, like the two caps back to back?
And no, KVL did not work with Lewin's circuit. You had to introduce that magical emf term to make your numbers check. That's Faraday at work. In fact, you cannot locate that voltage anywhere with a voltmeter, can you? I am talking about that circuit, do not try to modify it. Let down those scissors, I tell you!!!
EDIT: Repetitia juvant.
What happens if we pull the resistors out of the loop and make sure we cannot interfere with the flux that is generating the emf? That we have a series of two resistors and a black box with two terminals. Now you can call that the secondary of a hidden transformer. Now you can located the voltage it 'generates' with a voltmeter. It's right there, at its two terminals! Now you can delude yourself KVL works, and call it, instead of Faraday's Law, "extended KVL" or "modified KVL" or "modern KVL". Lumped circuit theory works, all voltages we can measure are uniquely defined. Now the quarrel "KVL vs Faraday" is just a language barrier.
But when the resistors are inside the loop, say goodbye to lumped circuit theory and uniquely defined voltages. You have to take paths into account.

It looks like you are trying to say you can define emf only if you can identify an area to associate to it.
Well, that's progress. That's what Faraday has tried to tell you since the nineteenth century.
Alright i have to apologies because i did get one detail about voltage in an open loop wrong. Straight wires require a special case to produce no EMF in the field (I will go back and add a note about this in my previous posts)
I finally found an article that explains how voltages in stationary open loops work when exposed to a varying uniform field:
Induced voltage in an open wire by K. Morawetz, M. Gilbert, A. Trupp
www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=581270 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=581270)
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=581273;image)
It is indeed solved by closing the loop using a wire flowing a path that generates no EMF. However such a wire does not directly connect the ends of the open loop wire segment. What is required instead is two straight wires that travel to the geometric origin of the uniform magnetic field. Such straight wires that pass trough or touch the geometric origin point of the field generate no EMF. This was causing problems for me because i did not realize that even ideal uniform fields have a center point. However in the case of a close loop coil the center point becomes irrelevant because it affects the entire loop and averages out by the time you get all the way around. So technically the beloved closed loop is just a special case of a open loop that closes in on itself(Or the open loop being a special case of a closed loop, whatever way around you want to think about it).
So there you do get voltage induced in a open loop of wire (Proven using Maxwell even).
Correct, but not as weird as you think.
I suggest to brush up your physics on some good book, like Purcell (Electricity and Magnetism, second volume of the Berkeley physics series), and then look up the practical applications of the basic concepts in books like Ramo, Whinnery, VanDuzer (Fields and Waves in Communication Electronics).
I do have at least some understanding on all of those areas, just that some i don't know well in to the detail and especially not down into the deep math behind it. Its just not something i deal with on a regular basis. Electronics engineering has so many abstractions in place that there is no need to delve this deep into the fundamental math under it all. Hence why most electronics engineers know about Maxwell and what he did, but they never used his equations on the job. Its just easier and faster to use the derived "easy bake" equations for calculating everything you would need, but if you dig down and dissect a lot of those equations you tend to find some Maxwells equation somewhere in there.
Contrary to popular belief engineers are mostly not math geniuses, they are just really good at looking up the right equation and quickly punching it into a calculator. Its simply the fastest way to get work done on a deadline.
As for the further goalpost shifting at the end of your post, please... Leave caps out  we are trying to keep things simple here. If we are having trouble understanding each other with a simple circuit like that, what do you think would happen if you introduce another paradox generating element, like the two caps back to back?
The capacitor in an inductive loop is just my proposed experiment to show that an open loop can generate a voltage. Circuit analysis is well understood for RLC circuits so we can easily use it to predict the behavior, then actually do the experiment and see if the results match. Capacitors don't create any more of a paradox than inductors. Can you propose a simpler experiment that shows or disproves the presence of voltage in open loops of wire (aka fractional turns)? If the experiment can be done with equipment and materials found in a reasonable electronics lab i will recreate it.
The purpose of this experiment was to show that fractional turns can indeed take part in a circuit and pick up EMF just like complete loops can.
And no, KVL did not work with Lewin's circuit. You had to introduce that magical emf term to make your numbers check. That's Faraday at work. In fact, you cannot locate that voltage anywhere with a voltmeter, can you? I am talking about that circuit, do not try to modify it. Let down those scissors, I tell you!!!
Its not introducing a magical emf out of nowhere.
The cirucit mesh model simply needs to know about the properties of a wire. You do agree that a coil of wire with 100 turns placed across two points in a circuit is modeled using an inductor symbol right? Well these inductors are not closed loops as they have two terminals that connect to other components of a circuit (just like a straight wire).
A straight piece of wire is basically the same thing except with much less inductance since magnetic flux is not being reused multiple times on the same wire by coiling. This website provides a helpful calculator for this: https://www.eeweb.com/tools/wireinductance (https://www.eeweb.com/tools/wireinductance) . Among other things it also provides a calculator for loop inductance that comes useful later(mutual inductance)
If you place two such 100 turn coils in close proximity you can get some of the same magnetic field passing trough both coils. This turns them into coupled inductors where they not only have self inductance, but also something called a mutual inductance (This is essentially a transformer). The value of self and mutual inductance for each is all that is needed to describe the magnetic properties of them. Any number of coils can be added to this magnetically coupled inductor, not just two. The coupled inductor model is the "mathematical adapter" that brings Maxwells equations into a form that fits into circuit analysis theory. Once it fits inside the circuit analysis abstraction all other circuit analysis tools can be applied(Kirchhoff being only one of them). Its sort of like a software API, but with math rather than code. By putting an inductor into the mesh we simply create an instance of the inductor model that deals with magnetic effects for us.
So since a straight piece of wire is simply a inductor with less turns than a coil of wire we can model a piece of wire in the exact same way. Tho due to it having essentially zero turns means the self inductance is pretty low(but NOT zero) while the mutual inductance is likely significantly larger as soon as it forms a larger loop with other components of the circuit that it connects to. This mutual inductance is where the loop inductance is if you connect multiple segments of wire together into a complete loop.
We are still using Maxwells equations and Faradays law deep inside the equation that calculated the inductance value in Henrys. So why is modeling a length of wire as an inductor incorrect? Is using Maxwells equations as part of another equation forbidden?
EDIT: Repetitia juvant.
What happens if we pull the resistors out of the loop and make sure we cannot interfere with the flux that is generating the emf? That we have a series of two resistors and a black box with two terminals. Now you can call that the secondary of a hidden transformer. Now you can located the voltage it 'generates' with a voltmeter. It's right there, at its two terminals! Now you can delude yourself KVL works, and call it, instead of Faraday's Law, "extended KVL" or "modified KVL" or "modern KVL". Lumped circuit theory works, all voltages we can measure are uniquely defined. Now the quarrel "KVL vs Faraday" is just a language barrier.
But when the resistors are inside the loop, say goodbye to lumped circuit theory and uniquely defined voltages. You have to take paths into account.
Yes that is correct, see its not that hard to think in terms of circuit mesh models. You can indeed fix things by adding a black box transformer into the circuit. However Dr. Lewins experiment is about the voltage on points A and B. Once we lump all of the loop inductance into one black box we loose points A and B.
But wait! We can fix that. Instead of lumping all of it into one black box we can just lump each wire segment into its own black box. This way we get 4 such black boxes that are located between the resistors terminals and the points of interest.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=581279;image)
This way points A and B are maintained while each black box is now one of the 4 secondary coils to the solenoid coil creating the original field. They all know about each other trough mutual inductance. If we suddenly also want a point C that's halfway between A and the left resistor we simply cut the black box into two blackboxes with half the inductance value. Point C now pops out as the midpoint between the two new blackboxes. This is why i was trying to explain above that open wire segments can interact with magnetic fields just as much as wire loops can, the black boxes are models of a open wire segment.
As i said KVL is not just a different form of Faradays law. Its is like comparing an apple to a car, they are two completely different things. Faradays law calculates the relationship between voltage and magnetic flux change in loops. Kirchhoffs voltage law just calculates voltage relationships in abstract electrical circuit meshes. It has nothing to do with magnetic or electric fields. Its just a law that is part of circuit analysis methods, those will then call upon Faradays law whenever circuits have to deal with inductance. Circuit analysis wraps Faradays law into the form of an inductor. The process of mesh analysis eventually marries together the equation for an inductor model (That contains Faradays law deep inside it) with Kirchhoffs voltage and current laws to produce a mathematical model of the circuit. Both KVL and Faradays law exists together in that resulting circuit equation, you can't see it in the form that Faradays law is written but if you expand the equations backwards far enough you could eventually get it to pop out Faradays law in textbook form. KVL can't deal with anything other than voltages so it relies on other laws to do it instead. It can't even understand resistance, it needs help from Ohms law to tell it the voltage on a resistor. Because of that we don't say KVL is for the birds because Ohms law handles it better.
So the only thing that Faradays law and KVL have in common is that during circuit analysis KVL makes use of Faradays law to be able to understand magnetic fields. They are great friends even if circuit analysis sometimes demands it to do unusual things such as fractional loop segments(That still work fine, see above). Is it forbidden to plug the results from one law into another law?
Circuit models are not meant to describe the underlying physics, they are about as real as the imaginary part of complex numbers is real. But circuit models use just enough physics to accurately describe the behavior of the circuit on a macroscopic level.

I've modified one of the openEMS examples to try and simulate this experiment numerically via the openEMS FDTD field solver. In the attached image of the geometry, you can see the physical model of the excitation coil with feedline (copper) and resistor, the wire loop (copper), two resistors (100/900 ohms) / voltage/current probe elements, and two infinite resistance voltage probes measuring the voltage on the wire segments on either side of the resistors. The infinite resistance flags openEMS not to add any material properties for these probes (so they are unaffected by the fields and cause no loading). The mesh is something close to 4 million cells which is probably a bit overkill, but wanted to make sure everything got integrated. The simulation is configured to dump the volume of the magnetic field (Hfield) and results in about 12GB of vtr files that you can view as an animation in paraview. The attached matlab file can be used to create the geometry file and run the openEMS simulation.
[edit] removed sim files. I'm an idiot. I'l post a working sim when I have it finished.

I will admit i don't fully understand the underlying magic that determines why things move in the specific directions inside fields but the overall effects this causes seam to point towards this.
I would love to live in a simpler universe but magnetic and electric effects are linked trough the effects of Einsteins relativity and that stuff does all sorts of weird things.
Our brains are not hardwired to admit space being "warped" by any kind of changing field, be it magnetic, electric, gravitational or whatever.
Fortunately our brains are equipped with reason, so we can painstakingly break free from our basic intuitions and build a reasoning that will lead us to new levels of understanding. It takes time and effort, but it's worth the journey.
You might know that Maxwell is a theory that accounts for our four little happy dimensions of the spacetime in which we are immersed. The road to Maxwell starts with calculus, which is nothing more than the mathematical (i.e. formal) study of change. You know, we live in an ever changing universe. So someone had to invent a theory to give us tools to deal with that.
I happen to have a happy little video about calculus.
Calculus For Young Players  BSFEEChannel #2
https://www.youtube.com/watch?v=mT6FGdfeCNo (https://www.youtube.com/watch?v=mT6FGdfeCNo)
That won't make anyone an expert but is going to give viewers an idea of what it is and how to immediately apply it to simple electronic circuits. However, if the viewer got interested in learning more, a good introduction to calculus is the series of 31 lectures given by Professor Richard Delaware at UMKC, which inspired my video above.
https://www.youtube.com/watch?v=CtRAHmeWSC0&list=PL65FC200C611F0E27 (https://www.youtube.com/watch?v=CtRAHmeWSC0&list=PL65FC200C611F0E27)
Then you'll come to vector calculus, also known as vector analysis. This is the theory that will give you tools to deal with change over whatever lines, surfaces, and volumes, because things are not all in the same place at the same time. There is no absolute simultaneity in the universe (blame Einstein). A good start is the book Electromagnetic Waves and Radiating Systems by Edward C. Jordan and Keith G. Balmain. The first chapter is dedicated to introduce you to vector analysis. Interestingly enough, the first section discusses the limitations of circuit theory (i.e. Kirchhoff) without neglecting its importance, while demonstrates why the more complicated field theory (a.k.a Maxwell) is worth the effort.
Now that you upgraded your brain to think fourthdimentionally, you can tackle Maxwell with ease. And that's what that book does when you reach chapter 4.
The cool thing about electromagnetism is that, since the electromagnetic force is 10³⁶ times stronger than gravity, mind boggling things that defy common sense happen right on top of your bench at human scale compared to gravitational phenomena that are only relevant at astronomical scale. This video shows just an example.
https://www.youtube.com/watch?v=sENgdSF8ppA (https://www.youtube.com/watch?v=sENgdSF8ppA)

I do have at least some understanding on all of those areas, just that some i don't know well in to the detail and especially not down into the deep math behind it. Its just not something i deal with on a regular basis. Electronics engineering has so many abstractions in place that there is no need to delve this deep into the fundamental math under it all. Hence why most electronics engineers know about Maxwell and what he did, but they never used his equations on the job. Its just easier and faster to use the derived "easy bake" equations for calculating everything you would need, but if you dig down and dissect a lot of those equations you tend to find some Maxwells equation somewhere in there.
Contrary to popular belief engineers are mostly not math geniuses, they are just really good at looking up the right equation and quickly punching it into a calculator. Its simply the fastest way to get work done on a deadline.
If we engineers deliberately neglect the fundamentals, how can we criticize Lewin who is teaching them?

The explanation video promised by Prof. Walter Lewin.
https://www.youtube.com/watch?v=AQqYs6O2MPw (https://www.youtube.com/watch?v=AQqYs6O2MPw)
I haven't made it all the way through this entire thread yet, but that response video was excellent. I still need to watch his lecture #20. This quick video should clear things up for anyone who watches it though.

If we engineers deliberately neglect the fundamentals, how can we criticize Lewin who is teaching them?
I would not call high level abstraction as negligence. It is common sense. We criticize Dr.Lewin because he neglect fundamentals himself (read "Lewin’s Circuit Paradox" by Dr. Kirk T. McDonald  you'll see). I do not see anybody who is against Maxwell's equations or saying that Kirchhoff's law *always* hold. Those who do not agree (to "KVL for the birds") say that Kirchhoff’s loop equations apply to Lewin’s circuit.

If we engineers deliberately neglect the fundamentals, how can we criticize Lewin who is teaching them?
I would not call high level abstraction as negligence. It is common sense. We criticize Dr.Lewin because he neglect fundamentals himself (read "Lewin’s Circuit Paradox" by Dr. Kirk T. McDonald  you'll see). I do not see anybody who is against Maxwell's equations or saying that Kirchhoff's law *always* hold. Those who do not agree (to "KVL for the birds") say that Kirchhoff’s loop equations apply to Lewin’s circuit.
So, you criticize Lewin because someone else wrote an article criticizing him? Not because you yourself master the fundamentals and is in a position to confront him? What kind of engineers do we want to be? Just a bunch of dilettantes ranting at random in forums? Let's shut up and do our homework. Thank you.

We criticize Dr.Lewin because he neglect fundamentals himself (read "Lewin’s Circuit Paradox" by Dr. Kirk T. McDonald  you'll see). I do not see anybody who is against Maxwell's equations or saying that Kirchhoff's law *always* hold. Those who do not agree (to "KVL for the birds") say that Kirchhoff’s loop equations apply to Lewin’s circuit.
So, you criticize Lewin because someone else wrote an article criticizing him? Not because you yourself master the fundamentals and is in a position to confront him? What kind of engineers do we want to be?
I already provided my position here in this thread. That's why I just refer to article I agree to and do not repeat what is already said. Don't blame me if you did not read thread or do not remember what I did say or whatever.
Just a bunch of dilettantes ranting at random in forums? Let's shut up and do our homework. Thank you.
You better behave

I already provided my position here in this thread. That's why I just refer to article I agree to and do not repeat what is already said. Don't blame me if you did not read thread or do not remember what I did say or whatever.
Yeah, you said it clearly. And I quote.
Those who do not agree (to "KVL for the birds") say that Kirchhoff’s loop equations apply to Lewin’s circuit.
No they don't. Suppose that Kirchhoff didn't know about Faraday's law of induction. I show a loop of wire with two resistors and hide the solenoid under the table. I ask Kirchhoff to measure the voltages with a voltmeter. Kirchhoff wouldn't know how to explain how a loop of wire with two resistors and no voltage source has some voltage on them. Worse, he wouldn't know how to explain why the voltmeter shows diferent voltages depending on the position of the voltmeter.
Kirchhoff wouldn't know how to explain how two pieces of wire hanging out in the breeze (that today we call dipole antenna) suddenly have voltages and currents without no visible voltage source connected to them.
Although Faraday demonstrated the phenomenon of induction in 1831, he couldn't find a mathematical formulation and therefore his theories were rejected by the scientists of the time. Meanwhile in 1845 Kirchhoff came up with his law that do not account for any kind of varying field for that matter. In 1865, Maxwell could finally produce his now famous equations that gave a mathematical formulation to Faraday's law.
Kirchhoff died in october 1887. Hertz published his first paper confirming Maxwell's equations in november 1887.
So there is no paradox in Lewin's explanations. Kirchhoff died absolutely ignorant of the confirmation of Maxwell's theory so that's why his theory doesn't account for that. Period.
So who told you that the loop is a secondary of a transformer? Certainly not Kirchhoff. Because when that theory could finally be confirmed, he was DEAD. End of story.
You better behave
Here's a dollar, kid. Go get yourself a better education.

Kirchhoff died absolutely ignorant of the confirmation of Maxwell's theory so that's why his theory doesn't account for that. Period.
You think that Kirchoff's circuit laws shall explain electromagnetism?  Better save your dollar to get better education yourself, kid:
Here's a dollar, kid. Go get yourself a better education.

Here's a dollar, kid. Go get yourself a better education.
Don't you see how detrimental this attitude is to science and understanding?
IMHO, this is also the actual mistake Lewin is making.
Honest questioning and discussion should be valued.
Not everyone is as strong as a person as you or me or ogden. Not everyone wants to fight. Some may actually get upset about they way Lewin arrogantly attacks their "qualifications" when they just asked honest questions, especially if you are in the role of a student. They won't ask more questions, but instead, do as you teach them to do: close up your desire for understanding, just shut up and "learn". But, just reading isn't the way you learn science. You need to really understand, and for that, asking questions, yes, even questioning your professor  would be the right thing to do.
But I guess we'll disagree on this. And, I think you are genuinely a bad person for not even trying to think about this side of the coin  and the life goes on :).

So, you criticize Lewin because someone else wrote an article criticizing him? Not because you yourself master the fundamentals and is in a position to confront him? What kind of engineers do we want to be? Just a bunch of dilettantes ranting at random in forums? Let's shut up and do our homework. Thank you.
Okay i know there are a lot of opinions in this thread. But i personally was never trying to say that Dr. Lewin is a bad teacher. Id love to have him as my physics teacher when compared to all the teachers i have had. He does a great job of explaining things in a interesting way to help you understand it. I watched some of his other lectures and i enjoyed them.
His statements about KVL is the only part where i get to disagree with him. Nobody is saying Maxwell or Faraday is wrong, nobody is trying to prove them being wrong (You would have one hell of a time trying to do that). It just seams to me that Dr. Lewin has a different idea of what KVL actually is, this is what is leading him to the conclusion of KVL being just a special case of Faradays law with no magnetic field (Its not, you can't even stick an electric field into KVL).
No they don't. Suppose that Kirchhoff didn't know about Faraday's law of induction. I show a loop of wire with two resistors and hide the solenoid under the table. I ask Kirchhoff to measure the voltages with a voltmeter. Kirchhoff wouldn't know how to explain how a loop of wire with two resistors and no voltage source has some voltage on them. Worse, he wouldn't know how to explain why the voltmeter shows diferent voltages depending on the position of the voltmeter.
Kirchhoff wouldn't know how to explain how two pieces of wire hanging out in the breeze (that today we call dipole antenna) suddenly have voltages and currents without no visible voltage source connected to them.
Although Faraday demonstrated the phenomenon of induction in 1831, he couldn't find a mathematical formulation and therefore his theories were rejected by the scientists of the time. Meanwhile in 1845 Kirchhoff came up with his law that do not account for any kind of varying field for that matter. In 1865, Maxwell could finally produce his now famous equations that gave a mathematical formulation to Faraday's law.
Kirchhoff died in october 1887. Hertz published his first paper confirming Maxwell's equations in november 1887.
So there is no paradox in Lewin's explanations. Kirchhoff died absolutely ignorant of the confirmation of Maxwell's theory so that's why his theory doesn't account for that. Period.
So who told you that the loop is a secondary of a transformer? Certainly not Kirchhoff. Because when that theory could finally be confirmed, he was DEAD. End of story.
Kirchhoff indeed did not know about Faraday or Maxwell at the time. He came up with his laws quite a few years before them. He did not understand induction and was not even trying to. He was dealing with circuits of resistors powered by batteries. Science at the time did not understand the underlying principle of how magnetism and electricity interact, but they knew very well that they do interact and experimentally determined a lot of the rules it follows. Its only when Maxwell came around with his equations that they had a concrete mathematical explanation of how the magnetic and electric worlds interact. They knew about induction and loop area and even had equations that can calculate it before that time, but those equations simply came from applying the best fitting equation onto the experimental results. Maxwells equations turned out to fit perfectly in all of those experimentally determined equations so he knew he was onto something big (Its incredibly unlikely this would happen to fit so many equations by chance).
Maxwell didn't go "Hah suck it Faraday, your math is wrong cause mine works so much better". He was instead using the work of Faraday and many other scientists to be able to come up with his equations. He surely went trough a lot of trial and error with mental models and math before he found a set of equations that fit in. Much like other scientist did before him to make other famous equations. Science builds on top of itself.
In science we can't know what is right and what is wrong. But we can use scientific methods to find the theories that seam to fit our universe the best. Every so often a new theory comes up that explains something better and so its adopted as the new best thing. Heck for a long time we didn't even know what atoms and molecules look like, we went trough increasingly better ideas of what they are. Eventually we even figured out that something as fundamental as a electron can be taken apart into even more fundamental building blocks.
Kirchhoffs has many other contributions in other fields, but in the electrical field his contribution is used for circuit analysis, much like Thevenins or Nortons theorem. These things don't deal with electrical and magnetic fields, inches, permeability etc... They ONLY deal with volts and amps flowing trough ideal components. So Maxwells equations don't really have much to do with KVL. Where Maxwells equations touch circuit analysis laws is during circuit modeling. Maxwells equations are used deep down to turn a physical coil of wire into how many Henrys an ideal inductor model should have to act like that coil. After that step circuit analysis uses the inductor model without knowing about Maxwell even tho Maxwells equations are hidden inside that inductance value.

Don't you see how detrimental this attitude is to science and understanding?
Now we're talking.
IMHO, this is also the actual mistake Lewin is making.
Honest questioning and discussion should be valued.
Not everyone is as strong as a person as you or me or ogden. Not everyone wants to fight. Some may actually get upset about they way Lewin arrogantly attacks their "qualifications" when they just asked honest questions, especially if you are in the role of a student. They won't ask more questions, but instead, do as you teach them to do: close up your desire for understanding, just shut up and "learn". But, just reading isn't the way you learn science. You need to really understand, and for that, asking questions, yes, even questioning your professor  would be the right thing to do.
Unfortunately people are not questioning honestly. An honest question requires an open mind to accept the answer.
Lewin, I and numerous others on this forum and perhaps on other places spent time and effort patiently explaining that a lot of phenomena are out of reach of Kirchhoff's theory. We wrote texts, drew sketches, made videos, recommended lectures, books, etc.
What is the reaction? Cool, I didn't know about this, I am going to study?
No. The reaction was variously like I am a "practical" engineer dedicated to "high level abstractions", which is just a wanky name for "I don't know the fundamentals and I don't care" and I want you to come with an explanation that conforms to my limited understanding of physics.
Sorry, but that ain't gonna happen. It's impossible to dumb Maxwell down. You'll have to make room in your head to accept a new idea, a.k.a., learn.
But I guess we'll disagree on this. And, I think you are genuinely a bad person for not even trying to think about this side of the coin  and the life goes on :).
Forum member rfeecs published a link to a video by Cyriel Mabilde, who said he'd prove that Lewin was "wrong". My comment then was polite.
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1987190/#msg1987190 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1987190/#msg1987190)
The fact is that that demonstration is a train wreck. Some of the errors were pointed out by rfeecs himself. Why is that?
At 33:17 Mabilde says: Invoking the theory of path dependency [i.e. Faraday/Maxwell] is not the right answer for explaining these simple measurements.
So he cannot interpret what he is measuring because he rejects the only theory capable of explaining what is going on right in front of his nose. To add insult to injury, his denial goes on: After all, spending more time and energy in a misinterpreted demonstration, I think it is time to tackle more serious problems, problems in this world, that concern all of us, such as the climate, injustice, violence, drugs, war and refugees.
He conveniently forgot to name ignorance as a world problem. Why? Because he chose ignorance. He chose not to learn. He chose to discredit Lewin instead. Because that's the easy path.
His video is a crime against humanity.
Who is being arrogant, after all? Mabilde and all those who recalcitrantly refuse to learn, or Lewin who dedicated an entire life to teaching?
This stubborn attitude is what is getting under our skin.
So don't fool yourself. You're not doing science a favor. If you really love science do as we all do: humbly learn.

It just seams to me that Dr. Lewin has a different idea of what KVL actually is, this is what is leading him to the conclusion of KVL being just a special case of Faradays law with no magnetic field (Its not, you can't even stick an electric field into KVL).
Kirchhoff (KVL) IS a special case of Faraday.
What does Maxwell say? That the EMF along a closed line in space is a function of how the surface integral of a magnetic field across an arbitrary surface bounded by the closed line varies in relation to time.
The magnetic field can vary in intensity and direction. The surface can vary in size, direction and/or shape (including the closed line).
When that surfce integral does not vary with time, EMF is zero. And that coincides exactly with what Kirchhoff said: that the sum of the voltages around a mesh (a closed line) is zero.
In what circumstances does the surface integral equal zero? When the magnetic field AND the surface are constant, for example, among many other cases.
So Kirchhoff ended up being a subset Faraday. I even drew it as a Venn diagram many messages ago in this thread.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=583322;image)

Kirchhoff (KVL) IS a special case of Faraday.
What does Maxwell say? That the EMF along a closed line in space is a function of how the surface integral of a magnetic field across an arbitrary surface bounded by the closed line varies in relation to time.
The magnetic field can vary in intensity and direction. The surface can vary in size, direction and/or shape (including the closed line).
When that surfce integral does not vary with time, EMF is zero. And that coincides exactly with what Kirchhoff said: that the sum of the voltages around a mesh (a closed line) is zero.
In what circumstances does the surface integral equal zero? When the magnetic field AND the surface are constant, for example, among many other cases.
Yes this is what i find to be the issue. Faraday and Kirchhoff are put into the same basket while they describe different things.
Here is a definition of Faradays law:
"The electromotive force induced in a circuit by variation of the magnetic flux through the circuit is proportional to the negative of the time rate of change of the magnetic linkage"
Here is a definition of Kirchhoff voltage law:
"The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero"
So Faradays law only talks about the induced EMF, it does not say anything about other voltages (Like voltage drops on components or batteries pushing voltage). This is very useful because we can use it to calculate the induced EMF. Kirchhoff on the other hand does talk about the voltages summing to zero. Notice that it says "all the voltages" so this implies induced EMF too as that's a voltage inside the loop. Also notice that it says "algebraic sum", this infers that the circuit mentioned afterwards is a circuit mesh model rather than a real circuit. Had it been a real circuit means that he would be using an integral of electric fields around the circuit, rather than just summing together voltages on components.
So if "all the voltages" in Kirchhoff law includes induced EMF voltage then KVL needs to know how big this voltage is. And how do we calculate that? Well we use Faradays law of course.
In a circuit mesh schematic a wire has zero length, zero resistance and zero reactance. These wires are immune to all field effects. Building the two resistor circuit with such wires in the real world results in a circuit that must have a circumference of zero, this means it also must have a loop area of zero, zero area means no induced EMF and KVL works. This however has a problem because Dr. Lewins circuit clearly has a loop area larger than zero so it makes the circuit mesh model act different(You get 0V on both resistors). We fix this by replacing out ideal wires with inductors. This plugs in Faradays law and tells it about how big the loop area is. Now the circuit model does get voltage induced in it and KVL still appears to work.
YES I KNOW that Kirchhoffs voltage law does indeed break in certain special cases, i'm not saying it always works. I know why it breaks in those special cases. But Dr. Lewins experimental circuit is not one of these special cases since i could throw together a equivalent lumped model in 5 minutes, it worked exactly like his experiment first try.
Can you explain in what way is it a special case of Faradays law, if the two laws describe two separate concepts?
So Kirchhoff ended up being a subset Faraday. I even drew it as a Venn diagram many messages ago in this thread.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=583322;image)
That diagram i fully agree with. Kircchhoffs laws are an abstracted application of Maxwells equations and are meant to be only used on lumped circuit meshes.
Dr. Lewin is not applying KVL to a lumped circuit hence why it does not work for him. Works perfectly fine for me when i apply KVL to my lumped equivalent version of his circuit. Is my lumped circuit model wrong in some way? (I always welcome constructive criticism)

I've updated the openEMS FDTD simulation (3D field solver for Maxwell's equations). More turns to the coil, Added PerfectMatchedLayer (8 levels) to the boundary conditions. Added two more voltage probes right next to each other at points approximately 90 degrees around the loop from the resistors. I did some experimentation with a stepped pulse instead of the nice Gaussian, but still working on that.
I really don't see how Kirchhoff's law could possibly be used to analyze something like this (and truly be successful). Not saying that to be controversial, I just don't see how KVL could be useful for much other than static DC analysis and this circuit is definitely not that.
[edit] removed sim files. I'm an idiot. I'll post a good sim when I have it ready.

Are you perhaps using a current source to power the dense coil in the middle?
The parasitic capacitance between the turns and the inductance of the coil are likely forming a parallel LC tank circuit. Parallel tank circuits are easily exited into oscillation by a current source due to the current source providing freedom to the voltage to swing as much as it wants. Similar thing happens if a voltage source step powers a series LC tank.
To test out my theory i replaced the voltage source in my LT Spice model with a current source and assigned the solenoid coil some parasitic capacitance. And yes this does appear to be the case. Try powering the inner coil with a voltage step instead.

I did some experimentation with a stepped pulse instead of the nice Gaussian, but still working on that.
You shall try to make pulse which results in waveforms demonstrated by Dr.Lewin in his SUPER DEMO. Also voltages on resistors (< 1mV) are way too small  does not match those seen in SUPER DEMO.
I really don't see how Kirchhoff's law could possibly be used to analyze something like this (and truly be successful).
Of course! Kirchhoff's law can't be used to analyze electromagnetism :) As your results do not look like those shown by Dr.Lewin, shall I conclude that Maxwell's equations can't be used as well? [kidding] :D

I'll have to work on this more later, but here is some output from an attempt at using a stepped voltage source (vs. Gaussian current source). I will see if there is a way to scale things on the voltages, but I think is pretty standard for excitation pulses to be 1 Volt in these sims. For now, I have just been looking at how one might come to the conclusion that loop voltages add up to zero. I thought maybe there was something special about this configuration. I'm not particularly impressed by the triggered scope captures, but would be nice to see something close to that. This output might come closer to that depending on what point in time / voltage trigger level you look at I guess.
Anyway, I probably have it screwed up. Let me know if somebody knows how to fix this sim up. I have used openEMS for designing UHF microstrip planar BPF filters in the past (that work), so I have confidence in the solver itself.
[edit] I did have it all screwed up. I'll post a better sim when I have it ready.

Yeah the image of those scopes is a bit fuzzy in the video but i got pretty much the same results when recreating the experiment myself:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1987562/#msg1987562 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1987562/#msg1987562)
The purple trace at the bottom is the voltage on the solenoid coil, i was using that as a stable trigger signal.
So you need to apply a similar voltage step response across your solenoid coil (Not just a pulse). Also your time scale appears to be very short in the simulation. The pulse you applied seams to last only a few picoseconds, this gives it a bandwidth of >100GHz and hence why you get funny behavior as you are mostly simulating radio waves traveling around your scene. The whole simulation only lasting what appear to be around half a nanosecond. My experiment had the pulse last 500 microseconds so about 1 000 000 times longer than your simulation time.
I don't have any experience with that EM simulation tool but it does look pretty cool.

So you need to apply a similar voltage step response across your solenoid coil (Not just a pulse).
Right. Lewin uses just positive step. If possible, magnetic core shall be added as well.
I think is pretty standard for excitation pulses to be 1 Volt in these sims.
0dBV for RF PCB simulations is good default choice, but this is solenoid :) We know that EMF of experiment is 0.1V or so.

Yes this is what i find to be the issue. Faraday and Kirchhoff are put into the same basket while they describe different things.
Kirchhoff lives inside Faraday. So, if you put Faraday in a basket, Kirchhoff will be there too. The guy who realized that was Maxwell.
Here is a definition of Faradays law:
"The electromotive force induced in a circuit by variation of the magnetic flux through the circuit is proportional to the negative of the time rate of change of the magnetic linkage"
Here is a definition of Kirchhoff voltage law:
"The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero"
What happens if your EMF is ZERO? Doesn't that ring you a bell? Where did you see ZERO before?
Ahh! KIRCHHOFF! He says that "The algebraic sum of all the voltages around any closed loop in a circuit is equal to ZERO"!!!!!!!
Kirchhoff on the other hand does talk about the voltages summing to zero. Notice that it says "all the voltages" so this implies induced EMF too as that's a voltage inside the loop.
Here is where your problem lies. When Kirchhoff says all the voltages, he is not considering any kind of EMF. In Kirchhoff's wonderful world there is absolutely NO EMF whatsofluxingever!
In a circuit mesh schematic a wire has zero length, zero resistance and zero reactance. These wires are immune to all field effects. Building the two resistor circuit with such wires in the real world results in a circuit that must have a circumference of zero, this means it also must have a loop area of zero, zero area means no induced EMF and KVL works.
Philosophical question: if Kirchhoff only applies to circuits that cannot exist, why do we need his stupid theory?
This however has a problem because Dr. Lewins circuit clearly has a loop area larger than zero so it makes the circuit mesh model act different(You get 0V on both resistors). We fix this by replacing out ideal wires with inductors.
If, however, you have a constant magnetic flux, Kirchhoff holds. So Lewin has no problem with Kirchhoff.
This plugs in Faradays law and tells it about how big the loop area is.
Faraday is not a plugin, it is the chassis. It is the base upon which Kirchhoff stands. There's no Kirchhoff without Faraday.
YES I KNOW that Kirchhoffs voltage law does indeed break in certain special cases, i'm not saying it always works.
Kirchhoff's law breaks MOST of the cases. Faraday is the rule. Kirchhoff is the exception.
Can you explain in what way is it a special case of Faradays law, if the two laws describe two separate concepts?
We've done it several times along this thread.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=583322;image)
That diagram i fully agree with. Kircchhoffs laws are an abstracted application of Maxwells equations and are meant to be only used on lumped circuit meshes.
You do not only have a problem with Kirchhoff, Maxwell and Lewin. You also have a problem with Georg Cantor.
Between you and me. Forget all you know about circuits. Follow the guidelines I published in a previous message. Study calculus, vector analysis and a good book on electromagnetism. You'd be better off than struggling with theories you do not master.

Since the mid20th century, it has been understood that Maxwell's equations are not exact, but a classical limit of the fundamental theory of quantum electrodynamics.
from https://en.wikipedia.org/wiki/Maxwell%27s_equations#Limitations_for_a_theory_of_electromagnetism (https://en.wikipedia.org/wiki/Maxwell%27s_equations#Limitations_for_a_theory_of_electromagnetism)
you might have to fix your Venn diagram.
Does that mean Maxwell "is for the birds"?

When Kirchhoff says all the voltages, he is not considering any kind of EMF.
WTF are you talking about here? ://
If, however, you have a constant magnetic flux, Kirchhoff holds. So Lewin has no problem with Kirchhoff.
Try to wrap discrete time measurement into your head. Levin even uses term "voltage at given time" and demonstrates experiment using oscilloscopes. Obviously "at given time"  during infinitely small time moment of observation, magnetic flux does not change. You just said that in such case Kirchhoff holds. That' it, case closed.

Since the mid20th century, it has been understood that Maxwell's equations are not exact, but a classical limit of the fundamental theory of quantum electrodynamics.
from https://en.wikipedia.org/wiki/Maxwell%27s_equations#Limitations_for_a_theory_of_electromagnetism (https://en.wikipedia.org/wiki/Maxwell%27s_equations#Limitations_for_a_theory_of_electromagnetism)
you might have to fix your Venn diagram.
If we are restricted to classical physics, which is the physics of circuit analysis, that won't be necessary. But if we consider QED, which applies to phenomena at the subatomic scale, that won't change the status of Kirchhoff as being owned by Faraday.
To really understand the limits of Maxwell, you'll have to study quantum mechanics. But do you believe that the people who are lazy enough to study Maxwell will have the cojones to study QM? I doubt it.
Does that mean Maxwell "is for the birds"?
I don't know. Do birds study calculus, vector analyses and electromagnetism?

That depends on the symmetry of the induced field. Let me give you my take on that paper (who appears to be a draft considering there is at least a minor error and a (?) meaning what, exactly? Do you know if this was ever published and where is the definitive version?)
Well, it's interesting but it is nonetheless amazing that to compute the emf on an open path, the area always pops out.
Well this paper is what i could find on the topic freely accessible on the internet. Flowing sources and searching on the topic shows more work on the topic but most of it is locked behind paywalls (The usual thing with scientific publications). I'm not a university student anymore to have access to those for free. Feel free to dig deeper into it if you want.
It makes sense to me that the geometric origin of the field would be important since that's the single point where nothing happens to the magnetic field lines as the flux changes. The integral of an area just happens to be a good way to capture the fact that a combination of two spatial dimensions affect the result. Since both Faradays law and a wire segment require it they both use an area (And besides its both magnetic induction so you expect something similar to happen). Area integrals pop up a lot in electronics just because how useful they are.
But yeah the question weather there is voltage on the open loop of wire depends on how you look at it. The EMF will balance out with the electric field of charge separation so technically the voltage is zero but there are more electrons on one end than the other. Circuit analysis makes use of this concept for making wire segments in the form of inductors.
What happens if your EMF is ZERO? Doesn't that ring you a bell? Where did you see ZERO before?
Ahh! KIRCHHOFF! He says that "The algebraic sum of all the voltages around any closed loop in a circuit is equal to ZERO"!!!!!!!
Kirchhoff on the other hand does talk about the voltages summing to zero. Notice that it says "all the voltages" so this implies induced EMF too as that's a voltage inside the loop.
Here is where your problem lies. When Kirchhoff says all the voltages, he is not considering any kind of EMF. In Kirchhoff's wonderful world there is absolutely NO EMF whatsofluxingever!
In a circuit mesh schematic a wire has zero length, zero resistance and zero reactance. These wires are immune to all field effects. Building the two resistor circuit with such wires in the real world results in a circuit that must have a circumference of zero, this means it also must have a loop area of zero, zero area means no induced EMF and KVL works.
Philosophical question: if Kirchhoff only applies to circuits that cannot exist, why do we need his stupid theory?
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=583322;image)
That diagram i fully agree with. Kircchhoffs laws are an abstracted application of Maxwells equations and are meant to be only used on lumped circuit meshes.
You do not only have a problem with Kirchhoff, Maxwell and Lewin. You also have a problem with Georg Cantor.
Between you and me. Forget all you know about circuits. Follow the guidelines I published in a previous message. Study calculus, vector analysis and a good book on electromagnetism. You'd be better off than struggling with theories you do not master.
Well Faradays law says that with no flux change the induced EMF voltage equals zero. There are other voltages possible in circuits that are not coming from induced EMF, batteries also produce voltage that is NOT induced. So saying that the induced EMF is zero does not automatically mean the sum of all voltages is zero as induced EMF is not the only voltage possible in a circuit
Kirchhoffs laws are a circuit analysis tool, not a law that governs how the universe works. Circuit analysis is just an practical application of physics, while physics is a practical application of mathematics.
Physics has no use for Kirchhoffs law since it doesn't deal with anything physical. Maxwells equations and the things that come from them (like for example Faradays law) are completely sufficient to explain what is going on. Okay we did discover even more fundamental quantum effects a layer deeper than Maxwell explains, but Maxwell still works perfectly on a macroscopic level so that's good enough, we can't say its wrong because of that (Just slightly abstracted that's all)
So then why do we even need Kirchhoffs law anyway if it appears to be useless in physics? Heck why do we even need circuit analysis if physics can already describe anything electrical? Lets just use physics instead!
Well.. we could. The problem is that calculating all of this for a real physical circuit involving only a few components would already result in a LOT of math. Engineers regularly deal with circuits that involve 10 to 1000 components, not just 3, this causes the math complexity to skyrocket and it simply becomes unpractical to calculate. Have a look at how hard EM simulations are on computers. They take a ton of memory and take a significant time to compute even on a modern PC.
Turns out engineers often have to calculate the behavior of circuits as part of there work. When they wonder how a RC low pass filter circuit acts at audio frequencies they simply don't care what happens with magnetic and electric fields around there circuit. To solve this problem the science of circuit analysis was created. This cherry picks the effects from physics that matter and condenses them down into a simpler form of math.
The engineer can now chose if he wants to take in account the magnetic fields or not, rather than it simply being part of the process that must be included for everything to function. Our universe breaks down if you suddenly have magnetic fields disappear, circuit mesh models keep working. If the engineer wants to ignore magnetic effects they simply leave them out and the circuit continues to work as if they are not there. However the circuit now behaves as if it is made out of these mythical ideal wires. In most cases this results in identical circuit behavior. If these effects cause a significant difference in behavior(Such as Dr. Lewins circuit) then the engineer must realize this and chose to add them. In this case this is done by adding an equivalent model of the wire in the form of inductor. The inductor model then calls upon Maxwell to only solve that single wire, this is quick to do because we have generalized easybake equations already prepared from Maxwell.
So KVL only interacts with Faradays law when circuit mesh modeling deems it necessary. Its all just part of a elaborate mathematical shortcut that we call "circuit analysis". Engineers use it to calculate stuff faster and you apply it outside of that there is no grantee it will work. It might still work in special cases outside of circuit meshes but that's just a special case, not intended use.

Physics has no use for Kirchhoffs law since it doesn't deal with anything physical.
Kirchhoff, one of the most important physicists of the 19th century, must be rolling over in his grave.
The problem is that calculating all of this for a real physical circuit involving only a few components would already result in a LOT of math.
You don't get it. You have an impressive equipment on your bench all of it making extensive use of Maxwell and yet you have no clue about the theory used to design it.
In Kirchhoff's world you wouldn't have coaxial cables, ground planes, canned circuits, EMI certification, impedance matching, delay lines, coupling, decoupling, transformers, inductors, motors, generators, radiation, etc., etc., etc.
Kirchhoff is from a time when the only source of electrical energy widely available were batteries. There were no changing fields. No transients. No kind of interference. Only wellbehaved DC circuits. Today, even toys using batteries have SMPSs with inductors and transformers, these specifically making use of Faraday's law.
So you can't escape Maxwell. It's everywhere these days. When we say Kirchhoff, we are in reality saying Maxwell, or Faraday in case of induction, under certain VERY special conditions. But it is still Maxwell.
Don't fool yourself or you'll end up like Cyriel Mabilde: an advocate of ignorance.
So KVL only interacts with Faradays law when circuit mesh modeling deems it necessary.
So you're saying that on your planet the laws of Nature obey the desires of the engineer? I'm moving there right now.

Physics has no use for Kirchhoffs law since it doesn't deal with anything physical.
Kirchhoff, one of the most important physicists of the 19th century, must be rolling over in his grave.
Sorry if i worded that a bit too broadly. I did not mean to include any of Kirchhoffs other laws! Those are indeed very important for physics.
I meant to say that only for Kirchhoffs circuit laws. Maxwells equations can already describe the behavior found in Kirchhoffs cirucit laws, so physics doesn't really need KVL and KCL. In that way i guess i could say that Dr. Lewin could say that KVL is "for the birds"
But for circuit analysis really does need KVL and KCL to work.
The problem is that calculating all of this for a real physical circuit involving only a few components would already result in a LOT of math.
You don't get it. You have an impressive equipment on your bench all of it making extensive use of Maxwell and yet you have no clue about the theory used to design it.
In Kirchhoff's world you wouldn't have coaxial cables, ground planes, canned circuits, EMI certification, impedance matching, delay lines, coupling, decoupling, transformers, inductors, motors, generators, radiation, etc., etc., etc.
Kirchhoff is from a time when the only source of electrical energy widely available were batteries. There were no changing fields. No transients. No kind of interference. Only wellbehaved DC circuits. Today, even toys using batteries have SMPSs with inductors and transformers, these specifically making use of Faraday's law.
So you can't escape Maxwell. It's everywhere these days. When we say Kirchhoff, we are in reality saying Maxwell, or Faraday in case of induction, under certain VERY special conditions. But it is still Maxwell.
Don't fool yourself or you'll end up like Cyriel Mabilde: an advocate of ignorance.
I was never trying to say that Maxwell is useless. I was going among the lines that its rare that you absolutely need to get down and dirty with electric and magnetic fields. Yes Kirchhoff is not going to do much in helping you understand how a coax cable works, but for 99% of use cases i can just think of a coax cable as a delay line with some attenuation and characteristic impedance, wack that into the equivalent circuit model and done.
Why doesn't everyone write software in a hex editor? Its the most fundamental way of doing it after all. Its just simply more practical to work on a higher level with a compiler. Yes you are missing out on some fine details with all these high level language abstractions, but in 99% of cases it doesn't matter and it does get the job done significantly faster.
Not saying one should ignore the underlying physics. One should indeed understand how it works underneath for the sake of the big picture. I was making an example of why circuit analysis is useful in order to justify why one might want to use KVL rather than the more the accurate alternatives (the answer is deadlines). This is my argument for why KVL is not "for the birds"
Im not trying to get away from Maxwell. His equations do an amazing job in explaining how electricity works. Just showing where KVL fits in to it all.
So KVL only interacts with Faradays law when circuit mesh modeling deems it necessary.
So you're saying that on your planet the laws of Nature obey the desires of the engineer? I'm moving there right now.
Nah sadly the same stubborn laws of nature apply to the planet i live on. But in the world of mesh circuits they do indeed obey the desires of the engineer, so far no airline is offering one way trips into that world so i guess we are out of luck. But at least the bent laws help things calculate faster in my real world, the trick is bending them just right so that it acts almost the same as in the real world while only taking 1% of the math to get there. Bending these laws just this right way is the responsibility of the engineer.
Applying KVL without modeling the effects of wires to Dr Lewins experimental circuit is an example of bending the "circuit mesh world" laws too far, creating a circuit that behaves significantly different compared to real life where all the laws apply all the time.

If I believe that in two same points there will be the same voltage ALWAYS (I cut the part with the two identical multimeters) regardless the "path", does it implies I do not undesrtand Mr. Maxwell?
I don't get it. Sorry I am an idiot.

Looking at a circuit theory textbook, "Basic Circuit Theory" by Desoer and Kuh, they devote the first 10 pages of a 900 page book to "Lumped circuits and Kirchoff's laws". They state:
KVL applies to any lumped electric circuit; it does not matter whether the circuit elements are linear, nonlinear, active, passive, timevarying, timeinvariant, etc. In other words, KVL is independent of the nature of the elements.
You can't leave out the word lumped in that statement! They also point out that the entire book only applies to lumped circuits.
Yes, you can make a lumped circuit model for just about anything. You can even model a circuit with an antenna by replacing the antenna with a lumped element that represents it's terminal impedance.
But for this example, why bother? For a circular magnetic flux region, you can easily calculate the electric field. It goes around in circles:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=584825;image)
If you insert the loop of wire with resistors into the electric field loop, you will get a current. Also, the charges in the wire will arrange themselves to cancel the electric field in the wire. (this also would happen to an unconnected segment of wire in the electric field). So the wire has no (tangential) electric field inside it or at it's surface, but it does have a charge distribution.
Some of these papers are just defining the voltage across a section of the wire as the electric scalar potential. This is saying: take the electric field caused by the charge distribution only and integrate it along the path of the wire. Call this the "voltage". Here's another paper by Kirk McDonald where he is doing this:
http://www.hep.princeton.edu/~mcdonald/examples/volt.pdf (http://www.hep.princeton.edu/~mcdonald/examples/volt.pdf)
So they are making up an imaginary voltage that would be created by the charge distribution in the wire. But actually there is no field there, because it is cancelled by the induced electric field. So you can't measure that "voltage" unless you could freeze the charge distribution and place it outside the field. Or if you could form a probing loop that is unaffected by the field, then you could measure the effect of that charge distribution because it would cause a field in your meter. I suppose this is what Cyriel Mabilde is trying to do.

so physics doesn't really need KVL and KCL.
And I thought KVL and KCL were descriptions of physical phenomena. My life is a lie.
Why doesn't everyone write software in a hex editor? Its the most fundamental way of doing it after all. Its just simply more practical to work on a higher level with a compiler. Yes you are missing out on some fine details with all these high level language abstractions, but in 99% of cases it doesn't matter and it does get the job done significantly faster.
Abstraction and neglect of the fundamentals are orthogonal things.
Abstraction means to take away from the designer tasks and routines that are necessary but will not have any kind of influence on the result. So, if you have a menial task to do, you hand it down to a computer, or another person, or company, or the compiler, etc., so that you can concentrate on the specifics of your project. However this doesn't remove from the designer the responsibility to have full mastery of the fundamental concepts of his field.
If abstraction were the same as neglect of the fundamentals, any computer science or software engineering course will be just a class on some stupid "high level" language and nothing more.
I was making an example of why circuit analysis is useful in order to justify why one might want to use KVL rather than the more the accurate alternatives (the answer is deadlines).
So. You have, say, a radar to design. You have a tight deadline. You turn to your colleague and say "Bugger that! Let's use Kirchhoff and go home."
But at least the bent laws help things calculate faster in my real world, the trick is bending them just right so that it acts almost the same as in the real world while only taking 1% of the math to get there.
The math required for the work with Kirchhoff requires a decade or so of learning. You do not learn Kirchhoff in the first grade, do you? If the math required for Kirchhoff were so simple, you wouldn't have spice programs out there to solve them for you.
The basic math required to work with Maxwell requires less than 100 hours of study. And if the equations get really complex, you also have proper software to deal with them.
So, never try anymore to hide your lack of knowledge behind excuses like that. Convince yourself and others of the need to be ready to learn something new every day.

So, never try anymore to hide your lack of knowledge behind excuses like that.
You are troll. Shame on you and respect to Berni.

Abstraction and neglect of the fundamentals are orthogonal things.
Abstraction means to take away from the designer tasks and routines that are necessary but will not have any kind of influence on the result. So, if you have a menial task to do, you hand it down to a computer, or another person, or company, or the compiler, etc., so that you can concentrate on the specifics of your project. However this doesn't remove from the designer the responsibility to have full mastery of the fundamental concepts of his field.
If abstraction were the same as neglect of the fundamentals, any computer science or software engineering course will be just a class on some stupid "high level" language and nothing more.
And this is exactly why KVL is an abstraction of Maxwells equations. It makes things easier while not influencing the result (when used correctly).
Don't worry i seen plenty of programmers that don't understand how a computer works and consider C being too low level. Some even stick to purely interpreted languages like javascript, php or python. I do think they should at least conceptually understand the inner workings of computers. Large software projects are often massive cobbled together messes with chunks of code that nobody understands why they are needed and how they work but if you touch them things break horribly so everyone stays away from them and works around them. Tight deadlines encouraging to just cobble on more rushed code until the project becomes unmaintainable. But that's a topic for another day.
So. You have, say, a radar to design. You have a tight deadline. You turn to your colleague and say "Bugger that! Let's use Kirchhoff and go home."
Actually i was working on some phased array stuff recently and i used even more abstraction than just Kirchhoff.
I was trying to calculate the directionality of a phased array and i wanted to do it fast so that i could later use iterative optimization methods on it. I could have simulated each point in space and its interaction to the neighboring points so that i get a simulation of wave propagation trough the medium. Takes a lot of computation to do and im too lazy to program all of that. Well... instead i just did trigonometry to find the distance to each element and pretended there is an ideal delay line with its delay proportional to the distance. Worked great and it would spit out a directionality graph for all possible angles in the blink of an eye(Without even trying to optimize the code). Is this magical delay line what is actually happening on a phased array? Hell no. Does it act similar enough? For my use case plenty enough.
When the abstraction works i will definitely say "Bugger that!" to the more complicated alternatives. If the abstraction doesn't work then i will go down the long path. I don't work in an academic institution to needlessly waste time obsessing about the underlying mechanisms for cases where they are simply not important.
The math required for the work with Kirchhoff requires a decade or so of learning. You do not learn Kirchhoff in the first grade, do you? If the math required for Kirchhoff were so simple, you wouldn't have spice programs out there to solve them for you.
The basic math required to work with Maxwell requires less than 100 hours of study. And if the equations get really complex, you also have proper software to deal with them.
So, never try anymore to hide your lack of knowledge behind excuses like that. Convince yourself and others of the need to be ready to learn something new every day.
Well i was introduced to Kirchhoffs laws before high school. Then actually had to use them in high school to manually solve circuit meshes. Inside the circuit mesh abstraction its really easy to use.
Maxwell on the other hand i only had it mentioned in high school without really explaining what it is. In university i did get it explained to me why Maxwell is so important, but ultimately never used his equations directly to calculate a real practical example with actual numbers. We dealt with calculating electric and magnetic fields, induced EMF etc... in real examples but it was all with equations that are derived from Maxwell to calculate a certain situation (Such are Faradays law when dealing with induction in a loop).
We heavily used circuit analysis methods in university to manually calculate the behavior of all sorts of circuits. Not only ones with batteries and resistors (We did that in high school) but circuits that involve capacitors, inductors and even semiconductors (dioes, BJTs, FETs, tryristors, diacs etc). Circuit analysis can handle all of this by simply plugging in appropriate models. Try calculating a circuit with transistors using only Maxwells equations, its going to be a major pain.
Heck we even used circuit analysis methods on non electrical things. We used a circuit model to simulate heat propagating trough a wall (thermal conductance being a resistor and thermal mass being a capacitor), to calculate hydraulic flows trough pipe networks, or even turning magnetic circuits into mesh schematics to more easily calculate them. Circuit mesh analysis (and the Kirchhoffs laws used in it) worked great in all these situations. Its all a matter of modeling your circuit correctly. So go ahead and say "Kirchhoffs laws are the plumbers" instead.

Oh and i was to add that with the using schematic circuits to calculate heat flow trough a wall, water flow trough a pipe or magnetic flow trough a core is mostly something that electrical engineers do when they have to deal with something non electrical. Its sort of just swapping out the abstraction layer underneath so they can keep using familiar analysis methods. Im pretty sure other kinds of engineers don't "misuse" schematics for this.
But this trick does show how in nature everything appears to have two intertwined quantities:
Electricity: Volt and Amps
Mechanics: Force and Distance
Rotational mechanics: Torue and RPM
Fluids: Pressure and Flowrate
Magnetics: Magnetic density(H) and Magnetic flux(B)
Thermal: Temperature and Thermal flux
etc...
In all of these cases if you multiply these two intertwined quantities you get power(P) in Watts. Ohms law works for all of these(Tho units are not in ohms anymore) and each of these has a inductor/capacitor equivalent that provides time dependence.
All of these act the same, just use different units because they are different physical things. Because of this cirucit mesh analysis also works on all of these as long as you know how to model it as a schematic. Once its a schematic you can apply KVL and KCL to it just fine and it still works fine, just like all the other circuit analysis tools such as Thenevnins and Nortons theorem. Circuit schematics ware never designed to do this but it just happens to work due to how nature works.
I found this realization of intertwined units quite eye opening back in university. It can help you understand how non electrical things work a lot faster.

And this is exactly why KVL is an abstraction of Maxwells equations. It makes things easier while not influencing the result (when used correctly).
Because in many of your "abstractions" you used KVL instead of Maxwell, you think that KVL is an abstraction of Maxwell. Don't say that anymore.
Saying that means that every time you have a problem solvable by Maxwell, you can immediately apply KVL "used correctly" and that's it.
It implies that you can get away without understanding the underlying phenomena. No, you can't.
That's what Cyriel Mabilde disastrously did. That's what Lewin is desperately trying to warn you about.
Don't worry i seen plenty of programmers that don't understand how a computer works and consider C being too low level. Some even stick to purely interpreted languages like javascript, php or python. I do think they should at least conceptually understand the inner workings of computers. Large software projects are often massive cobbled together messes with chunks of code that nobody understands why they are needed and how they work but if you touch them things break horribly so everyone stays away from them and works around them. Tight deadlines encouraging to just cobble on more rushed code until the project becomes unmaintainable. But that's a topic for another day.
Why you can get away with that in computing? Because those languages, including machine code, are all equivalent in computing power. So you can get a program working without knowing the details under the hood at the expense of a messy code.
Kirchhoff and Maxwell are NOT equivalent. If Kirchhoff and Maxwell were languages, Kirchhoff would describe a machine with LESS computing power than Maxwell.
Actually i was working on some phased array stuff recently and i used even more abstraction than just Kirchhoff.
I was trying to calculate the directionality of a phased array and i wanted to do it fast so that i could later use iterative optimization methods on it. I could have simulated each point in space and its interaction to the neighboring points so that i get a simulation of wave propagation trough the medium. Takes a lot of computation to do and im too lazy to program all of that. Well... instead i just did trigonometry to find the distance to each element and pretended there is an ideal delay line with its delay proportional to the distance. Worked great and it would spit out a directionality graph for all possible angles in the blink of an eye(Without even trying to optimize the code). Is this magical delay line what is actually happening on a phased array? Hell no. Does it act similar enough? For my use case plenty enough.
When the abstraction works i will definitely say "Bugger that!" to the more complicated alternatives. If the abstraction doesn't work then i will go down the long path. I don't work in an academic institution to needlessly waste time obsessing about the underlying mechanisms for cases where they are simply not important.
Again. Who told you that you could reduce the problem to KVL? Kirchhoff? Certainly not. Kirchhoff is a bird. He doesn't know anything about propagation, delay lines, fields, etc.
You had to use MAXWELL, and you did it almost unconsciously, to reduce to problem to Kirchhoff. So you confirm what I said in one of my first messages on this thread about how we engineers are so used to that practice that we forget that we are in fact using Maxwell and implicitly reducing the problem to Kirchhoff.
You can abstract, but you cannot use this as an excuse to ditch the fundamentals. What people are doing is not even trying to study Maxwell, consequently not understanding what the flux is going on and criticizing Lewin for THEIR ignorance.
This is the most stupid educational move I've seen in decades.
Well i was introduced to Kirchhoffs laws before high school. Then actually had to use them in high school to manually solve circuit meshes. Inside the circuit mesh abstraction its really easy to use.
...[snip]
I found this realization of intertwined units quite eye opening back in university. It can help you understand how non electrical things work a lot faster.
TLDR.
Now that I've made you a convert, let's help others to avoid saying stupid things like "Physics has no use for Kirchhoffs law since it doesn't deal with anything physical."
I was almost using that quote as a signature. But then I decided to give you a second chance.

The thing is.
Berni, Electroboom and Cyriel Mabilde know how to measure the voltage in the demonstration circuit.
They all demonstrated it properly.
Clearly bsfeechannel and Dr Lewin don't know how to measure the voltage.
The moment you put voltmeter on as Dr Lewin did, you are measuring a scalar voltage. He did that.
But unfortunately he did it incorrectly and drew the wrong conclusion.
MaxwellFaraday is a model the same as any other. It has limitations, and can be used successfully if it fits within them.
It is not magic. It isn't even particularly complex.
btw bsfeechannel please update your venn diagram to fix your mistake, people will get the wrong idea.

Berni, Electroboom and Cyriel Mabilde know how to measure the voltage in the demonstration circuit.
They all demonstrated it properly.
They have no idea what they're measuring.
Clearly bsfeechannel and Dr Lewin don't know how to measure the voltage.
I have a series of videos where I design and build an isolation transformer. The first video starts with an explanation why a transformer works. It obviously employs Maxwell/Faraday, because transformers are a direct result of Faraday's research. After I understand what to expect, I reduce the problem to Kirchhoff and then I design, build, test and characterize it.
It was a very successful project. The transformer met all the specs and works a treat.
https://www.youtube.com/watch?v=B9OhDcLnGFY&list=PLdj8HcWkeZqf_bG3ve0Fes8lrlKvlAv2 (https://www.youtube.com/watch?v=B9OhDcLnGFY&list=PLdj8HcWkeZqf_bG3ve0Fes8lrlKvlAv2)
The moment you put voltmeter on as Dr Lewin did, you are measuring a scalar voltage. He did that.
But unfortunately he did it incorrectly and drew the wrong conclusion.
Isn't it annoying when Nature does not conform to our preconceived notions of reality?
MaxwellFaraday is a model the same as any other. It has limitations, and can be used successfully if it fits within them.
It is not magic. It isn't even particularly complex.
btw bsfeechannel please update your venn diagram to fix your mistake, people will get the wrong idea.
As I said, I don't need to upgrade anything for circuit analysis. There is no mistake. The theory is sound. When you study it, as I, Lewin, and many others on this forum did, you'll understand it as clear as crystal. If you need any assistance in upgrading your knowledge, we are here to help.

Your venn diagram was wrong because you had Maxwell covering in all other cases.
It's an important point because it glosses over the limitations of modelling natural phenomena.
Dr Lewin seemingly had no idea what he was measuring, I make this judgement because he said it would blow their minds.
It certainly confused people but didn't blow minds.
Isn't it annoying when Nature does not conform to our preconceived notions of reality?
I guess it would be.
If Berni, Electroboom and Cyriel Mabilde got it wrong then let us know what you think voltages are on the loop in Dr Lewins experiment.

But on a brighter note we seem to agree that KVL is at lease useful for characterising transformers.
ps. I would have liked to have watched your video further but the robot voice was hurting me.
Maybe someone on EEBblog could do an English (or other language) voice over?

But on a brighter note we seem to agree that KVL is at lease useful for characterising transformers.
ps. I would have liked to have watched your video further but the robot voice was hurting me.
Maybe someone on EEBblog could do an English (or other language) voice over?
I wrongly thought that since my videos are directed to a technical audience, my viewers would not be bothered by a computergenerated voice. If someone, especially a native speaker of English, could do the voiceover that would be wonderful. It would be a voluntary work, though, since my channel is not monetized. I was mustering the courage to do it myself. But I am not sure how the viewers would react.
Anyway, thanks for watching.

Hey, bsfeechannel, where do you come from?

And this is exactly why KVL is an abstraction of Maxwells equations. It makes things easier while not influencing the result (when used correctly).
Because in many of your "abstractions" you used KVL instead of Maxwell, you think that KVL is an abstraction of Maxwell. Don't say that anymore.
Saying that means that every time you have a problem solvable by Maxwell, you can immediately apply KVL "used correctly" and that's it.
It implies that you can get away without understanding the underlying phenomena. No, you can't.
That's what Cyriel Mabilde disastrously did. That's what Lewin is desperately trying to warn you about.
That's because abstractions also have there limits. So do Maxwells equations when you get down to really small scales where quantum effects take over. You have to know about those limits and simply make sure you don't use that particular abstraction when outside of them.
Why you can get away with that in computing? Because those languages, including machine code, are all equivalent in computing power. So you can get a program working without knowing the details under the hood at the expense of a messy code.
Kirchhoff and Maxwell are NOT equivalent. If Kirchhoff and Maxwell were languages, Kirchhoff would describe a machine with LESS computing power than Maxwell.
In theory yes any truing complete language can do anything.
In practice the capabilities of programing languages vary a lot. Some languages are simply faster to compute a given task, no matter how well you optimize your program (While others complete it with less program code). But there is also certain low level functionality that many languages are simply not capable of. Modern CPUs often have special instructions that most compilers don't know how to use so they don't. There are special locked registers in CPUs that require a sequence of instructions that a lot of high level languages can't reproduce. These special things are usually not something that most programs need to do, but operating systems or hypervisors and such really need it, as they have to do things like set up the MMU, manage execution privilege levels, perform context switching, switch the CPU from 8086 compatibility mode into the full instruction set on boot etc... Normal programs running under a OS also make use of some special features such as JIT compiling where the whole program is basically self modifying code that compiles itself on the fly as it runs by jumping back into the compiler whenever needed. All of this is simply not possible in high level languages like python (Well apart from loading raw binary data into memory and then crashing the program in just the right way that the CPU ends up executing that area by mistake, but that's basically bypassing the language and using a hex editor to program)
This is much how Kirchhoff and Maxwell are NOT equivalent. Kirchhoff can do most things one would normally need to do, but not everything. The things it can do it usually does in a way that is move convenient than the alternative, for the things it can't do then you have no choice but to use the alternative.
Again. Who told you that you could reduce the problem to KVL? Kirchhoff? Certainly not. Kirchhoff is a bird. He doesn't know anything about propagation, delay lines, fields, etc.
You had to use MAXWELL, and you did it almost unconsciously, to reduce to problem to Kirchhoff. So you confirm what I said in one of my first messages on this thread about how we engineers are so used to that practice that we forget that we are in fact using Maxwell and implicitly reducing the problem to Kirchhoff.
You can abstract, but you cannot use this as an excuse to ditch the fundamentals. What people are doing is not even trying to study Maxwell, consequently not understanding what the flux is going on and criticizing Lewin for THEIR ignorance.
This is the most stupid educational move I've seen in decades.
Kirchhoff was not involved in in that phased array. I was making an example why wave propagation doesn't automatically make Maxwell necessary, or even make physics necessary.
I was making use of physics of wave propagation to abstract the problem down to just geometry. Waves traveling in a constant uniform medium always travel at the same speed, this leads to a conclusion that the time delay from the transmitter to the receiver is only a function of distance. With that i can craft simple factor to multiply with in order to translate distance into time delay. With this number in hand i can then predict the waveform this element will receive and feed that on into the phased array beam steering math. No physics involves what so ever, only geometry.
The results it gave matched up with other tools and with experimental results.
You only have to understand enough of the underlying physics to determine what abstraction is appropriate (if any). No need to calculate the whole thing using fundamental physics first. The understanding is more valuable than being able to blindly put numbers into famous equations. Sticking numbers into equations blindly without trying to understand what they are is ignorance. Applying understanding of the subject to form a simpler abstraction to make things easier and faster is instead called "getting stuff done".
TLDR.
Now that I've made you a convert, let's help others to avoid saying stupid things like "Physics has no use for Kirchhoffs law since it doesn't deal with anything physical."
I was almost using that quote as a signature. But then I decided to give you a second chance.
Made me convert to what?
Kirchhoffs cirucit laws still are not some fundamental law of the universe or something. Its just one of the sets of laws that make circuit meshes work. I have yet to see Kirchhoffs laws be wrong when they are used as intended. Its a great abstraction that helps you make sense of physical things.
You have demonstrated in the transformer video how useful the circuit mesh abstraction is. Transformers don't have additional winding that make leakage inductance, they don't have a physical resistor inside them that causes core losses. Yet it acts pretty much like that was the case so that's why the real transformer model uses it. It makes things much simpler to work with while acting close enough. You even use such simplifications before you get to the equivalent circuit model. For example you consider two turns in a coil as simply being 2 times a single turn, while showing segments of wire that go up diagonally to connect the two and a set of wires coming out and then showing a voltage across the two wires without closing them into a loop. I'm not saying its wrong to do this, it makes perfect sense to do it, but for these same reasons is why other people had issues with my lumped model of Dr. Lewins experimental circuit. For some reason i was not allowed to insert inductors into the equivalent model and not allowed to have a voltage on a non closed loop wire segment.
Absolutely nothing wrong in that video (Okay maybe apart from the voice)

For some reason i was not allowed to insert inductors into the equivalent model and not allowed to have a voltage on a non closed loop wire segment.
It's privilege of physics [selfacclaimed] gurus only. As you did not worship Dr.Lewin  you are not worthy to use inductor models.
Absolutely nothing wrong in that video (Okay maybe apart from the voice)
Gloves :D
Hey, bsfeechannel, where do you come from?
My guess would be: Brazil?

Sorry you still don't get it.
The only thing the oscilloscope reads is the voltage at its terminals.
It displays a representation of that scalar voltage.
It doesn't show the voltage at at A and D even though the probes are connected to A and D.
If you want the oscilloscope to read the voltage at A and D you must not add extra flux into the loop.
Cyriel Mabilde demonstrated how to do this.
It is not magic.
It is measurable.
He even knows the value.
I think 15 year olds would understand this better than some older people seem to be able to do.

You have demonstrated in the transformer video how useful the circuit mesh abstraction is. Transformers don't have additional winding that make leakage inductance, they don't have a physical resistor inside them that causes core losses. Yet it acts pretty much like that was the case so that's why the real transformer model uses it. It makes things much simpler to work with while acting close enough.
I had to make a lot of implicit assumptions to REDUCE the model. That is stated in the video. These assumptions were only possible because Maxwell told me what is going on. Kirchhoff can't explain them in any way. For instance, where does the leakage inductance come from? What exactly produces it? How can it be modeled as a lumped component? Why do we have a magnetizing current on the primary even without a load on the secondary. Is that a "parasitic" current? Can we reduce it? If we can, how? How will this affect the other parameters?
While I think about that and derive the calculations to model the device, Kirchhoff sits in the corner like Jack Horner. I only call him to the party in the last minute, when all the components of my model are figured out.
So Kirchhoff is just a fancy interface in the end to hide a complicated mechanism. It serves no purpose in the design of the transformer.
You even use such simplifications before you get to the equivalent circuit model. For example you consider two turns in a coil as simply being 2 times a single turn, while showing segments of wire that go up diagonally to connect the two and a set of wires coming out and then showing a voltage across the two wires without closing them into a loop.
The arrow indicates where you are going to place your voltmeter, and then the loop will be closed. If the diagonal wire bothers you, just rotate the top loop clockwise a little until the connecting wire becomes perpendicular.
For some reason i was not allowed to insert inductors into the equivalent model and not allowed to have a voltage on a non closed loop wire segment.
Because my transformer and Lewin's experiment have a crucial difference. While the transformer has a fixed topology, Lewin's experiment doesn't. And Maxwell showed that topology is everything in electromagnetism.
If you move the voltmeter an isty bitsy tiny little femtometer, it will measure a different voltage. Your voltmeter may not be sensitive enough to catch very small variations, but they will be there. There's simply no right way to measure voltages on Lewin's experiment. It is undefined.
Since Kirchhoff knows nothing about how your circuit is arranged in space, if you want to reduce Lewin's experiment to Kirchhoff you have to define the topology, either explicitly, or implicitly like in the case of a transformer, but once you do that, it will not be Lewin's experiment anymore.
For more details, revisit this post:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1962869/#msg1962869 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1962869/#msg1962869)
Absolutely nothing wrong in that video (Okay maybe apart from the voice)
Thanks.

If Berni, Electroboom and Cyriel Mabilde got it wrong then let us know what you think voltages are on the loop in Dr Lewins experiment.
After all these posts, you still don't get it.
We've been discussing this topic for a month now and, although apparently the vast majority of EEs on this forum understands what is at stake, there are still a few people who think that Mehdi is a hero, Lewin is a charlatan, I am a troll, and Maxwell is just a complicated version of Kirchhoff.
The problem seems to be that Lewin's "Kirchhoff is for the birds" rant is being perceived as an attack on those who learned to rely on Kirchhoff. But Lewin's rant is directed at some of those who TEACH circuit analysis.
What he is exposing is not new. Somewhere on the thread I recommended the book "Electromagnetic Waves and Radiating Systems" by Jordan and Balmain. Its first edition is from 1950. The very first section of the first chapter approaches the problem using very well chosen words and taking care not to offend susceptibilities.
But the issue is the same. Circuit analysis (a.k.a Kirchhoff) is being taught by some as an equivalent theory to Maxwell. Worse than that: it is being taught as a theory based on different postulates, as if Maxwell had nothing to do with Kirchhoff. Worse still: Maxwell is an extension of Kirchhoff for very limited cases where Kirchhoff, surprisingly, doesn't work. Even worse still: Kirchhoff is a series of tricks to solve circuits, it has nothing to do with physics. Maxwell has nothing to do with practical engineering: it is a thing of interest to physicists disconnected from the reality of practical engineering.
All of this is absolutely far from the truth. And the attempts at remedying it are timid.
We must admit that Lewin had a lot of balls to defy the educational establishment and maintain his integrity even after having retired from teaching.

you must not add extra flux into the loop
So, let me ask you again: what is 'extra flux'?
Not sure why you cant understand me.
I mean any non zero net flux that is intercepted by the act of probing the points A and D.
Watch Mabilde he knows how to probe a voltage correctly.
The reason why I call it a voltage and not an emf is because the oscilloscope can only probe voltages.
You do realize you are saying that the reading does not depends on the endpoints only but also on the path?
Yes
So, you are saying Lewin is right.
No
And yet, you still talk about "voltage on the loop" as if it were a property of the loop.
?? I talked about measuring the voltages at A and D but only because I think that is what Dr Lewin is trying to do.
Anyway I think I have said my piece.
Thanks for the discussion all.
ps . I like Dr Lewins lectures. I have only seen a few though.

Nobody here was trying to say that Maxwells equations or Faradays law are wrong or even just an extension of Kirchhoffs laws.
I don't have anything against Dr. Lewin and i think he makes some amazing lectures. Its just his explanation of Kirchhoffs law that i don't agree with. Not that i have some secret love relationship with Kirchhoff, but from my experience with the electronics engineering field i never saw this way of using Kirchhoffs voltage law to be the correct use for it, hence why it does not work in his case.
I had to make a lot of implicit assumptions to REDUCE the model. That is stated in the video. These assumptions were only possible because Maxwell told me what is going on. Kirchhoff can't explain them in any way. For instance, where does the leakage inductance come from? What exactly produces it? How can it be modeled as a lumped component? Why do we have a magnetizing current on the primary even without a load on the secondary. Is that a "parasitic" current? Can we reduce it? If we can, how? How will this affect the other parameters?
While I think about that and derive the calculations to model the device, Kirchhoff sits in the corner like Jack Horner. I only call him to the party in the last minute, when all the components of my model are figured out.
So Kirchhoff is just a fancy interface in the end to hide a complicated mechanism. It serves no purpose in the design of the transformer.
Leakage inductance are simply magnetic field lines that don't pass trough both coils (Including connecting wires to the coils). The field has to be simulated in space to find this inductance computationally since it heavily depends on the coil placement and core design. It behaves like extra uncoupled inductance so can be modeled as a inductor. Magnetizing current is determined by the core properties(or in an abstract way by inductance and frequency). It can be reduced by changing the number of turns or swapping out the core for a higher permeability one. Alternatively the reactive part of this current can be completely removed using a compensation capacitor while the real current can only be reduced using lower resistance coils and lower loss material in the core. It affects other parts of the transformer depending on what you do but in most cases makes the transformer larger and heavier or more expensive to produce(Ferrite core).
All of this is indeed all Maxwell. I never said Maxwell was useless. Just that its not always the best choice if there are simpler alternatives.
Never said that Kirchhoff could do everything. It also can't calculate how many miles per gallon my car can do. Its simply not what Kirchhoff is for. Its only job is to describe how currents and voltages work inside ideal circuit meshes. That's all it does, it doesn't do anything more than that.
The arrow indicates where you are going to place your voltmeter, and then the loop will be closed. If the diagonal wire bothers you, just rotate the top loop clockwise a little until the connecting wire becomes perpendicular.
Yes but the path you take when connecting your voltmeter matters. So the sensible way to connect it is in a way that makes no EMF on the wires, as i have did before. Nothing wrong with that method, yet it was somehow wrong when i used it.
Because my transformer and Lewin's experiment have a crucial difference. While the transformer has a fixed topology, Lewin's experiment doesn't. And Maxwell showed that topology is everything in electromagnetism.
If you move the voltmeter an isty bitsy tiny little femtometer, it will measure a different voltage. Your voltmeter may not be sensitive enough to catch very small variations, but they will be there. There's simply no right way to measure voltages on Lewin's experiment. It is undefined.
Since Kirchhoff knows nothing about how your circuit is arranged in space, if you want to reduce Lewin's experiment to Kirchhoff you have to define the topology, either explicitly, or implicitly like in the case of a transformer, but once you do that, it will not be Lewin's experiment anymore.
For more details, revisit this post:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1962869/#msg1962869 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1962869/#msg1962869)
Lewins experiment had no moving parts, the wires to the resistor and wires to both oscilloscopes remained stationary throughout the experiment.
Maxwell also would need to know the exact femtometer accurate path the wire takes to make an accurate prediction. Such measurements ware not provided so i assumed the wires to run perfectly in the same path as does his math. In my case Maxwell was used to obtain the inductance of the wire segments. After all of it i had a circuit that acts within the margin of error like Dr. Lewins experiment.
I fully agree that there are two voltages over points A and B in Dr. Lewins circuit. The math does work out that way.
I just don't agree in his application of Kirchhoffs law to prove its wrong. It needs a lumped circuit mesh to work right and i was able to turn his circuit into a valid and accurately behaving circuit mesh in 5 minutes where it shows that Kirchhoff indeed works.
So let me ask you then what is the correct use of Kirchhoffs laws?

I just don't agree in his application of Kirchhoffs law to prove its wrong. It needs a lumped circuit mesh to work right
? If you are referring to the mesh shown in "Science and believing..." (or what is the name), you are mistaken.
It might look like a lumped circuit mesh, but it's not. In fact, the emf is not lumped anywhere.
This is why we keep saying he's using Faraday.
and i was able to turn his circuit into a valid and accurately behaving circuit mesh in 5 minutes where it shows that Kirchhoff indeed works.
I will get to the shortcomings of the lumped representation later, but for now, let me ask you: how did you dimension the probe's inductors? Would those values change if the probes' cables were twice as long, and covered a different area?

https://youtu.be/Q9LuVBfwvzA (https://youtu.be/Q9LuVBfwvzA)

Yes that video does indeed clear up a lot of things. Its also worth taking a look at the document that Dr. John W. Belcher wrote on the topic of his videos.
I will get to the shortcomings of the lumped representation later, but for now, let me ask you: how did you dimension the probe's inductors? Would those values change if the probes' cables were twice as long, and covered a different area?
I got it from seeing how his experiment is set up and applied Maxwells concepts to give wire segments a realistic inductance. Since all of these wire segments take the same path 1/4 turn around the circle means they all have to have the same inductance value (All of it being coupled inductance rather than self inductance)
Of course they would change if you move the wires. Its the inductor values that are capturing the physical and magnetic properties of a circuit. So changing the wire paths changes the circuits behavior so its a new different circuit. Update the inductance values to match it and the equivalent lumped circuit will again behave the same as the real one.
You have to put new updated numbers into Maxwells equations too if you change the path, right?

It's sad to hear Dr. Lewin attack Mehdi with the education jab, just so unnecessary.
Mehdi's approach and professional comments on this topic clearly show he is of the highest moral character and only wishes to constructively discuss the topic. A very well done to him.
Anxious to hear Lewin's response to the last video.

It's sad to hear Dr. Lewin attack Mehdi with the education jab, just so unnecessary.
The title of his first video is "Disagreeing with a master". Science has no word of authority. It seems that Mehdi wanted to provoke that kind of reaction and Lewin fell prey beautifully.
If you go to the comment section of Mehdi latest video, the most popular comments are all bashing the octogenarian professor, with hearts conceded by Mehdi. It gives us the impression that that's what Mehdi was after the whole time. But it is just an impression and I may be wrong.
Mehdi's approach and professional comments on this topic clearly show he is of the highest moral character and only wishes to constructively discuss the topic. A very well done to him.
I read Belcher's paper. Nowhere he says KVL always holds or that Lewin is wrong.
He says: In this sense [i.e. not always], KVL holds, as argued by Mehdi Sadaghdar, but one must always remember that the voltage difference across the inductor is defined in a very different way compared to the voltage difference across the other three elements.
What is this different way Belcher refers to? It is described in The Feynman Lectures on Physics Vol II, p22‐2.
Feynman says: Suppose that we have a coil like an inductance except that it has very few turns, so that we may neglect the magnetic field of its own current. This coil, however, sits in a changing magnetic field such as might be produced by a rotating magnet, as sketched in Fig. 225. (We have seen earlier that such a rotating magnetic field can also be produced by a suitable set of coils with alternating currents). Again we must make several simplifying assumptions. The assumptions we will make are all the ones that we described for the case of the inductance. In particular, we assume that the varying magnetic field is restricted to a definite region in the vicinity of the coil and does not appear outside the generator in the space between the terminals.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=587351;image)
It is still true, however, that the line integral of E around a complete loop, including the return from b to a outside the generator, must be zero, because there are no changing magnetic fields.
One thing that Mehdi omits is that Feynman actually derives Kirchhoff's rules (not laws)by the way, Lewin also calls them rules, not lawsfrom Maxwell [Section 223]. And doesn't say anywhere that Kirchhoff always holds. What he says is: With those two rules it is possible to solve for the currents and voltages in any network.
Network of LUMPED elements, i.e., no changing fields outside of the components and this is the abc of Kirchhoff.
Feynman uses the line integral around a circuit just like Lewin does.
Anxious to hear Lewin's response to the last video.
Mehdi is not completely honest with his audience and the literature he recommends doesn't disprove in any way Lewin's experiment.
And that is what is really sad.

I read Belcher's paper. Nowhere he says KVL always holds or that Lewin is wrong.
You can troll twist it as you like, but Belcher says that KVL holds for Lewin's circuit (page 16), at the same time agreeing to Mehdi.

We've been discussing this topic for a month now and, although apparently the vast majority of EEs on this forum understands what is at stake, there are still a few people who think that Mehdi is a hero, Lewin is a charlatan, I am a troll, and Maxwell is just a complicated version of Kirchhoff.
The problem seems to be that Lewin's "Kirchhoff is for the birds" rant is being perceived as an attack on those who learned to rely on Kirchhoff. But Lewin's rant is directed at some of those who TEACH circuit analysis.
I am afraid the problem is deeper than that.
I had a look at Mehdi's latest video (the "conclusion") and the ensuing comments and it's beyond sad. It's scary.
December the third should mark the birth of scientific populism.
And he even links an essay by a professor telling him what the field is inside the conductors! (who's gonna break it to Mabilde, now?)
All he did was to pretend the beef was about what they decided to call KVL. Then showed what it intended with 'extended KVL' and showed that it works (duh!) for lumped circuits. And even Feynman says so!
And when he tries to apply to a nonlumped circuit he tries to locate v/2 on the conductor as if potential difference had a meaning and says... "now that's not wrong but it's a bit misleading...".
"A bit misleading". "Not wrong".
And all the fanboys chanting "lock Lewin up!" (metaphorically speaking  some say he's so old he lost his wits, other point out he has an ego problem, others highlight why he was let go from MIT, others expect this to be called ElectroBoom's law...).
And he linked a document saying "if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires" and showing how the superposition of the coulomb and induced field is such to give (almost) zero field in the conductors and charge accumulation on the resistors (just as Lewin always said).
Science validated by upvoting.
This is worrisome.

Mehdi fought the old professor and lost. But made a video to appear that he won. He can fool his supporters (after all he needs their money), but not those who are experienced and versed in the theory.
Although his comment section is a despicable scene, and he has nothing really to contribute, at least he makes me laugh with his antics.

Science validated by upvoting.
This is worrisome.
Come on. When there's paper with real arguments you suddenly [conveniently] talk about youtube comments??
Prof. Belcher's document (link below) shall be considered as peer review of Lewin's experiment.
Mehdi fought the old professor and lost. But made a video to appear that he won.
You really shall read Prof. Belcher's document which says that Mehdi won his argument.
http://www.electroboom.com/share/FaradaysLaw_Mehdi.pdf (http://www.electroboom.com/share/FaradaysLaw_Mehdi.pdf)

When there's paper with real arguments you talk about youtube comments??
I promised not to interact with you on this matter, but... are you asking me where is the paper stating what I put into quotes in my previous post?
Well, it's Belcher's document.
You really shall read Prof. Belcher's document
Yup. You should indeed.
which says that Mehdi won his argument.
Of course, reading is necessary but not sufficient condition to understand what it says.

I promised not to interact with you on this matter, but... are you asking me where is the paper stating what I put into quotes in my previous post?
Well, it's Belcher's document.
Well, then in case you missed that  same document states "KVL holds, as argued by Mehdi Sadaghdar"

You can not measure two different voltages when you measure in the exact same two points at the exact same point in time.
I will give it a go at explaining the problem but I'm to lazy to draw something so I will rely on my bad English and your capability to reconstruct the proposed experiments in your mind.
1) Imagine a copper loop say it is a ring with a resistance of 1Ohm and an emf of 1V thus creating a round 1A current trough the ring.
Now get an ideal voltmeter and probe two opposite points on the ring so that the ring is exactly split in two equal parts by this two points.
What do you think the reading will be ? It will be 0V.
It will not make any sense to try and probe with two voltmeters there is nothing to be proven with that as they will read the exact same thing.
2) While point 1 should be enough to demonstrate my point let me get another example.
I imagine the same ring but this time half of the ring has 0.9Ohm and the other half has 0.1Ohm. (same 1V / 1A).
Same ideal voltmeter connected at the points where those two half rings intersect will read what ? :)
Answer will be the same as if you have an equivalent circuit with two 0.5V ideal sources one on each half and with a 0.1Ohm series resistor on one side and 0.9Ohm resistor on the other side.
So 400mV (the sign will also be fixed but to keep things simple I did not provided all the info).

You can not measure two different voltages when you measure in the exact same two points at the exact same point in time.
Aaaaand... we're back to square one.
I will give it a go at explaining the problem but I'm to lazy to draw something
Let me guess, you are too lazy to read the other posts in the previous thirteen pages of this thread as well.
<sigh>
Well, then in case you missed that  same document states "KVL holds, as argued by Mehdi Sadaghdar"
Thank you for proving my point about the disjointness of reading and understanding.
Maybe if you read it again you will see that section 11 KVL is about lumped circuits. You too should go back read all past posts.
I'm done talking with walls.

You can not measure two different voltages when you measure in the exact same two points at the exact same point in time.
Aaaaand... we're back to square one.
Please point out what part of my short statement is wrong.
And if that is not wrong then what was the point of that experiment?

You can not measure two different voltages when you measure in the exact same two points at the exact same point in time.
Aaaaand... we're back to square one.
Please point out what part of my short statement is wrong.
And if that is not wrong then what was the point of that experiment?
I do have to agree with Sredini this time.
The problem is that this ideal voltmeter still needs wires to connect to the points of interest on the circle and that's how you can get different voltages depending on what path these wires take, they are as much part of the circuit as the loop itself.
If you take the formal definition of voltage that says that the voltage is the integral of all forces acting on electrons along a path. Then you do get a different number depending on what path do you take trough the loop. By definition there are indeed two possible voltages across the two points. This is because both the electric field of charge separation and the magnetic EMF count towards the total voltage.
Voltmeters only read the charge separation part of the voltage because that's what drives current trough its internal resistance. If you connect the voltmeter with the wires taking such a path that the magnetically induced EMF is zero you get to measure that charge separation and you get the single result you expect (The result is indeed 0.4V). This is the same result that circuit mesh analysis will give (that is called KVL here, but its more than just KVL).
The voltage from charge separation is always defined as a single number for all points in any circuit. Its simply how many electrons are sitting there. More electrons more negative the voltage. Its only the magnetic EMF part of the voltage that depends on what path you take, this is because that EMF is pulling the electrons into a certain direction. This makes electrons motivated to move in that direction even if there is already the same amount of electrons there, but only in that direction.
So to conclude yes there are two voltages across A and B in Dr. Lewins circuit according to the formal definition of voltage, but this is not useful voltage that can be harnessed, its just a incomplete calculation of voltage that requires the rest of the loop to be added in too and that then gives you a single result. In your case that is a single result of voltage across the voltmeter terminals.
These multiple voltage across two points in electrical engineering do sort of the same thing as complex numbers in math. The imaginary part of complex numbers don't really physically exist, but it is there to make the math work out that otherwise wouldn't be possible(Such as square roots of negative numbers). Same goes here with Dr. Lewins example. The voltages are indeed there according to the math, but its not a real voltage you can "physically touch" in the real world. Much like a voltage of 6 V or 5.66+j2 V look the same to a voltmeter but are not the same in the math.
EDIT: Note there are no complex numbers involved in Dr. Lewins example. I was just making a comparison to math. Tho if you want you can still stick complex values of voltage and current into Kirchhoffs circuit laws and it still works(very useful when you have AC sources and reactive components)

I think that regardless of absolute right or wrong Mehdi is to be commended for questioning (politely) an academic of note, creating a reasoned hypothesis of his own, testing and working through his thoughts in a practical manner on a difficult concept in a way to not turn off those not as technically minded. :+
Some of the comments on youtube and the initial ego driven reply from Lewin did nothing to help solve the question. There is scope for rigorous scientific experimental verifiable testing of this to maybe get closer to a resolution, living room maths on a whiteboard and playing on a kitchen bench isn't going to do it.
Musing to myself over a Beer Crazy Beard to with guests of Crazy Hair and Crazy Unibrow at some point in the very distant future on proper measurement and probing techniques would be a fun watch too 8)
https://www.youtube.com/watch?v=2vzvWUqUtb8&t=2282s (https://www.youtube.com/watch?v=2vzvWUqUtb8&t=2282s)

Please point out what part of my short statement is wrong.
And if that is not wrong then what was the point of that experiment?
Allow me to apologize for being so blunt, but I was really disappointed by Electroboom's latest video and the reaction of his fans.
The answer to your question, though, is in the many many posts of this thread. Please, browse through it and you will see that it is indeed possible for two voltmeters whose probes' tips are attached to the very same two points to read different values at the same time. There are also youtube video showing this, if you do not believe it.
The reason is in the different flux intercepted by the two meshes the circuit is partitioned into.
If you are curios, there are thirteen pages awaiting for you.

I do have to agree with Sredini this time.
The problem is that this ideal voltmeter still needs wires to connect to the points of interest on the circle and that's how you can get different voltages depending on what path these wires take, they are as much part of the circuit as the loop itself.
What will be the point of a real voltmeter in this example ? They will need to be added as components to the circuit and will only complicate the demonstration but not change the result if you correctly add them.
If you take the formal definition of voltage that says that the voltage is the integral of all forces acting on electrons along a path. Then you do get a different number depending on what path do you take trough the loop. By definition there are indeed two possible voltages across the two points. This is because both the electric field of charge separation and the magnetic EMF count towards the total voltage.
The result will be the same 0V for first example and 0.4V for the second example and it the second case not just the value will be the same but also the polarity. We are talking about a fixed moment is time and the real voltage not the indication of two real voltmeters that are part of the circuit and inside the magnetic field measuring something else than the real voltage between those two points.
Allow me to apologize for being so blunt, but I was really disappointed by Electroboom's latest video and the reaction of his fans.
The answer to your question, though, is in the many many posts of this thread. Please, browse through it and you will see that it is indeed possible for two voltmeters whose probes' tips are attached to the very same two points to read different values at the same time. There are also youtube video showing this, if you do not believe it.
The reason is in the different flux intercepted by the two meshes the circuit is partitioned into.
If you are curios, there are thirteen pages awaiting for you.
See the replay above made to Berni. I did read most of this tread (about 70%) and seen the a few videos from both sides.
Is not about believing is about real world as we are currently able to understand and in this universe there can be only one voltage at a fix moment in time.
The reason is in the different flux intercepted by the two meshes the circuit is partitioned into.
That is what I was answering above as in you are not measuring the actual voltage at the tip of the probes.
You can even completely remove the ring made of two resistors and keep just the two voltmeter's and you will read something but not what it will be at the tip of those two voltmeters.

Maybe if you read it again you will see that section 11 KVL is about lumped circuits. You too should go back read all past posts.
I thought that this forum agreed about lumped circuit of Dr.Lewin's experiment, yet you woke up. Aaaaand... we're back to square one. To talk about Maxwell's equations make sure you know laws of nature as well. Seems, I am done with this thread disregarding what sofa experts like you say. Your copy/paste skills are not even entertaining anymore. :=\

I think that regardless of absolute right or wrong Mehdi is to be commended for questioning (politely) an academic of note, creating a reasoned hypothesis of his own, testing and working through his thoughts in a practical manner on a difficult concept in a way to not turn off those not as technically minded. :+
Politeness is commendable, but we are engineers. We design serious stuff: buildings, bridges, cars, airplanes, lifesupporting systems, telecommunication systems, power systems.
If we give up our integrity, people die.

I think that regardless of absolute right or wrong Mehdi is to be commended for questioning (politely) an academic of note, creating a reasoned hypothesis of his own, testing and working through his thoughts in a practical manner on a difficult concept in a way to not turn off those not as technically minded. :+
Politeness is commendable, but we are engineers. We design serious stuff: buildings, bridges, cars, airplanes, lifesupporting systems, telecommunication systems, power systems.
If we give up our integrity, people die.
Not maintaining Integrity? Explain please?
I see NO where he didn't maintain his integrity at the highest level which has little or nothing being proven correct or incorrect in the long run. If English is not your first language then best you check the definition of the word. Your attacking of the mans integrity and not debating the technicalities of the subject is out of order!

I think that regardless of absolute right or wrong Mehdi is to be commended for questioning (politely) an academic of note, creating a reasoned hypothesis of his own, testing and working through his thoughts in a practical manner on a difficult concept in a way to not turn off those not as technically minded. :+
Politeness is commendable, but we are engineers. We design serious stuff: buildings, bridges, cars, airplanes, lifesupporting systems, telecommunication systems, power systems.
If we give up our integrity, people die.
Not maintaining Integrity? Explain please?
I see NO where he didn't maintain his integrity at the highest level which has little or nothing being proven correct or incorrect in the long run. If English is not your first language then best you check the definition of the word. Your attacking of the mans integrity and not debating the technicalities of the subject is out of order!
The first thing I did was to analyze his latest video from the technical standpoint. And I've been discussing the technical points of Lewin's experiment from my post #1 in this thread.
I've been an engineer for long enough to know what integrity means and I don't need the English language to tell me that.

Clearly you do need a dictionary and some basic decency and manners. Attacking the integrity of the person and not the ideas as you have just done is what in Australia we would call a c... act amongst others! In particular where the person in question is not here to defend themselves. You clearly can't show where Mehdi has compromised his 'integrity'!
interesting
A quick check shows you have maybe 40 posts in this thread so clearly you have a major bee in your bonnet and in a chunk of those posts you have decided to play the man not the subject. I will leave others to decide what this says about your character.

Please point out what part of my short statement is wrong.
All of it.
Suppose that we have the circuit of the schematic below.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=587654;image)
All the components are lumped, and we only have batteries. The real value of the voltages and resistances are not important. However, to simplify our calculations, let's suppose the two resistors have the same value (it could be any other known proportion). Connected at the same two points in the circuit we have five voltmeters.
We agree that the five voltmeters will measure exactly the same voltage.
Now let's remove the batteries and apply a magnetic field that rises linearly in intensity with time, points towards you and is confined in the total area of the circuit, i.e., A1 + A2 + A3 + A4.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=587660;image)
According to Maxwell, this field will generate a constant EMF that will be proportional to the area enclosed by a circuit and whose polarity will be defined by the corkscrew rule. In short, the topology now counts. To simplify our calculations, let's suppose that the EMF generated by the loop enclosed by all four areas is 1V.
The voltages seen by the voltmeters will now be like that (in volts):
#1
0.5
#2
( A1  ( A2 + A3 + A4 ) ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#3
( ( A1 + A2 )  ( A3 + A4 ) ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#4
( ( A1 + A2 + A3 )  A4 ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#5
+0.5
So, what voltmeter is measuring the "correct" voltage?

Clearly you do need a dictionary and some basic decency and manners. Attacking the integrity of the person and not the ideas as you have just done is what in Australia we would call a c... act amongst others! In particular where the person in question is not here to defend themselves. You clearly can't show where Mehdi has compromised his 'integrity'!
You're young. You need a hero. I'm old. I do not have time for this kind of nonsense.
A quick check shows you have maybe 40 posts in this thread so clearly you have a major bee in your bonnet
I like to contribute. Is that a problem?
and in a chunk of those posts you have decided to play the man not the subject. I will leave others to decide what this says about your character.
I'm not the subject of this thread. Mehdi and his (now debunked) claims are.

All the components are lumped, and we only have batteries. The real value of the voltages and resistances are not important. However, to simplify our calculations, let's suppose the two resistors have the same value (it could be any other known proportion). Connected at the same two points in the circuit we have five voltmeters.
We agree that the five voltmeters will measure exactly the same voltage.
Now let's remove the batteries and apply a magnetic field that rises linearly in intensity with time, points towards you and is confined in the total area of the circuit, i.e., A1 + A2 + A3 + A4.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=587660;image)
According to Maxwell, this field will generate a constant EMF that will be proportional to the area enclosed by a circuit and whose polarity will be defined by the corkscrew rule. In short, the topology now counts. To simplify our calculations, let's suppose that the EMF generated by the loop enclosed by all four areas is 1V.
The voltages seen by the voltmeters will now be like that (in volts):
#1
0.5
#2
( A1  ( A2 + A3 + A4 ) ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#3
( ( A1 + A2 )  ( A3 + A4 ) ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#4
( ( A1 + A2 + A3 )  A4 ) / ( 2 * ( A1 + A2 + A3 + A4 ) )
#5
+0.5
So, what voltmeter is measuring the "correct" voltage?
With your example, you are either claiming that both resistor values in you example are equal in value, or identical current is flowing on each side like a perfect mirror, otherwise the EMF field will be lopsided due to the different load of the resistors.
What I would like to see is having modify the original loop so that it bends inwards to the center at the measurement point, insert a tiny 6 pin sot23 MCU right on a watch battery directly in the middle sampling the voltage at 10msps, not connection anywhere else, and optically feeding out the readings.

With your example, you are either claiming that both resistor values in you example are equal in value, or identical current is flowing on each side like a perfect mirror, otherwise the EMF field will be lopsided due to the different load of the resistors.
What I would like to see is having modify the original loop so that it bends inwards to the center at the measurement point, insert a tiny 6 pin sot23 MCU right on a watch battery directly in the middle sampling the voltage at 10msps, not connection anywhere else, and optically feeding out the readings.
Have a look at this:
http://www.hep.princeton.edu/~mcdonald/examples/lewin.pdf (http://www.hep.princeton.edu/~mcdonald/examples/lewin.pdf)
See equation 17 on page 5.
Here you will get the answer as per doing what you describe above.
There is actually no need for the meter to be 'in the middle' of the magnetic field. Remember its the loop path enclosing the magnetic flux that matters. Thus putting the meter in the middle of the magnetic field and having the probes divide it is no different to the meter being outside the magnetic field and having one probe divide it up the middle, as shown in the link above on page 5 circuit diagram.
In the case of Lewins original circuit you will read 0.4V so long as the area containing the flux is enclosed equally on both sides. As you move the meter from left to right you will read 0.1 to +0.9 simply depending on the ratio of the flux encircled on each side. It really is that simple.

You're young. You need a hero. I'm old. I do not have time for this kind of nonsense.
Seriously Not young at all and yet you decide this based on what? As to 'nonsense' you have time to attack Mehdi's integrity but not tell us where didn't maintain his integrity? Still waiting?
I like to contribute. Is that a problem?
I'm not the subject of this thread. Mehdi and his (now debunked) claims are.
When you descend into criticism of the person or others here you open yourself up to becoming a subject of discussion for your behavior and personal attacks.
And Mehdi's claims are 'debunked' as decided by you? WOW your verbosity and frequency of posting must have made it so awesome work you have me instantly convinced....

With your example, you are either claiming that both resistor values in you example are equal in value, or identical current is flowing on each side like a perfect mirror, otherwise the EMF field will be lopsided due to the different load of the resistors.
EMF has nothing to do with the value of the resistors according to Maxwell, only with the varying field and the geometry of the circuit. If you change the proportion of the resistors, the voltmeters will read different values from what you see above, but they will all show different values among themselves.
In particular, if you choose the make the left resistor nine times greater than the right resistor, you will have the following voltages.
#1
0.9
#2
( A1  9 * ( A2 + A3 + A4 ) ) / ( 10 * ( A1 + A2 + A3 + A4 ) )
#3
( ( A1 + A2 )  9 * ( A3 + A4 ) ) / ( 10 * ( A1 + A2 + A3 + A4 ) )
#4
( ( A1 + A2 + A3 )  9 * A4 ) / ( 10 * ( A1 + A2 + A3 + A4 ) )
#5
+0.1
What I would like to see is having modify the original loop so that it bends inwards to the center at the measurement point, insert a tiny 6 pin sot23 MCU right on a watch battery directly in the middle sampling the voltage at 10msps, not connection anywhere else, and optically feeding out the readings.
So you are suggesting to change the TOPOLOGY of the circuit to measure what you would like to see? What if you can't do that?
What if the wires are in fact the traces of a PCB? Or any other kind of installation where you cannot move them?

Seriously Not young at all and yet you decide this based on what?
You looked young to me.
As to 'nonsense' you have time to attack Mehdi's integrity but not tell us where didn't maintain his integrity? Still waiting?
He tried to pass the impression that professor Belcher endorsed his claims against Lewin's demonstration. He even invoked the "ghost" of Feynman to bless his "honest questioning".
We read the literature Mehdi recommended and found nothing to discredit Lewin. Actually we realized that Lewin employs the same terminology and concepts Feynman uses. And that everything we discussed here that proves that Lewin's demonstration is right is in perfect accordance to what Feynman describes. No wonder. We, Feynman and Lewin studied Maxwell.
The comment section of his videos is full of people making personal attacks against Lewin. This means nothing because Youtube comments mean precisely dick (I don't know what this means but I found the phrase cute).
However, Mehdi congratulates with those who post that kind of comment and even capitalizes on all the brouhaha (Is that an English word?).
The title of his latest video on the subject is absolutely misleading. "Kirchhoff vs. Faraday"? Can we have a "Newton vs. Einstein?" Or perhaps a "Euclid vs. Hilbert"?
So you judge his integrity. You're right. I do not have time for that.
When you descend into criticism of the person or others here you open yourself up to becoming a subject of discussion for your behavior and personal attacks.
Fair enough. Mehdi and his "integrity" are targets, because he decided to target Lewin personally. He cleverly does not do that in his videos, but his comment section betrays him.
And Mehdi's claims are 'debunked' as decided by you?
No. Maxwell.
WOW your verbosity and frequency of posting must have made it so awesome work you have me instantly convinced....
Good to read that.

So, what voltmeter is measuring the "correct" voltage?
Correct voltage in your example assuming those two resistors are equal and circuit is symmetrical (uniform magnetic field from the middle of the circuit) will be 0V same as in my example number 1.
And if you want you can add those voltmeters to the circuit but then they will be part of the circuit. Each will measure a different thing but not the voltage between those two points of interest except for the one in the middle number 3 that could read the correct value of 0V assuming it was shielded since a real voltmeter will likely not be perfectly symmetrical in internal construction.

Each will measure a different thing but not the voltage between those two points of interest except for the one in the middle number 3 that could read the correct value of 0V assuming it was shielded since a real voltmeter will likely not be perfectly symmetrical in internal construction.
Excellent. So let's get rid of the other voltmeters and stick to the voltmeter #3. Let's suppose that its display has seven digits (pretty common on modern bench multimeters) and let's suppose it is properly "shielded", etc.
I hadn't defined the areas, but now let's suppose that their common side is 10cm, and that x+y = 20cm like in the picture below.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=588280;image)
So, V3 = ( ( A1 )  ( A2 ) ) / ( 2 * ( A1 + A2 ) ), x + y = 0.2 m and, since A1 = x * 0.1 and A2 = y * 0.1, and A1 + A2 = 0.02m², we will have that V3 in volts:
V3 = ( ( x * .1 )  ( y * .1) ) / ( 0.04 ) = ( x  y)/0.4
If x = y, then V3 should read 0.000000V.
But now, let's imagine for a moment that this circuit doesn't have the voltmeter and then suddenly someone decides to connect it.
Look what happens if the unfortunate engineer assigned with that task misses the exact point of connection and places the voltmeter 200nm to the right. 200 nanometers. In that case x = 0.1000002 m, and y = 0.0999998 m.
V3 = (0.1000002  0.0999998) / 0.4 = 0.000001 V
So it's affecting the precision of the measurement. It's no biggie in this case because we know what to expect ( 0V). But what if the resistors didn't have exactly the same value? How do I know that this error is not due to a resistor mismatch? Because I could nanometrically place the voltmeter in the "correct" spot, adjusting it so that its voltage read the expected 0.000000V. But what if a mismatch in the value of the resistors is giving me a false reading?

Each will measure a different thing but not the voltage between those two points of interest except for the one in the middle number 3 that could read the correct value of 0V assuming it was shielded since a real voltmeter will likely not be perfectly symmetrical in internal construction.
Excellent. So let's get rid of the other voltmeters and stick to the voltmeter #3. Let's suppose that its display has seven digits (pretty common on modern bench multimeters) and let's suppose it is properly "shielded", etc.
I hadn't defined the areas, but now let's suppose that their common side is 10cm, and that x+y = 20cm like in the picture below.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=588280;image)
So, V3 = ( ( A1 )  ( A2 ) ) / ( 2 * ( A1 + A2 ) ), x + y = 0.2 m and, since A1 = x * 0.1 and A2 = y * 0.1, and A1 + A2 = 0.02m², we will have that V3 in volts:
V3 = ( ( x * .1 )  ( y * .1) ) / ( 0.04 ) = ( x  y)/0.4
If x = y, then V3 should read 0.000000V.
But now, let's imagine for a moment that this circuit doesn't have the voltmeter and then suddenly someone decides to connect it.
Look what happens if the unfortunate engineer assigned with that task misses the exact point of connection and places the voltmeter 200nm to the right. 200 nanometers. In that case x = 0.1000002 m, and y = 0.0999998 m.
V3 = (0.1000002  0.0999998) / 0.4 = 0.000001 V
So it's affecting the precision of the measurement. It's no biggie in this case because we know what to expect ( 0V). But what if the resistors didn't have exactly the same value? How do I know that this error is not due to a resistor mismatch? Because I could nanometrically place the voltmeter in the "correct" spot, adjusting it so that its voltage read the expected 0.000000V. But what if a mismatch in the value of the resistors is giving me a false reading?
I do not disagree with anything you mentioned in you last replay. Correct measurement will read a single value and that is the real 0V no multiple voltages at a single defined point in time.
Of course if you move the measurement point you get a different reading that is normal in any circuit not just this particular case.

Hence why understanding how your probing works is important. Especially when expecting that sort of accuracy from the measurement.
It is why i thought it would be important for Dr. Lewin to explain the path the voltmeter wires take. His experiment only gives these results when the voltmeter wires hug the circuit loop wires tightly. You can get nearly any other voltage you want if you move the voltmeter wires around.
Once you start regularly using oscilloscopes for things >10MHz or with fast changing large currents you encounter all sorts of probing anomalies. Its part of the engineers job to determine if the measurement they did is accurate enough to be useful.
Yes according to the math there are two voltages across A and B, but this is not a voltage that can be used for anything until wires are run to it to connect it to something(Such as a voltmeter). Once that is done the path is defined completely and the resulting voltage is only a single well defined voltage appearing across the voltmeter you connected it to. What sort of EMF the voltmeters wires experience is totally up to you, but usually its most usefully that there is zero EMF because you can then consider the wire as being an ideal connection between two circuit nodes.

Yes according to the math there are two voltages across A and B, but this is not a voltage that can be used for anything until wires are run to it to connect it to something(Such as a voltmeter). Once that is done the path is defined completely and the resulting voltage is only a single well defined voltage appearing across the voltmeter you connected it to. What sort of EMF the voltmeters wires experience is totally up to you, but usually its most usefully that there is zero EMF because you can then consider the wire as being an ideal connection between two circuit nodes.
What is the math for the above example and what will those two different voltages be ? 0V and +0V :)
From my understanding of physics in this universe (going to assume there is no parallel universe with same experiment running at the exact same time) there will always be a single voltage between any two points at a fixed moment in time no mater if there is a measurement device in there or not.

Yes according to the math there are two voltages across A and B, but this is not a voltage that can be used for anything until wires are run to it to connect it to something(Such as a voltmeter). Once that is done the path is defined completely and the resulting voltage is only a single well defined voltage appearing across the voltmeter you connected it to. What sort of EMF the voltmeters wires experience is totally up to you, but usually its most usefully that there is zero EMF because you can then consider the wire as being an ideal connection between two circuit nodes.
What is the math for the above example and what will those two different voltages be ? 0V and +0V :)
From my understanding of physics in this universe (going to assume there is no parallel universe with same experiment running at the exact same time) there will always be a single voltage between any two points at a fixed moment in time no mater if there is a measurement device in there or not.
This is the reason why its so confusing.
First of all this is not a weird quantum mechanics thing like Schrodingers cat thought experiment that the cat is both dead and alive simultaneously until you look at it. Instead it is actually the fault of how voltage is defined in textbooks.
The more common way of thinking about voltage is that more electrons there are in one place the more negative that point is, connect this area with lots of electrons to an area with few electrons and you get current between them as the charges want to even out.
The way voltage is actually formally defined is "An integral of all forces working on charges along a path between two points". These forces include the electric field that bunched together electrons create, but it also includes the magnetic forces pushing electrons around (Any charged particle is affected by a changing magnetic field). This force is dependan't on where you are in the magnetic field. This results in a different result of the integral of the force and hence a different voltage.
In Dr. Lewins example you get the magnetic EMF adding to the resistors voltage if you go around one way, but subtracting from the resistors voltage if you go around the other way. Hence the integral is different and there is different voltage. Its just how the math ends up working out. The actual electron charge density at the points A and B is always a single well defined number. The voltage you measure by connecting a voltmeter as you shown will measure this electron density. Hence why the voltmeter shows one voltage.
The two different voltages result from Dr. Lewins example could be sort of a incomplete result of the voltage so far, you need to include the rest of the circuit to properly define the voltage. Think of the two voltages as sort of like complex number math, they don't necessarily exist in the real world but they make the math work.

This is the reason why its so confusing.
It's made to be confusing as presented by Dr.Lewin and his cultists, but it's not. It confuses only those who can't understand that voltmeter wire can be EMF source. The same "path dependent voltage" mind tricks can be played using other EMF sources like chemical batteries or photovoltaic cells, but those are not so confusing because "such batteries cannot be easily hidden in the wires" :)

This is the reason why its so confusing.
First of all this is not a weird quantum mechanics thing like Schrodingers cat thought experiment that the cat is both dead and alive simultaneously until you look at it. Instead it is actually the fault of how voltage is defined in textbooks.
The more common way of thinking about voltage is that more electrons there are in one place the more negative that point is, connect this area with lots of electrons to an area with few electrons and you get current between them as the charges want to even out.
The way voltage is actually formally defined is "An integral of all forces working on charges along a path between two points". These forces include the electric field that bunched together electrons create, but it also includes the magnetic forces pushing electrons around (Any charged particle is affected by a changing magnetic field). This force is dependan't on where you are in the magnetic field. This results in a different result of the integral of the force and hence a different voltage.
In Dr. Lewins example you get the magnetic EMF adding to the resistors voltage if you go around one way, but subtracting from the resistors voltage if you go around the other way. Hence the integral is different and there is different voltage. Its just how the math ends up working out. The actual electron charge density at the points A and B is always a single well defined number. The voltage you measure by connecting a voltmeter as you shown will measure this electron density. Hence why the voltmeter shows one voltage.
The two different voltages result from Dr. Lewins example could be sort of a incomplete result of the voltage so far, you need to include the rest of the circuit to properly define the voltage. Think of the two voltages as sort of like complex number math, they don't necessarily exist in the real world but they make the math work.
I know it has nothing to to with Schrodingers cat :) but it sounds like that is what you are trying to say.
I asked what those two different voltages are, at a fixed moment in time and I do not see that in your replay.

Ah okay you want to know the voltages. Given that the total EMF is 1V the result is 0.5V on one side and + 0.5V on the other side. This is because wires show up as having no voltage while the resistors show a voltage according to Ohms law. Since the current trough the loop is identical everywhere this means both resistors have to show the same drop (given they are the same value). Sine the current is flowing upwards in one resistor and down the other you get opposite voltage polarity. So you do get two voltages.
To be honest tho such a result is not very useful when you are trying to understand what the circuit does. Dr Lewins math is not wrong about this (Its wrong when it comes to KVL)
The more useful way of analyzing this circuit is using lumped circuit mesh analysis. This is thought in every EE Highschool and gives more useful results. Here all lengths of wire are modeled as coupled inductors. Since we are interested in the voltage at only one point in time we can calculate the voltage using Faradays law and just pretend there is a battery there. With this, the loop on the left and right of the voltmeter get a 0.5V battery (each loop is half of the whole loop). Because the resistors also have a 0.5V drop the result is 0V for both halves and you get the result of the voltmeter reading 0V (Not +0V and 0V, just a single well defined 0V). If you want to connect the voltmeter to other points you have to recalculate the loop areas accordingly.KVL holds just fine here.
In the experiment he just connects the scope with wires in just the right way to expose the two voltages. If you cosider his scope wires as part of the circuit you will get the same result with regular circuit mesh analysis. The two scopes are connected to two different parts of the circuit since each connects via its own wire. The EMF in those wires added up is the exact amount the readings on the two scopes differs. The actual voltage on the two points stays the same (It's the average of the two scopes when probing the middle like that)

I don't know if someone has previously posted this link. Its worth watching.
https://youtu.be/JpVoT101Azg (https://youtu.be/JpVoT101Azg)

I do not disagree with anything you mentioned in you last replay. Correct measurement will read a single value and that is the real 0V no multiple voltages at a single defined point in time.
Of course if you move the measurement point you get a different reading that is normal in any circuit not just this particular case.
Well, in case of the first circuit supplied by batteries with no varying magnetic flux, you agreed with me that all five voltmeters would read the same, i.e. the real position of the voltmeters didn't matter. But let's forget that for the moment.
Because I agree with you that in this particular case, any misplacement of the voltmeter will reflect on the precision of the measuring.
But my question remains unanswered.
How do I know that this imprecision is due to the voltmeter not being exactly in the place it should be, and not due to a resistor mismatch?
You know, resistors change their values, either with temperature, or age, or both, etc.

I don't know if someone has previously posted this link. Its worth watching.
Yes indeed it was posted.
Next time please do read the thread or at least use search.

Ah okay you want to know the voltages. Given that the total EMF is 1V the result is 0.5V on one side and + 0.5V on the other side. This is because wires show up as having no voltage while the resistors show a voltage according to Ohms law. Since the current trough the loop is identical everywhere this means both resistors have to show the same drop (given they are the same value). Sine the current is flowing upwards in one resistor and down the other you get opposite voltage polarity. So you do get two voltages.
You can only read 0.5V and +0.5V if you cut the circuit in half on those two measurement points and then measure each of the half circuits but then that is a completely different circuit and it is no different from a circuit where you have batteries. A real battery has the internal impedance distributed trough the battery is not like there is an ideal source inside and then a separate impedance as it is represented in a diagram.
Wires do have a resistance unless they are supercondutors and my original example specifically had only wires that had a stated resistance was 1Ohm in both examples just that first had a loop made of same type of wire half the ring was 0.5Ohm and the other half 0.5Ohm while the second example had a ring made of two half rings soldered together one with 0.1Ohm and the other with 0.9Ohm resistance.
My examples where meant to get rid of the confusion of having wires and separate resistors but any example will work the same.
Also my example allows you to imagine swiping the virtual voltmeter probes around the ring similar to a potentiometer.
You can use KVL to find out voltage between any two points on those example rings.
If you make an infinitely small cut in any of those two example rings so that there is no current then using the same potentiometer method to measure any two points you will get the same result for both example rings as resistance no longer plays a role.
Well, in case of the first circuit supplied by batteries with no varying magnetic flux, you agreed with me that all five voltmeters would read the same, i.e. the real position of the voltmeters didn't matter. But let's forget that for the moment.
Because I agree with you that in this particular case, any misplacement of the voltmeter will reflect on the precision of the measuring.
But my question remains unanswered.
How do I know that this imprecision is due to the voltmeter not being exactly in the place it should be, and not due to a resistor mismatch?
You know, resistors change their values, either with temperature, or age, or both, etc.
Not sure what sort of point you want to make. The discussion here is that there is only one voltage between the two defined points at a fixed moment in time and that KVL applied correctly will give you the correct result.
Of course real circuits are not perfect and that is why you have tolerances but you add those tolerances in your calculation and your result will have a margin of error proportional with those tolerances.

My examples where meant to get rid of the confusion of having wires and separate resistors but any example will work the same.
[...]
You can use KVL to find out voltage between any two points on those example rings.
Ok, let's take a loop made of two big resistors  physically big  and some copper wire. Let's say the resistors are shaped into an arc spanning 45 degrees. One is 0.1 ohm, the other one is 0.9 ohm. Emf in the loop is 1V.
What is the real and only voltage across the resistors?
What is the real and only voltage across the remaining two portions of wire (say it's copper)?
Edit: added plurals.

Not sure what sort of point you want to make.
I'm just trying to understand what you said in your first post. Of course if you please.
The discussion here is that there is only one voltage between the two defined points at a fixed moment in time and that KVL applied correctly will give you the correct result.
OK. That's exactly what I am discussing too.
Of course real circuits are not perfect and that is why you have tolerances but you add those tolerances in your calculation and your result will have a margin of error proportional with those tolerances.
Fine. So let's suppose now that we don't know the value of the resistors. We don't and we can't know ( for some reason, doesn't matter). The "correct" voltage will obviously be measured when we find the exact right place that in our case demands a nanometric precision.
Let's suppose that the voltmeter now indicates something like 0.437582 V. How can we be sure that this is the correct value? Because now, since the resistances and their relation are unknown, we don't know what to expect. How can we know that we are not a couple of hundreds of nanometers off?

Ok, let's take a loop made of two big resistors  physically big  and some copper wire. Let's say the resistors are shaped into an arc spanning 45 degrees. One is 0.1 ohm, the other one is 0.9 ohm. Emf in the loop is 1V.
What is the real and only voltage across the resistors?
What is the real and only voltage across the remaining two portions of wire (say it's copper)?
The copper wire is also a resistor so you need to provide the resistance of those in order for me to be able to give you the exact answer.
But all you did was split the ring in to 4 equal parts and have 4 resistors two with equal low resistance (the copper wires) and the other two with higher resistance 0.1Ohm and 0.9Ohm
If you assume the wires are made of superconducting material then result is same as in my original experiment 0.4V across the same two opposite points (middle of each copper wire).
In case you measure across the quarter of the ring you will measure say +650mV across the 0.9Ohm resistor and then 150mV across the 0.1Ohm resistor this values will be slightly different if those are not superconductors but copper wires.
The equivalent circuit to make the calculations will be made of 4 voltage sources each equal with 0.25V and each with a series resistance corresponding to whatever that quarter resistance is.
Still there is no point in your slightly more complex example as the voltage on any of the points will be clearly defined and you will never have two different values at a fixed moment in time.

But all you did was split the ring in to 4 equal parts
Not equal (360  2x45 = 270; 270/2 = 135 != 45), but that's immaterial.
and have 4 resistors two with equal low resistance (the copper wires) and the other two with higher resistance 0.1Ohm and 0.9Ohm
Correct. So, let's make the resistors span 90 degrees instead of 45 so we can use your numbers.
you will measure say +650mV across the 0.9Ohm resistor and then 150mV across the 0.1Ohm resistor
The only and true voltage across the 0.9 ohm resistor is .65 V. Ohm would say there's a current of .65/.9 = .72 amps
The only and true voltage across the 0.1 ohm resistor is .15 V. Ohm would say there's a current of .15/.1 = 1.5 amps
Now, .65 + .15 = .80 V. EMF is 1V, I suppose you want to put that into 'modified KVL', so did you bungle the calculation or are you assuming there are 0.20 voltage drop on the copper wires? If we assume 0 resistance that would mean ohm would think there's infinite current.
But let's leave ohm alone for the moment because you might want to put some EMF here and there.
Can you put KVL into a formula with numbers? Please make the (possibly corrected, if required) numbers of all the 'true' voltage drops in the loop and show that KVL balance.

But all you did was split the ring in to 4 equal parts
Not equal (360  2x45 = 270; 270/2 = 135 != 45), but that's immaterial.
and have 4 resistors two with equal low resistance (the copper wires) and the other two with higher resistance 0.1Ohm and 0.9Ohm
Correct. So, let's make the resistors span 90 degrees instead of 45 so we can use your numbers.
you will measure say +650mV across the 0.9Ohm resistor and then 150mV across the 0.1Ohm resistor
The only and true voltage across the 0.9 ohm resistor is .65 V. Ohm would say there's a current of .65/.9 = .72 amps
The only and true voltage across the 0.1 ohm resistor is .15 V. Ohm would say there's a current of .15/.1 = 1.5 amps
Now, .65 + .15 = .80 V. EMF is 1V, I suppose you want to put that into 'modified KVL', so did you bungle the calculation or are you assuming there are 0.20 voltage drop on the copper wires? If we assume 0 resistance that would mean ohm would think there's infinite current.
But let's leave ohm alone for the moment because you might want to put some EMF here and there.
Can you put KVL into a formula with numbers? Please make the (possibly corrected, if required) numbers of all the 'true' voltage drops in the loop and show that KVL balance.
Sorry I confused your 45 degree with 90 degree but I guess that still makes the point you wanted to make.
The formula is very simple each quarter of the ring (90 degree) will see a quarter of that 1V so 0.25V
Thus depending on the direction of the current you have +0.9V across the 0.9Ohm resistor but you subtract 0.25V thus +650mV
On the other side of the ring (again my assumption the other resistor is on the other half) you have 0.1V on the resistor and subtract 0.25V so 150mV
The copper wires are treated the same as the resistors so a 0.25V source and whatever resistance those wires have say is 1mOhm for each quarter segment in series
Then total ring resistance will be 1.002Ohm and thus the current will be smaller 0.998A thus the values calculated before will be slightly influenced by this but not much.
If you disagree with this please provide your numbers and how you got to them.

Mehdi posted a followup video:
Well, thank you for coming with old news (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg2010251/#msg2010251). Thread is "boiling" about it few days already ;) Maybe next time read the thread please?

The formula is very simple each quarter of the ring (90 degree) will see a quarter of that 1V so 0.25V
Thus depending on the direction of the current you have +0.9V across the 0.9Ohm resistor but you subtract 0.25V thus +650mV
On the other side of the ring (again my assumption the other resistor is on the other half) you have 0.1V on the resistor and subtract 0.25V so 150mV
The copper wires are treated the same as the resistors so a 0.25V source and whatever resistance those wires have say is 1mOhm for each quarter segment in series
Ok, so you are Mabildelike.
Hence you believe that the emf is located inside the wire in the form of a distributed voltage generator.
Can we summarize your KVL balance as
net voltage drop across 0.9 ohm + voltage gain across copper + net voltage drop across 0.1 ohm + voltage gain across copper = 0
(0.9 +0.25) + 0.25 + (0.1 + 0.25) + 0.25 = 0
Does that mean that there is an electric field inside the copper conductor? (either perfect or as you wish with 1mohm resistance per arc)?
If you disagree with this please provide your numbers and how you got to them.
I do not believe in a 'true' voltage (actually it's not a belief, the formulas tell me). In this case it all depends on how you measure it  I can get your numbers by suitably partitioning the disk with the probes, or many other values. But I tell you how I can balance Faraday here:
EMF = 1V, total loop resistance 1 ohm, current 1 amp
integral of E dl in 0.9 ohm + integral of E dl in 0.1 ohm + nearly nothing in copper = EMF
0.9 + 0.1 + 0 = 1
(signs come about when you consider the correct conventions)
My ohm's law still work. I had to give up uniqueness of voltage between two points, though.
Most importantly, there is practically no field inside the copper conductor, as predicted by Maxwell's equations.
In your case, well, what is the field inside the copper parts, if you have 0.25 V across each of them?

I do not believe in a 'true' voltage (actually it's not a belief, the formulas tell me). In this case it all depends on how you measure it  I can get your numbers by suitably partitioning the disk with the probes, or many other values. But I tell you how I can balance Faraday here:
EMF = 1V, total loop resistance 1 ohm, current 1 amp
integral of E dl in 0.9 ohm + integral of E dl in 0.1 ohm + nearly nothing in copper = EMF
0.9 + 0.1 + 0 = 1
Right. Summary E field in resistors including wire resistance is equal to EMF of the loop, 1V. You shall not ignore EMF in the big, long resistors or we can even name them segments of resistive wire. This is where you add and subtract 0.25V EMF in them accordingly.
In your case, well, what is the field inside the copper parts, if you have 0.25 V across each of them?
If superconductive, then E field is 0.0V. In this case it is 0.002 V because wire is specified as 0.001 Ohms per segment.
[edit] We don't measure E field or EMF between two points of the circuit. We usually measure potential difference.

If you disagree with this please provide your numbers and how you got to them.
I do not believe in a 'true' voltage (actually it's not a belief, the formulas tell me). In this case it all depends on how you measure it  I can get your numbers by suitably partitioning the disk with the probes, or many other values. But I tell you how I can balance Faraday here:
EMF = 1V, total loop resistance 1 ohm, current 1 amp
integral of E dl in 0.9 ohm + integral of E dl in 0.1 ohm + nearly nothing in copper = EMF
0.9 + 0.1 + 0 = 1
(signs come about when you consider the correct conventions)
My ohm's law still work. I had to give up uniqueness of voltage between two points, though.
Most importantly, there is practically no field inside the copper conductor, as predicted by Maxwell's equations.
In your case, well, what is the field inside the copper parts, if you have 0.25 V across each of them?
So are you saying that voltage across the 0.9Ohm resistor in the current example is 0.9V ? because that sure is not the case unless the resistor has an infinitely small size not a quarter of the ring (90 degree arc).
The copper parts are no different from the resistors as they are basically all resistors so same rule will apply.
You may want to think on what voltages you will read if the ring was open no current.
Maybe think on the same ring (no matter if the resistors are there or not) and you make a small cut (so no current) and insert there the world smallest voltmeter with almost infinite internal impedance. What do you think the reading will be ?
If you guest approximately 1V you will be right. That will be the case even if the ring was all made of superconducting material so how can you explain the measured 1V (assuming you agree).
So across the 0.9Ohm resistor will be 0.650V and not 0.900V and also as important there will be only one voltage there 0.650V and no multiple voltages at the same point in time as implied in the Lewin experiment.
If superconductive, then E field is 0.0V. In this case it is 0.002 V because wire is specified as 0.001 Ohms per segment.
[edit] We don't measure E field or EMF between two points of the circuit. We usually measure potential difference.
Thanks I'm worse on expressing myself :) so your replay is shorter and more to the point.

I'd like to kindly ask the Kirchhoff experts what tools do Kirchhoff rules give me to calculate the "right" voltage of the loop below. Except for the irregular perimeter, all conditions are the same as for my rectangular loop above.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589078;image)
I need to know the exact points where to connect the voltmeter and its precise location. Any reply will be appreciated.

So are you saying that voltage across the 0.9Ohm resistor in the current example is 0.9V ?
If I measure from outside, and without crossing the flux varying region, yes.
Note that I did not use 'voltage drop' but the integral of E.dl in my balance.
because that sure is not the case unless the resistor has an infinitely small size
No, no, that's the case and it is due to the fact that charge accumulate at the resistors end, where there is a gradient in conductivity. This makes the field strong along the resistors, and nearly zero in the copper conductor, just as expected by Maxwell's equations, the equation of continuity and the constitutive relation in the conductor.
Basically, all the EMF falls across the resistors.
It's a matter of charge displacement and the ensuing superposition of field.
If superconductive, then E field is 0.0V. In this case it is 0.002 V because wire is specified as 0.001 Ohms per segment.
[edit] We don't measure E field or EMF between two points of the circuit. We usually measure potential difference.
Thanks I'm worse on expressing myself :) so your replay is shorter and more to the point.
So, you measure electric field in volts?
You need to brush up on basic physics.
Please, humor me and try again: what is the field inside the copper conductor and how do you justify  with formulas  that there is a 0.25 volts drop difference across it?

I'd like to kindly ask the Kirchhoff experts what tools do Kirchhoff rules give me to calculate the "right" voltage of the loop below. Except for the irregular perimeter, all conditions are the same as for my rectangular loop above.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589078;image)
I need to know the exact points where to connect the voltmeter and its precise location. Any reply will be appreciated.
bsfeechannel, you dirty bastard! :DD

So, you measure electric field in volts?
You need to brush up on basic physics.
I did not mention any units at all. You need to check your vision.
Please, humor me and try again: what is the field inside the copper conductor and how do you justify  with formulas  that there is a 0.25 volts drop across it?
You really need to check your vision. I said there is 0.25 volts EMF and 0.002V drop (in 0.002 ohms conductor). Don't you know Ohms law? BTW you did use it yourself to calculate drop across 0.1 and 0.9 Ohms resistors.

So are you saying that voltage across the 0.9Ohm resistor in the current example is 0.9V ?
If I measure from outside, and without crossing the flux varying region, yes.
Note that I did not use 'voltage drop' but the integral of E.dl in my balance.
V = IR  EMF so voltage at the terminals of that resistor is as mentioned 0.650V (for the 0.9Ohm resistor) The EMF will only be zero for a infinitely small resistor and as that is not the case in our example where resistor is a quarter of the loops size thus 0.250V
Same of course apply to a section of copper say 0.001Ohm with 0.001V drop thus voltage measured will be 0.249V
I sort of feel like I deal with trolls and I hope that is not the case.

I sort of feel like I deal with trolls
Me too. What a coincidence :DD

So, you measure electric field in volts?
You need to brush up on basic physics.
I did not mention any units at all. You need to check your vision.
You agreed with ogden, who expressed electric field in volts. You should have read better, before saying that his reply was more to the point.
But, anyway, ok.
I know you specified the emf, but I am asking you about the electric field in the copper.
Sorry I used 'voltage drop', I corrected my self shortly after with 'difference', but you were already answering and quoted my previous sentence.
So, let me ask you again, because this is important:
What is the field inside the copper conductor and how do you justify  with formulas  that there is a (0.250.002) volts difference across it?
Assume standard conductivity for copper, say 5.8 10^7 mhos per meter and a copper section of 1 mm in diameter (or any real world value you can attribute to a circuit similar to those shown by Lewin, Mehdi or Mabilde  it's about 10 cm diameter loop, suppose half of it is allocated by the big resistors, but it's not important).
I am asking for the electric field E inside the conductor  to be more precise, the tangential component that contribute to the integral of E.dl .
I can tell you that in my case it would be in the mV/m range.
What value do you get in your case?

I sort of feel like I deal with trolls and I hope that is not the case.
What are you afraid of? If your claims are sound, you would instantly know the answer for the questions we've posed. Even for the one Sredni found amusing. If you think that that question is out of proportion, think again. That could very well be traces on a PCB or wires on any real installation. If your Kirchhoff only works for perfectly rectangular or round loops, with known resistors within tolerances, it is a useless theory.
And here is one more challenge for your Kirchhoff. You know the drill. We need to know the correct way to measure the correct voltage on this loop. The B field is now concentrated on half of the area, but all other conditions hold. Good luck.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589189;image)

Have you discovered magnetic monopoles? Amazing. ;)

Have you discovered magnetic monopoles?
No.

I am asking for the electric field E inside the conductor  to be more precise, the tangential component that contribute to the integral of E.dl .
I can tell you that in my case it would be in the mV/m range.
What value do you get in your case?
OK I think I understand what part you do not understand so I will try to find a bit of a different example to explain the problem.
Imagine you have a ring (closed loop) made of superconducting material (set flat on a table) and somewhere above it you have a magnet.
As long as magnet and ring are stationary there will be no EMF so of course also no current in that ring.
Now I drop that magnet that will start to accelerate thus there is a change in magnetic field and there will be a current induced inside the ring that will create a field that opposes the magnetic field from the magnet.
This opposing magnetic field will slow down the magnet and in this particular case it will be slowed down to zero thus you will end up with a levitating magnet.
Now what happened is that energy from the falling magnet induced a current in the coil that created an opposing magnetic field and since coil is made of superconducting material there is no IR loss as R=0 so that energy remains conserved (you can even slowly remove the magnet and that current will remain in that ring).
If we repeat the experiment but instead of the superconducting ring we now use a copper conductor but say is fairly think very low resistance the magnet will still slow down but since there is a bit of IR loss magnet will not levitate and fall all the way down until will hit the table or floor.
Now third experiment you can have a copper cor super conductor ring but it will be an open loop so a very small small cut and you can install a voltmeter there but should be with almost infinite impedance.
In this case magnet will not slow down at all (we ignore the air resistance) but voltmeter will read a voltage that is basically the EMF as IR is zero I=0
EMF = Velocity x Bflux x length so if you want to increase EMF you will need to increase the speed in this case you need to apply some additional force to the magnet or drop it from a higher place or increase the length of the loop but then you also need to increase the size of the magnet so Bflux remains the same.
We never mentioned in earlier examples the Bflux or the length of our loop as we had enough other information like we established that current trough the loop was 1A and the loop resistance was 1Ohm this was to have small round numbers.
All this discussion is off topic and not sure it helped but the the Lewin claim was that at the same moment in time you can have two completely different voltages on the same exact two points. That is just bad measurement methods as he did not considered the voltmeter leads as part of the circuit.
What are you afraid of? If your claims are sound, you would instantly know the answer for the questions we've posed. Even for the one Sredni found amusing. If you think that that question is out of proportion, think again. That could very well be traces on a PCB or wires on any real installation. If your Kirchhoff only works for perfectly rectangular or round loops, with known resistors within tolerances, it is a useless theory.
I'm afraid of you being a troll and wasting my time.
Read the replay above as it may be relevant if you are not a troll.
Shape of the loop will make no difference as long as Bflux is uniform but if that is not the case then you will not be able to calculate that with just pen and paper (you may be able to approximate something) but you will need a computer simulation tool to solve that and of course all details to scale.
And even if flux is uniform you will need to know the total length of that loop and the length between the two points you want to make the measurement then calculation is the same as for the simple ring model as shape alone makes no difference.

I am asking for the electric field E inside the conductor  to be more precise, the tangential component that contribute to the integral of E.dl .
I can tell you that in my case it would be in the mV/m range.
What value do you get in your case?
OK I think I understand what part you do not understand so I will try to find a bit of a different example
Can you or can you not compute this electric field?
Our circuit is stationary, nothing is moving.
What is the electric field inside your conductor?
You are not telling because you do not know how to compute it, or because you cannot justify a 0.25 V (yeah, minus 0.002V) voltage difference at its ends?
Because that's the point.

Can you or can you not compute this electric field?
Our circuit is stationary, nothing is moving.
What is the electric field inside your conductor?
You are not telling because you do not know how to compute it, or because you cannot justify a 0.25 V (yeah, minus 0.002V) voltage difference at its ends?
Because that's the point.
This tread is here to discuss about the silly idea that you can read two different voltages measured between the exact same two points at the exact same moment in time.
But good news :).
I came up with an experiment that you can do to understand EMF
It involves either a transformer or if you prefer a brushless motor/generator (maybe you have one small servo motor around).
Say it is the servo motor as it is more visual and shows a bit more information.
EMF output 100V at 1000RPM and coil resistance 10Ohm
You just connect a voltmeter (you can ignore the 1Mohm) and while the generator spins at 1000RPM you will read 100V
Now you connect at 100Ohm restive load and again spin at 1000RPM what do you think the voltmeter will read now at the output terminal (in parallel with the 100Ohm load) ?
It will of course take more work to spin at 1000RPM when the 100Ohm load is connected but the EMF will be the same 100V
So you have 100V and the close loop will have 100 + 10 = 110Ohm thus current will be 0.909A
IR Voltage drop on the internal 10Ohm coil will be 9.09V thus the voltmeter will read 100V  9.09V = 90.9V
If you do not believe my calculations are correct then you can experiment. Fortunately the motor and transformer are both shielded so it will not mess with your measurement device.
Edit: This was my last attempt as there is not much else I can do.
I have to go back at creating equipment's that work based in part on what I tried to explain above. They are all open source as I think knowledge should be free and shared, and people should understand how things work.

Yes that generator example is spot on.
The last two pages of arguing in this thread seam to be all because of different definitions of voltage.
The correct formal definition used by Dr Lewin: Voltage is the integral of all forces on charges along a given path
The common definition used in circuit analysis: Voltage is the difference in charge density between two points
The formal definition is what results in the two voltages because it handles magnetic EMF differently. The EMF is path dependent and this makes the voltage path depend an as well. Because some part of the path is missing this gives multiple results until you close the path using a voltmeter. In this definition a superconductor can't have any voltage across it.
The other definition just focuses on how many electrons there are in that spot. It essentially ignores any magnetic EMF and instead observes the charge separation effect that the magnetic fields cause. Since there can only be a single number for how many electrons are there means this never gives multiple voltages as a result. In this definition superconductors can have a voltage across them if they are a open loop, the magnetic forces bunch up the electrons to one end of the wire and you can measure this voltage with a voltmeter. This is because voltmeters read this definition of voltage. I call this "aparrant voltage"
So I suggest that you make it clear in further discussion what kind of voltage you are talking about.
Edit: Autocorect mistakes

Yes that generator example is spot on.
The last two pages of arguing in this thread seam to be all because of different definitions of voltage.
The correct formal definition used by Dr Lewin: Voltage is the integral of all forces on charges along a given path
The common definition used in circuit analysis: Voltage is the difference in charge density between two points
[...]
So I suggest that you make it clear in further discussion what kind of voltage you are talking about.
Just out of curiosity...
Have you ever heard the term "dimensional analysis"?
(Also, I guess you won't tell us what the field inside the conductor is... Kirchhoffians are allergic to electric fields, it appears)
I am not sure I can sort this mess.

I sort of feel like I deal with trolls
Me too. What a coincidence :DD
More like my probing technique is bigger in 'theory' than yours ;)
Far to much theoretical waffle and going around in circles or in some cases non circular circuits. Given this is a forum for EE's not theoretical Physicists with very average probing technique, get on design the experiment, test it and prove or disprove it and then get it repeated by others.

You agreed with ogden, who expressed electric field in volts. You should have read better, before saying that his reply was more to the point.
Well, ok. I admit that ogden (*me) did not answer your trolling question "what is the field inside the copper conductor" correctly. Expressing Volts, I missed to mention "integral of E.dl". Hopefully it is resolved now and we can return to the roots of our conversation.
What is the field inside the copper conductor and how do you justify  with formulas  that there is a (0.250.002) volts difference across it?
BTW wire fragment resistance is 0.001 Ohms so it is (0.250.001) Volts, not (0.250.002).
Inside our conductor there are two E fields: E.induced and E.coloumb. Total electric field E = E.coloumb + E.induced. Coulomb electric field in the wire is opposite the direction of the induced electric field  that's the justification of voltage difference. Potential difference (integral of E.dl) at the ends of that copper conductor you calculate using same formula as for 0.25V chemical battery that has 0.001 Ohm internal resistance and 1A current load. Answer is mentioned already here in this thread.
Assume standard conductivity for copper, say 5.8 10^7 mhos per meter
Do not introduce new unnecessary conditions.

What is the field inside the copper conductor and how do you justify  with formulas  that there is a (0.250.002) volts difference across it?
BTW wire fragment resistance is 0.001 Ohms so it is (0.250.001) Volts, not (0.250.002).
Ok.
Inside our conductor there are two E fields: E.induced and E.coloumb. Total electric field E = E.coloumb + E.induced. Coulomb electric field in the wire is opposite the direction of the induced electric field
Ok, this is real progress.
 that's the justification of voltage difference.
Please clarify.
The field inside the copper conductor is the sum of E.coloumb with E.induced, you said (and I agree). How do you think the copper can tell which is which? The copper sees the net, resulting, field. (and THIS is the point)
What is this sum?
Potential difference (integral of E.dl) at the ends of that copper conductor you calculate using same formula as for 0.25V chemical battery that has 0.001 Ohm internal resistance and 1A current load. Answer is mentioned already here in this thread.
Please, indulge me. Give me the number in V/m (volts per meter).
Assume standard conductivity for copper, say 5.8 10^7 mhos per meter
Do not introduce new unnecessary conditions.
I am looking forward to seeing how you compute the field and how well it fits with the 0.250.001 volts difference at the extremes.

Yes that generator example is spot on.
The last two pages of arguing in this thread seam to be all because of different definitions of voltage.
The correct formal definition used by Dr Lewin: Voltage is the integral of all forces on charges along a given path
The common definition used in circuit analysis: Voltage is the difference in charge density between two points
[...]
So I suggest that you make it clear in further discussion what kind of voltage you are talking about.
Just out of curiosity...
Have you ever heard the term "dimensional analysis"?
(Also, I guess you won't tell us what the field inside the conductor is... Kirchhoffians are allergic to electric fields, it appears)
I am not sure I can sort this mess.
Yes i have its getting units in order in equations.
What so problematic about the field? You get a electric field caused by charge separated electrons that is precisely proportional to the amount of charge separation. There is also an apparent electric field caused by the magnetic field that is exactly the same size and opposite in direction than the electric field from before (Given this conductor is an open loop or a superconductor)

I'd like to kindly ask the Kirchhoff experts what tools do Kirchhoff rules give me to calculate the "right" voltage of the loop below. Except for the irregular perimeter, all conditions are the same as for my rectangular loop above.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589078;image)
I need to know the exact points where to connect the voltmeter and its precise location. Any reply will be appreciated.
Oh and also i solved your curvy wire example.
Here is where you have to put the voltmeter for it to read 0V
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589408;image)
Solved using Solidworks Fusion 360 due to it having a convenient area measurement tool.

The field inside the copper conductor is the sum of E.coloumb with E.induced, you said (and I agree). How do you think the copper can tell which is which?
What are you smoking?
The copper sees the net, resulting, field. (and THIS is the point)
What is this sum?
Integral of E.dl where E = E.coloumb + E.induced. EMF of wire segment is EMF.total/4 (because segment is 1/4 of loop) = 1/4V and voltage drop due to current is 0.001Ohm*1A = 0.001V. So, this sum is 0.25+(0.001) Volts. What's the point to ask question so many times?
Potential difference (integral of E.dl) at the ends of that copper conductor you calculate using same formula as for 0.25V chemical battery that has 0.001 Ohm internal resistance and 1A current load. Answer is mentioned already here in this thread.
Please, indulge me. Give me the number in V/m (volts per meter).
:// With same success you can ask me weight of the wire used in experiment. Before asking V/m, make sure you give enough data to calculate such (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg2016091/#msg2016091) :palm:
[p.s.] Trolls... One is shifting goalposts all over the place, I wonder when he will touch chemical composition of the copper wire? Another is stuck into selfinflicted mental loop of proving that Kirchoff's rules cannot be used in place of Maxwells equations. Fun!
[edit] Added reply to Q "What is this sum?"

Oh and also i solved your curvy wire example.
Here is where you have to put the voltmeter for it to read 0V
Solved using Solidworks Fusion 360 due to it having a convenient area measurement tool.
Wonderful. Much appreciated. Now we need to measure the voltage indicated by the calculations so as to confirm that they are right. But, alas, in the real circuit there is a physical obstruction, that in no way affects the magnetic field. This obstruction goes all the way with the field while it is perpendicular to the surface.
How can we measure measure that voltage? Thanks in advance for your kind reply.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589588;image)

I sort of feel like I deal with trolls
Me too. What a coincidence :DD
More like my probing technique is bigger in 'theory' than yours ;)
Far to much theoretical waffle and going around in circles or in some cases non circular circuits. Given this is a forum for EE's not theoretical Physicists with very average probing technique, get on design the experiment, test it and prove or disprove it and then get it repeated by others.
By the choice of your words you sense that there is probably something wrong with your "probing technique". It's not sponsored by any electronics engineering fundamentals which pretty much describes tried and true experimental phenomena along the past two centuries up to this day. You only rely on a couple of 10 min or so videos on the internet without even questioning their content. Any serious trade like ours upon which the lives of people depend deserves a little more rigor.

Oh and also i solved your curvy wire example.
Here is where you have to put the voltmeter for it to read 0V
Solved using Solidworks Fusion 360 due to it having a convenient area measurement tool.
Wonderful. Much appreciated. Now we need to measure the voltage indicated by the calculations so as to confirm that they are right. But, alas, in the real circuit there is a physical obstruction, that in no way affects the magnetic field. This obstruction goes all the way with the field while it is perpendicular to the surface.
How can we measure measure that voltage? Thanks in advance for your kind reply.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=589588;image)
That's just an engineering problem at this point.
1) Make a length of wire that would fit across those two points as if the pesky barrier was not there
2) Make a rigid wire structure that goes around the barrier as needed and connects to a voltmeter on the other end
3) Make another copy of the structure from 2, but short it using the piece of wire from 1
4) Place the structure from 2 onto the circuit to tap the voltage and place the structure from 3 anywhere near by
5) Subtract the readings of the voltmeters.
The compensation structure from 3 can be used multiple times to ensure the field is indeed uniform all around so that we know the placement of the structure has shown valid readings.
Alternatives are to just calculate the voltage of the compensation structure if you already know the exact properties of the field, or in that case if you know the properties of the field and the path of the wire you want to measure you can just apply Faradays law to the whole thing.
Remember im not trying to disprove anything about Faraday or Maxwell. Just saying that Kirchhoffs laws are convenient to use in some cases (And they do work when used correctly).

Wonderful. Much appreciated. Now we need to measure the voltage indicated by the calculations so as to confirm that they are right. But, alas, in the real circuit there is a physical obstruction, that in no way affects the magnetic field. This obstruction goes all the way with the field while it is perpendicular to the surface.
How can we measure measure that voltage? Thanks in advance for your kind reply.
Just to be sure rules are known  both resistors are equal and positioned symmetrically against midpoint of the the loop, right?
Sure  due to obstruction and EMF we can't measure potential difference between given points directly. First we measure EMF induced in the voltmeter test leads  by shorting them on far side and routing them around the obstruction, making sure our test lead loop is symmetrical and centered against outer loop. Then we can leave one lead where it is (connected to far side midpoint of the outer loop) and bring another to near midpoint, measure voltage across the outer loop noting that it is impaired by EMF in one of test leads. Then just either add or subtract 1/2 of test leads EMF voltage from measurement  depending on which test lead receives EMF and direction of magnetic field. What's the point of all this?
[p.s.] Let's name shape of this loop or maybe even whole experiment as "trail of the troll"...

Does Ohm's Law still work? I've got this LED I have to turn on and I need to know which side of the LED to put the resistor...

Does Ohm's Law still work? I've got this LED I have to turn on and I need to know which side of the LED to put the resistor...
LOL. You can rest assured  complex laws do not invalidate basic laws of physics and nature easily.
Thou in case you want detailed answer  you better start new thread in "n00bs" section ;)

The field inside the copper conductor is the sum of E.coloumb with E.induced, you said (and I agree). How do you think the copper can tell which is which?
What are you smoking?
ogden, I promised not to interact with you, but you are making this promise very hard to keep. If you interfere with my exchanges with other posters I have to reply to you as well.
Integral of E.dl where E = E.coloumb + E.induced. EMF of wire segment is EMF.total/4 (because segment is 1/4 of loop) = 1/4V and voltage drop due to current is 0.001Ohm*1A = 0.001V. So, this sum is 0.25+(0.001) Volts. What's the point to ask question so many times?
Because you guys keep telling me the voltage. I want to know the electric field.
Please, indulge me. Give me the number in V/m (volts per meter).
:// With same success you can ask me weight of the wire used in experiment. Before asking V/m, make sure you give enough data to calculate such (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg2016091/#msg2016091) :palm:
I gave all the data, and also allowed for some freedom in choosing the parameters. Go back and read what I wrote in Reply #379, yesterday at 12:52:37 pm
So, let me ask you again, because this is important:
What is the field inside the copper conductor and how do you justify  with formulas  that there is a (0.250.002) volts difference across it?
Assume standard conductivity for copper, say 5.8 10^7 mhos per meter and a copper section of 1 mm in diameter (or any real world value you can attribute to a circuit similar to those shown by Lewin, Mehdi or Mabilde  it's about 10 cm diameter loop, suppose half of it is allocated by the big resistors, but it's not important).
I am asking for the electric field E inside the conductor  to be more precise, the tangential component that contribute to the integral of E.dl .
I can tell you that in my case it would be in the mV/m range.
What value do you get in your case?
And still, no answer.
Edit: typo, added slant and bold.

Integral of E.dl where E = E.coloumb + E.induced. EMF of wire segment is EMF.total/4 (because segment is 1/4 of loop) = 1/4V and voltage drop due to current is 0.001Ohm*1A = 0.001V. So, this sum is 0.25+(0.001) Volts. What's the point to ask question so many times?
Because you guys keep telling me the voltage. I want to know the electric field.
I said (E = E.coloumb + E.induced). Are you satisfied now?
Assume standard conductivity for copper, say 5.8 10^7 mhos per meter and a copper section of 1 mm in diameter (or any real world value you can attribute to a circuit similar to those shown by Lewin, Mehdi or Mabilde  it's about 10 cm diameter loop, suppose half of it is allocated by the big resistors, but it's not important).
I am asking for the electric field E inside the conductor  to be more precise, the tangential component that contribute to the integral of E.dl .
I can tell you that in my case it would be in the mV/m range.
What value do you get in your case?
And still, no answer.
You can either provide solution yourself and tell what you want to say with it or stick that tangential component where it hurts. I do not see the point of solving your tasks. "Trail of the troll" was at least funny.

Because you guys keep telling me the voltage. I want to know the electric field.
I said (E = E.coloumb + E.induced). Are you satisfied now?
No, I want to know the value in V/m (or in J/C if you prefer).
You can either provide solution yourself and tell what you want to say with it or stick that tangential component where it hurts. I do not see the point of solving your tasks. "Trail of the troll" was at least funny.
Ok, you have no idea on how to compute the electric field inside a conductor. It's not a crime. Maybe all that facepalming has interfered with your mental processes but, fine.
Any other Kirchhoffian who believes that the 'real' voltage across the 0.9 ohm resistor is 0.65 V and the real voltage across one of the two arcs of copper is 0.250.001 V care to tell us what the electric field is inside said copper?

Does Ohm's Law still work? I've got this LED I have to turn on and I need to know which side of the LED to put the resistor...
This question is actually a lot more relevant than it appears here (due to its ironic nature), as the basic Ohm's law links voltage, resistance and current. Now what is voltage again? ;D
Incidentally, Kirchhoff (not him again!) reformulated Ohm's law as: J = sigma.E
So, may be on to something.

Does Ohm's Law still work? I've got this LED I have to turn on and I need to know which side of the LED to put the resistor...
This question is actually a lot more relevant than it appears here (due to its ironic nature),
Thanks, at least someone appreciates my work here.

Ok, you have no idea on how to compute the electric field inside a conductor. It's not a crime. Maybe all that facepalming has interfered with your mental processes but, fine.
Any other Kirchhoffian who believes that the 'real' voltage across the 0.9 ohm resistor is 0.65 V and the real voltage across one of the two arcs of copper is 0.250.001 V care to tell us what the electric field is inside said copper?
Yes, I have to dig into it to solve it. So what. Original Dr.Lewins experiment assumed that conductors have no resistance, so no coloumb Efield. Now you are modifying it to prove what exactly? That your debate opponents cannot calculate something during time they are willing to spend, so this is proof that you are right? BTW this is typical tactic of internet trolls  derail discussion into personal attacks.
Better tell your Efield number and make your point. Educate Kirchoff believers, don't let them compute what you can do in a snap.

Does Ohm's Law still work? I've got this LED I have to turn on and I need to know which side of the LED to put the resistor...
This question is actually a lot more relevant than it appears here (due to its ironic nature), as the basic Ohm's law links voltage, resistance and current. Now what is voltage again? ;D
Incidentally, Kirchhoff (not him again!) reformulated Ohm's law as: J = sigma.E
So, may be on to something.
Or maybe its just using metric volts instead of imperial volts. We already crashed a probe into mars because of this shit. ;D
(You do have a valid point there tho)

Ok, you have no idea on how to compute the electric field inside a conductor. It's not a crime. Maybe all that facepalming has interfered with your mental processes but, fine.
Any other Kirchhoffian who believes that the 'real' voltage across the 0.9 ohm resistor is 0.65 V and the real voltage across one of the two arcs of copper is 0.250.001 V care to tell us what the electric field is inside said copper?
Yes, I have to dig into it to solve it. So what. Original Dr.Lewins experiment assumed that conductors have no resistance, so no coloumb Efield.
No, so no resultant E field at all.
Now you are modifying it to prove what exactly? That your debate opponents cannot calculate something during time they are willing to spend, so this is proof that you are right? BTW this is typical tactic of internet trolls  derail discussion into personal attacks.
Coming from the person who constantly facepalms, calls other posters trolls and asks what they smoke, this is hilarious.
I've been extremely restrained with you, but you are like one of those small dogs that keep jumping and barking when their owners are trying to have a conversation.
Better tell your Efield number and make your point. Educate Kirchoff believers, don't let them compute what you can do in a snap.
I already told you my number. It's in the mV/m range. With 1 amp in a 1mm diameter copper wire it's about 30 mV/m; with 10 mA as in the original Lewin experiment is about 30 uV/m. And it is perfectly consistent with the constitutive equation j = sigma E.
Also, I already told what my aim is in one of my previous post: to show that since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes (much more in the case of Lewin's experiment, since there the resistors were much smaller).
The induced E field inside the conductor is compensated by the field caused by redistribution of charge. All the resultant electric field is located in the resistor region, with nothing left in the conductor.
This is the point.
Now, dig in and try to compute that field. Then try to explain why you have to give up on j = sigma E as well.
Edit: added "resultant electric", and some plurals I had missed

Ok, you have no idea on how to compute the electric field inside a conductor. It's not a crime. Maybe all that facepalming has interfered with your mental processes but, fine.
Any other Kirchhoffian who believes that the 'real' voltage across the 0.9 ohm resistor is 0.65 V and the real voltage across one of the two arcs of copper is 0.250.001 V care to tell us what the electric field is inside said copper?
Have you read my replay with the servo motor or transformer experiment. Please do that experiment as there your measurement device will be outside of the changing magnetic field and so you will get the correct result.
Even just reading that proposed experiment you should know that those will be the results that you will get and that they use the same logic that resulted in 0.65V on the 0.9Ohm resistor and 0.2500.001V on the two 90 degree copper arcs situated in an uniform magnetic flux.
A piece of wire is a low value resistor so you introducing that in my simplified example did not helped with anything other than complicating the example.
Maybe is worth noting that if you shield the 0.9Ohm resistor the EMF at the same point in time will drop from 1V to 0.75V and since it is uniform it will be distributed equally on the other 3 quarters of the circuit. I leave it to you to calculate what will be the voltage on the 0.9Ohm in this case.
Don't care what you use to solve this as long as the result is correct.

Have you read my replay with the servo motor or transformer experiment.
Sorry, I am not allowing mutatio controversiae. Let's stick to the ring and keep it as simple as possible, because heaven knows what excuses you people could come up with with slightly more complex systems.
Please do that experiment as there your measurement device will be outside of the changing magnetic field and so you will get the correct result.
So, when the voltmeter is outside the loop in the two resistor experiment, and measures 0.9V across the 0.9ohm resistors, that is the correct result?
Outside the loop there is no changing magnetic field.
Your rule does not apply here?
And, just to be clear, I know that if you measure the voltage on the ring following radial path as Mabilde did, the voltmeter will read the value you say. What I am trying to tell yuo is that such value is perfectly compatible with the application of Faraday's law and does not require for any resultant Efield inside the conductor.
On the other hand, you need that field to justify 0.25 volts across 78 cm of copper wire.

Also, I already told what my aim is in one of my previous post: to show that since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes
Wait... What you just said?  That in ideal conductor can't be EMF (induced field)? I am speechless to be honest. We are back to square one where you stop posting and go watch videos of Dr.Lewin. He is brilliant teacher BTW.
The induced E field inside the conductor is compensated by the field caused by redistribution of charge.
This is exactly what I was telling multiple times already, E = E.coloumb + E.induced.

Also, I already told what my aim is in one of my previous post: to show that since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes
Wait... What you just said?  That in ideal conductor can't be EMF (induced field)? I am speechless to be honest. We are back to square one where you stop posting and go watch videos of Dr.Lewin. He is brilliant teacher BTW.
The induced E field inside the conductor is compensated by the field caused by redistribution of charge.
This is exactly what I was telling multiple times already, E = E.coloumb + E.induced.
Yes i noticed the two being thrown into the same basket and considered as one thing all too often in this thread. The real electric field caused by charge separated electrons is a different thing that the apparent electric field that the electrons feel due to the magnetic interaction with them. The two have very different underlying mechanisms behind them.
Its especially important because voltmeters can only see the first kind of "electron pusher".
Oh and user electrodacus seams to be using the electron charge density kind of voltage everywhere. His claims are correct when you consider that. Tho i think he should look into what the other magnetic EMF part of the voltage looks like to see the whole picture in this thread.

Also, I already told what my aim is in one of my previous post: to show that since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes
Wait... What you just said?  That in ideal conductor can't be EMF (induced field)?
No, I said that in a perfect conductor there cannot be a nonzero resultant E field. While in copper you get a small field compatible with j = sigma E.
This is not what you said. You correctly say that E.coloumb in ideal conductor is zero, then you imply that it means that it is nonsense to have 0.25V induced field (EMF). Read your own words for god's sake: "since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes".
And still you can't see.
What I shall see? Enlighten me.
What is E, then?
E is sum of two fields, E.induced + E.coloumb  you can do the math and calculate (do integral over E.dl) potential difference at the ends of wire segment that is subject to both Efields. This part is explained by Lewin himself BTW.

Also, I already told what my aim is in one of my previous post: to show that since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes
Wait... What you just said?  That in ideal conductor can't be EMF (induced field)?
No, I said that in a perfect conductor there cannot be a nonzero resultant E field. While in copper you get a small field compatible with j = sigma E.
This is not what you said. You correctly say that E.coloumb in ideal conductor is zero, then you imply that it means that it is nonsense to have 0.25V induced field (EMF). Read your own words for god's sake: "since there could not be a significant electric field inside the copper (it is zero in a perfect conductor) it is nonsense thinking that you can still have an induced field capable of producing a 0.25V voltage at the extremes".
When there is the primary coil only, say in vacuum, you can find the induced E field in all space. It is directed in circles and has a module that grows with the distance r from the center inside the coil, while it decreases as 1/r outside of it.
Ok, there you can see the field, in vacuum.
Now you put your copper loop with the two resistors.
Do you still think that inside the copper there will be the same induced field? No, charges will be displaced, producing a coloumbian field that will compensate this field, actually erasing it inside the conductor. All that remains is zero in a perfect conductor and that tiny little field compatible with j = sigma E in a real conductor.
Your induced field is no mas. Obliterated by the field produced by the displaced charges  that will accumulate at the resistors ends and in general wherever there are gradients in conductivity and permeability.
So I confirm my words: "no significant electric field inside the copper (it is zero in a perfect conductor)" and that if you think that you can still have your unaltered induced field inside the copper you are thinking nonsense.
Just like thinking that you can have a radially direct Efield inside a conductor placed nearby a point charge.
E is sum of two fields, E.induced + E.coloumb  you can do the math and calculate (do integral over E.dl) potential difference at the ends of wire segment that is subject to both Efields. This part is explained by Lewin himself BTW.
So, after all this posts you still have to answer what is the value of the resulting E field in V/m in copper.
Edit: added the gradient eps and gradient sigma parts.

Do you still think that inside the copper there will be the same induced field?
if you think that you can still have your unaltered induced field inside the copper you are thinking nonsense.
I don't think so and never did. You just discovered EMF? We are long over this part, kid.
So, after all this posts you still have to answer what is the value of the resulting E field in V/m in copper.
If you want value of field *inside* copper segment, then this is all you get: (I*R)/length. Better just watch Dr.Lewin's famous video where he explains those questions

So, after all this posts you still have to answer what is the value of the resulting E field in V/m in copper.
You always ask silly questions that have no relevance to the problem. Showing that you do not understand the mechanisms behind all this.
Original problem had this as data
A closed loop made of two different resistors connected with some pieces of wire (nit that relevant as wire is also a resistor with lower value).
EMF = 1V (I think this was the same in my example and in Lewin example).
Resistor values 0.9Ohm and 0.1Ohm in my example not sure but I think it was 1000x more in Lewin example (not relevant).
Noting else was given and there is no need for anything else to find out what the voltage on those two symmetrically opposed points will be.
So let me explain to you what a 1V EMF means as you do not seem to understand (likely my fault as my examples should have been very clear).
You can have a wire open circuit no matter what shape how long or what type of conductor as long as you mention that EMF is 1V then you will measure 1V across that wire (this is a snapshot in time as of course there will be a variable magnetic field that generates this). There is also the assumption that magnetic field is uniform across the loop meaning that you will read 0.5V if you measure two points at half the wire length between them anywhere on the wire.
Say you close this wire in a loop (again not relevant what shape the loop has and is the exact same moment in time thus EMF=1V) then there will be a current generated in this loop that will be result of EMF divided by loop resistance.
Keep in mind that this is the case because the EMF = 1V was given as input for the closed loop meaning that the magnetic field was strong enough to generate that 1V EMF no matter how much current went trough the closed loop.
So in my example with a total loop resistance of around 1Ohm current was 1A and I think Lewin experiment had 1mA but there is no difference for the explanation.
Now if the loop was all made of copper wire with 1Ohm resistance it seems you do not have a problem with the fact that 1A will travel trough this wire as EMF is defined as 1V (am I correct in assuming that).
Your problem seems to be understanding why if say a quarter of this loop has 0.999Ohm and the remaining 3 quarters have 0.001Ohm
a) If this new loop is open circuit you will agree that you will read 1V between ends and not only that but you will read 0.5V on any half part of the loop.
b) If I cut this loop in two open parts one quarter size 0.999Ohm it will read 0.25V and the other 3 quarter size 0.001Ohm will read 0.75V
c) Each of this two separately can be equivalent with a battery with the respective internal resistance
Now can you understand why is simple to calculate the voltage in any two points on this close loop made of basically two resistors (you can add 10 different resistors in the loop if you want).
And you do not need to know anything else to calculate the voltage between any two points.
All your unrelated questions are useless and just show you do not understand what EMF is.
Just hope this made it clear to you and others as I love sharing and acquiring knowledge. If I'm not able to explain it so anyone can understand it means I do not understand it.

By the choice of your words you sense that there is probably something wrong with your "probing technique". It's not sponsored by any electronics engineering fundamentals which pretty much describes tried and true experimental phenomena along the past two centuries up to this day. You only rely on a couple of 10 min or so videos on the internet without even questioning their content. Any serious trade like ours upon which the lives of people depend deserves a little more rigor.
There is no real rigor left in this thread what you have all descended into is tit for tat point making among 5 or 6 of you and then arguing who has the biggest probe er I mean best resolution to the point then disagreeing on that point and going around again in a circle!
Attacking the person for having a different opinion is not ever going to solve anything! Attack the technicalities just might get a resolution but in this threads case I doubt it very very much.
'Any serious trade like ours upon which the lives of people depend deserves a little more rigor.' Yep because projects like the Manhattan one 'saved lives' with Physics and Engineering. You have used this same statement a few times and while it can be true it is also a logical falsehood.

There is no real rigor left in this thread
What kind of rigor can you expect from people who wriggle like eels and refuse to compute the field in their circuit?
I have seen lots and lots of words to go around that simple question. And the reason is that they will end up with inconsistent results.
They believe they can have .25 V across a piece of copper 7cm long, 1mm diameter with nearly zero field inside. Or nonnegligible field (much much higher than that allowed by the constitutive equation) inside a good conductor. What rigor can you expect?
This is why Lewin stopped answering questions about this matter. Flatearthers always come up with new excuses, no matter what.
Now there is 'apparent electric field'.

There is no real rigor left in this thread
What kind of rigor can you expect from people who wriggle like eels and refuse to compute the field in their circuit?
I have seen lots and lots of words to go around that simple question. And the reason is that they will end up with inconsistent results.
They believe they can have .25 V across a piece of copper 7cm long, 1mm diameter with nearly zero field inside. Or nonnegligible field (much much higher than that allowed by the constitutive equation) inside a good conductor. What rigor can you expect?
This is why Lewin stopped answering questions about this matter. Flatearthers always come up with new excuses, no matter what.
Now there is 'apparent electric field'.
Have you even read my last replay? Do you still do not understand the problem and the parameters given ?
Nothing else is needed to solve the problem and nothing else was specified in my examples or Lewin's
There was no mention anywhere about the loop size, diameter of the wires or magnetic field as they are not required to solve the problem and you can have an infinite combination of those to get the spec EMF but just the EMF was needed.
Please make sure you read that else it makes no sense for me to replay to you.

Flatearthers always come up with new excuses, no matter what.
When they are out of arguments in existing discussion, they invent new useless challenges  just like you.

Electrodacus
I read it and it shows that you have a high school student mentality. You see it as an exercises with 'givens' from the prof. and you have to find a value that coincides with the prof. result.
But getting the right number does not mean you are getting the theory behind it. In fact, Mabilde is getting the same number I would expect based on Faraday, the nearly zero field inside the copper and no little generators dispersed along the wire.
What I am doing here is trying to point out inconsistencies in your (erroneous) view of the phenomena.
If you compute the darn field inside your copper conductor you will find that you either have to give up j = sigma E or you have to renounce having that 0.25V located there.
And I have to resort to field theory (EDIT: to do that, and that should not be a problem: my view is perfectly consistent with that, can you say the same for yours?).
I can show you exactly how the charge distribution is affected by gradients in conductivity and in permeability, but that would require vector calculus and if you do not understand as basic a concept as the superposition of fields, what hope is there that you will understand that?
Stop making up other examples where you can find the right number. Focus on the underlying theory and principles and show me you do not find inconsistencies. My view has no inconsistency whatsoever: the field inside the copper is perfectly abiding j = sigma E. Can you say the same?
Also, did you answer my question about the voltmeter measuring 0.9V from outside the loop? No, you didn't.
You keep making up new examples to avoid facing the inconsistencies of your view.
While I have always been focused on the two resistor loop of RomerLewin.
Try to do the same.

When they are out of arguments in existing discussion, they invent new useless challenges  just like you.
A challenge is what distinguishes a professional from a wannabe. The versed from the amateur. The authentic from the impostor.

A challenge is what distinguishes a professional from a wannabe. The versed from the amateur. The authentic from the impostor.
LOL. Who would say so. BTW you also came with useless challenge. Now both of you can challenge each other until it hurts. This thread became :horse:  like both of you wanted.

Yes i noticed the two being thrown into the same basket and considered as one thing all too often in this thread.
Yes, and you should ask yourself why.
The real electric field caused by charge separated electrons is a different thing that the apparent electric field that the electrons feel due to the magnetic interaction with them. The two have very different underlying mechanisms behind them.
Do you think the copper can tell the difference?
Or will it just experience the superposition of both fields?
I gave up my hopes on ogden, but you might make it.
Here's a hint, from electrostatics.
The field produced from a point charge is radially directed and goes as 1/r^2.
Now put a piece of copper near it.
Will the field inside the piece of copper be still radially directed from the source?
Or maybe, the free charges in the conductor will distribuite themselves in such a way to compensate for that radial field, so that the resulting field will be zero inside the conductor?
Does it matter the underlying mechanism that produced the various contributions to the total field?
Where is it written that superposition of electric fields only works for... 'same mechanism origin' fields only?
Copper doesn't really care about the difference, it just enjoys its electrons roaming about wherever they want as metals tend to do.
And yes a similar effect happens with external electrostatic fields, but with the difference is that these fields act as a conservative field. Path does not matter with them and as such they are not capable of pushing current around a circuit loop. Due to this the wires used to connect the voltmeter subtract this effect back out and once again cause the voltmeter incapable of detecting it even tho it is essentially measuring the charge density (across its terminals, not across the ends of its probe wire)
One could reformulate Dr. Lewins two resistor experiment to work with electrostatics by simply removing the solenoid and placing the circuit between the plates of a large capacitor, then ramping the voltage across this capacitors terminals. You will again see voltage and currents in the circuit, so circuit mesh analysis will need a parasitic capacitor added in to work right, but both scopes would show the same voltage so it wouldn't be as cool of a demo.
So how does a voltmeter tell the difference if it only shows the field caused by electron density and not the magnetic EMF? (Hint: It does show some EMF too but not where you would typically want)
If voltmeters treat the two separately, why should we treat them as the same thing? We are trying to calculate what the voltmeter would show after all.
I'm not trying to pick sides here, or say anything negative about anyone. To me it seams that most people in this thread are not saying anything wrong for the most part, but the disagreement seams to stem from using a slightly different definition of things and more rarely a bit from just having a different thought process about this thing.

That's just an engineering problem at this point.
1) Make a length of wire that would fit across those two points as if the pesky barrier was not there
2) Make a rigid wire structure that goes around the barrier as needed and connects to a voltmeter on the other end
3) Make another copy of the structure from 2, but short it using the piece of wire from 1
4) Place the structure from 2 onto the circuit to tap the voltage and place the structure from 3 anywhere near by
5) Subtract the readings of the voltmeters.
The compensation structure from 3 can be used multiple times to ensure the field is indeed uniform all around so that we know the placement of the structure has shown valid readings.
Alternatives are to just calculate the voltage of the compensation structure if you already know the exact properties of the field, or in that case if you know the properties of the field and the path of the wire you want to measure you can just apply Faradays law to the whole thing.
Remember im not trying to disprove anything about Faraday or Maxwell. Just saying that Kirchhoffs laws are convenient to use in some cases (And they do work when used correctly).
After trying to follow your instructions, I am not sure if I understand what you mean without a drawing. So I decided to simplify the challenge. Let's suppose that the whole internal area of the loop is completely occupied by the obstruction.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=590755;image)
Perhaps that way it becomes easier for me to understand.

LOL. Who would say so. BTW you also came with useless challenge. Now both of you can challenge each other until it hurts. This thread became :horse:  like both of you wanted.
I told you: go get yourself a better education. Now you can see that praising Mehdi and Mabilde and bashing Lewin didn't get you smarter.
Next time, listen to the voice of experience.

LOL. Who would say so. BTW you also came with useless challenge. Now both of you can challenge each other until it hurts. This thread became :horse:  like both of you wanted.
I told you: go get yourself a better education. Now you can see that praising Mehdi and Mabilde and bashing Lewin didn't get you smarter.
Next time, listen to the voice of experience.
Being a loudmouth (or loud typist) and attempting to belittle others is not educational or helpful to a debate it is no more than behaving like a petty bully in the schoolyard. But as you claim to be an adult with the ability to read this may be of benefit but I doubt you would understand it. https://www.psychologytoday.com/au/blog/neurosagacity/201702/howtellyouredealingmalignantnarcissist (https://www.psychologytoday.com/au/blog/neurosagacity/201702/howtellyouredealingmalignantnarcissist)

LOL. Who would say so. BTW you also came with useless challenge. Now both of you can challenge each other until it hurts. This thread became :horse:  like both of you wanted.
I told you: go get yourself a better education. Now you can see that praising Mehdi and Mabilde and bashing Lewin didn't get you smarter.
Next time, listen to the voice of experience.
Being a loudmouth (or loud typist) and attempting to belittle others is not educational or helpful to a debate it is no more than behaving like a petty bully in the schoolyard. But as you claim to be an adult with the ability to read this may be of benefit but I doubt you would understand it. https://www.psychologytoday.com/au/blog/neurosagacity/201702/howtellyouredealingmalignantnarcissist (https://www.psychologytoday.com/au/blog/neurosagacity/201702/howtellyouredealingmalignantnarcissist)
Nah, I don't think ogden is a malignant narcissist. He's just ignorant and proud.
You can tell from his numerous nontechnical posts, whose sole intention is to belittle the efforts of the few people trying to bring a little physics in this 'technicians' den'.
But why did you quote Bsfeechannel exasperation post to tell him that? ;D

But why did you quote Bsfeechannel exasperation post to tell him that? ;D
Not even close to funny.
Being a bully in person or online isn't ok ever and when done under the guise of 'education and learning' it is just pathetic and nothing will be learned.
Like I posted yesterday attack the persons ideas or challenge a theory by all means people can learn from this sort of discourse.

And this is why it is nonsense to believe that you can locate a field big enough to give 0.25V voltage (integral of E.dl along the conductor) in the copper parts of the loop.
You would break the constitutive equation in copper. You would count twice the effects of the induced field.
I do not remember if I answered this concern you have in a direct way so I will do that now.
You asked several times about the size of the loop and I probably mentioned that is irrelevant for the problem so let me explain a bit better (I think).
emf = B * l * v
In the examples we were discussing the emf was a given none of the others after the equal sign where needed to calculate the potential difference between two points that was the topic of interest.
Now you are thinking on real world examples and somehow imagine a loop of a few centimeter (nowhere I ever mentioned anything about absolute length and neither what that the case in Lewin's example).
But looking at the formula you can understand that you can manipulate any of the 3 parameters and get the same emf (magnetic field, wire length and speed).
Any length of copper (or other conductor) will also be an inductor thus a energy storage device sort of the reverse of a capacitor but for magnetic field.
So using the analog of a battery that has an emf and an internal resistance is the correct way to view and simplify a piece of wire in a variable magnetic field when you consider this for a fixed moment in time else you need to integrate.

Not even close to funny.
It wasn't meant to be funny. It was a sarcastic grin.
I suggest you go back reading ogden's posts in this thread and revise your judgment. All he did was to facepalm, LOL, belittle and tell other people they were trolls, to stick it where it hurts and so on.
But no, we should put up with that shit and give him an award for just showing up and saying bullshit.
Sorry, not all posters in this forum align to the politically correctness craze that is so endemic to the US.
I tried not to respond to provocations, but to fault bsfeechannel for telling him to go study, is in my eye a bit excessive.
He is the incarnation of the people who do not know, but think they know Lewin was talking about.
Enough is enough.
You asked several times about the size of the loop and I probably mentioned that is irrelevant for the problem
Physical size is relevant to get the E field and current density j values.
I am beginning to suspect you think those are mytical quantities. Like unicorns.
I'll try to be more specific: if I know the current and I want to find the current density, I have to divide by the area of the wire's section. Also, voltage along a path is the integral of the electric field, do you think that knowing how long the path you are integrating on can have some relevance?

It wasn't meant to be funny. It was a sarcastic grin.
I suggest you go back reading ogden's posts in this thread and revise your judgment. All he did was to facepalm, LOL, belittle and tell other people they were trolls, to stick it where it hurts and so on.
But no, we should put up with that shit and give him an award for just showing up and saying bullshit.
Sorry, not all posters in this forum align to the politically correctness craze that is so endemic to the US.
I tried not to respond to provocations, but to fault bsfeechannel for telling him to go study, is in my eye a bit excessive.
He is the incarnation of the people who do not know, but think they know Lewin was talking about.
Enough is enough.
Nowhere have I defended any of you including Ogden that have resorted to name calling and petty or even malicious taunts. This has nothing to do with political correctness so don't use that as an excuse to continue disrespectful conduct! Do you behave like this professionally or just here behind a keyboard?
Stick to the subject and there may be hope!

It wasn't meant to be funny. It was a sarcastic grin.
I suggest you go back reading ogden's posts in this thread and revise your judgment. All he did was to facepalm, LOL, belittle and tell other people they were trolls, to stick it where it hurts and so on.
But no, we should put up with that shit and give him an award for just showing up and saying bullshit.
Sorry, not all posters in this forum align to the politically correctness craze that is so endemic to the US.
I tried not to respond to provocations, but to fault bsfeechannel for telling him to go study, is in my eye a bit excessive.
He is the incarnation of the people who do not know, but think they know Lewin was talking about.
Enough is enough.
Nowhere have I defended any of you including Ogden that have resorted to name calling and petty or even malicious taunts. This has nothing to do with political correctness so don't use that as an excuse to continue disrespectful conduct! Do you behave like this professionally or just here behind a keyboard?
Stick to the subject and there may be hope!
Disrespectful conduct?
What do you expect people to do? Hold hands and sing kumbaya when people tell you to stick it where it hurts, wasting space with useless comments that only expose their ignorance? The least you can expect is for those remarks to be sent back to the sender.
I was trying to stick to the subject, but I tell you  paraphrasing a certain Roy  I feel pretty much unappreciated.

Physical size is relevant to get the E field and current density j values.
I am beginning to suspect you think those are mytical quantities. Like unicorns.
I'll try to be more specific: if I know the current and I want to find the current density, I have to divide by the area of the wire's section. Also, voltage along a path is the integral of the electric field, do you think that knowing how long the path you are integrating on can have some relevance?
I have a hard time understanding your questions.
None of your questions are relevant to the problem (as far as I can see).
It sort of seems to suggest you disagree with the result's I got on those experiments. Is that the case ?
Or do you agree with the results but want to make some sort of point that I fail to see ?

That's just an engineering problem at this point.
1) Make a length of wire that would fit across those two points as if the pesky barrier was not there
2) Make a rigid wire structure that goes around the barrier as needed and connects to a voltmeter on the other end
3) Make another copy of the structure from 2, but short it using the piece of wire from 1
4) Place the structure from 2 onto the circuit to tap the voltage and place the structure from 3 anywhere near by
5) Subtract the readings of the voltmeters.
The compensation structure from 3 can be used multiple times to ensure the field is indeed uniform all around so that we know the placement of the structure has shown valid readings.
Alternatives are to just calculate the voltage of the compensation structure if you already know the exact properties of the field, or in that case if you know the properties of the field and the path of the wire you want to measure you can just apply Faradays law to the whole thing.
Remember im not trying to disprove anything about Faraday or Maxwell. Just saying that Kirchhoffs laws are convenient to use in some cases (And they do work when used correctly).
After trying to follow your instructions, I am not sure if I understand what you mean without a drawing. So I decided to simplify the challenge. Let's suppose that the whole internal area of the loop is completely occupied by the obstruction.
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=590755;image)
Perhaps that way it becomes easier for me to understand.
Same procedure still works, just needs longer probe wires to get around the larger obstruction.
Explaining it more simply you just measure your probe wires in the same field first by shorting them, then remove the short and actually connect them to the circuit, measure again and subtract out the first measurement to get the result. That way probe wires are compensated out. If you want to double check you can repeat the whole thing with probe wires taking a different path and the result will be the same.
Tho a lot of this thread has seam to have devolved into insults (Nothing towards me but towards others) rather than creative discussion so il probably stop participating in it if this continues.

Tho a lot of this thread has seam to have devolved into insults
From very beginning "Kirchoff for the birds" fans arrogantly insulted nearly everybody who disagree with them. Later rather than sooner it resulted in opposite reaction. I was part of it and not proud about it. Apologies to anyboody who got hurt in the process. Most likely I shall stay away from this thread which is/was just baseless "arguing (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1979633/#msg1979633) against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct", like broken record.

Same procedure still works, just needs longer probe wires to get around the larger obstruction.
Thank you for your reply. However I'm still not sure what you mean, perhaps due to my limited fluency in English. When you say the probe goes around the obstruction, where exactly do you place your voltmeter? I understand that, in the area of the obstruction, it'll be impossible.
Tho a lot of this thread has seam to have devolved into insults (Nothing towards me but towards others) rather than creative discussion so il probably stop participating in it if this continues.
Apparently, encouraging people to get smarter is offensive for some.

From very beginning "Kirchoff for the birds" fans arrogantly insulted nearly everybody who disagree with them.
There's no such thing as "Kirchhoff for the birds" fans. I myself was considered a king of circuit analysis when I was in college. I got my first job as an engineer because of that ability.
However, I know darn well that Kirchhoff can only be applied to lumped circuits and it doesn't work for anything under a varying electromagnetic field. Because, under that condition, a circuit becomes an "antenna", and antennas are everything but lumped. You'll have induction everywhere so it will be impossible to solve a circuit using Kirchhoff which does not provide the tools for either designing or probing your circuits.
How do I know that? By my own experience. When I got my first job as an engineer, digital circuits were leaving the domains of Kirchhoff and foraying into the realm of electromagnetism. Frequencies were such that the wavelengths were becoming as short as the size of the PCBs.
We had problems with the companies that designed our PCBs at the time, because they were kirchhoffalwaysholders (the cute name I decided to bestow upon those who think that Kirchhoff always holds) not by choice, but because they were used to low frequency circuits, where Kirchhoff is good enough.
We had to invite the help of our colleagues from the radio division, for whom Maxwell was second nature, and use their experience to instruct our designers how to properly design a PCB for higher frequencies, which is commonplace today.
This kirchhoffalwaysholdery sucks, therefore, because not only it is a pseudoscientific doctrine, it is an encumbrance for any serious electronics engineering today.
And apparently it is now taking the shape of a religious movement where its converts get very offended when it is shown in theory or practice that their nonsense dogma is false.
As Lewin says, "this tells you something about them".

I'm afraid of you being a troll and wasting my time.
Fear not. According to the dictionary, a troll is someone who posts deliberately inflammatory articles on an internet discussion board. I may rant or show I am indignant at some absurd fact sometimes, but I never troll. I don't have the time or the motivation for hanging around in forums posting provocative assertions just to see the world burn.
I'm just questioning your claims. That's what forums are for.
Read the replay above as it may be relevant if you are not a troll.
I did, thank you.
Shape of the loop will make no difference as long as Bflux is uniform but if that is not the case then you will not be able to calculate that with just pen and paper (you may be able to approximate something) but you will need a computer simulation tool to solve that and of course all details to scale.
And even if flux is uniform you will need to know the total length of that loop and the length between the two points you want to make the measurement then calculation is the same as for the simple ring model as shape alone makes no difference.
Thanks again for your reply. I thought of many other "challenges", but I won't tire you with an infinite list of questionings. I just wanted to understand the basic principles of your claim.

So how does a voltmeter tell the difference if it only shows the field caused by electron density and not the magnetic EMF? (Hint: It does show some EMF too but not where you would typically want)
If voltmeters treat the two separately, why should we treat them as the same thing? We are trying to calculate what the voltmeter would show after all.
I'm not trying to pick sides here, or say anything negative about anyone. To me it seams that most people in this thread are not saying anything wrong for the most part, but the disagreement seams to stem from using a slightly different definition of things and more rarely a bit from just having a different thought process about this thing.
I'm not clear what you are talking about. So the two voltmeters in this experiment are not affected by the EMF? Then why do they read different voltages?
Anyway, voltmeters don't read the field caused by electron density. They don't read the electrostatic potential. Take the example of a PN junction diode. It clearly has different electron densities in the P and N depletion region. There is an electrostatic potential difference due to the charge separation. But a voltmeter measures zero volts when connected to the leads of the diode.
If you integrate E dot dl through an unbiased diode, you get a voltage! Diodes violate KVL!
(https://i.stack.imgur.com/SaSH6.jpg)
Obviously using integral of E dot dl has a problem. Circuits with diodes would be another KVL fail according to Dr. Lewin's definition.

If you integrate E dot dl through an unbiased diode, you get a voltage! Diodes violate KVL!
Indeed. Chemical battery violates KVL as well. Resistor and any other lone component violates KVL. Kirchoff's Circuit Laws requires closed Circuit. As some insist that Dr.Lewin's loop cannot be split into lumped elements, then all this conversation is futile. When we agree that 1/4 of the Dr.Lewin's experiment (inner) loop receives EMF/4 and can be treated as lumped element meaning Berni model (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312) is correct  then there's ground for conversation. Honestly I do not see such time coming.
Some (you know who) can prove me wrong :popcorn:

If you integrate E dot dl through an unbiased diode, you get a voltage! Diodes violate KVL!
Indeed. Chemical battery violates KVL as well. Resistor and any other lone component violates KVL. Kirchoff's Circuit Laws requires closed Circuit.
That's not my point. You can make a closed circuit by connecting the diode leads together with a wire. Go around the loop and calculate the integral of E dot dl. For the wire it is zero, for the diode, it is not zero. So the integral of E dot dl around the loop is not zero. According to Dr. Lewin's definition, Kirchoff's Loop Rule is violated. So are Maxwell's equations? The world is flat.
But everyone knows the voltage across the diode is zero, and the voltage across the wire is zero. So KVL is OK, and the world is not flat.

You can make a closed circuit by connecting the diode leads together with a wire. Go around the loop and calculate the integral of E dot dl.
No. Kirchoff's Circuit Laws requires closed circuit of lumped elements. So diode is one lumped element of the circuit and wire supposedly with it's internal resistance  another. So two elements. When you do circuit analysis  you don't go around the loop integrating everything in the path. This is not how CIRCUIT analysis shall be done. You do E dot dl over diode and make it lumped element  black box with two terminals, you can name it as voltage source when subject to light for example. Then you do E dot dl with wire and again make it black box with two terminals, name it load. Both are lumped elements of our circuit. Connect those together and *then* check against Kirchoff's Laws using voltage/current measurements.
Shall I repeat? Pay close attention to term "lumped element":
When we agree that 1/4 of the Dr.Lewin's experiment (inner) loop receives EMF/4 and can be treated as lumped element meaning Berni model (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312) is correct  then there's ground for conversation.
[edit] Better stick to electromagnetism.

Take the example of a PN junction diode. It clearly has different electron densities in the P and N depletion region. There is an electrostatic potential difference due to the charge separation. But a voltmeter measures zero volts when connected to the leads of the diode.
The reason for that is that to connect to the silicon you have to create ohmic contacts (nonrectifying contacts) and...
Nah, I'll use the first link.
https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction (https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction)

Take the example of a PN junction diode. It clearly has different electron densities in the P and N depletion region. There is an electrostatic potential difference due to the charge separation. But a voltmeter measures zero volts when connected to the leads of the diode.
The reason for that is that to connect to the silicon you have to create ohmic contacts (nonrectifying contacts) and...
Nah, I'll use the first link.
https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction (https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction)
Don't believe everything you read on the internet.
The voltmeter reads the difference in Fermi levels between the two contacts:
https://en.wikipedia.org/wiki/Fermi_level (https://en.wikipedia.org/wiki/Fermi_level)
Sometimes it is said that electric currents are driven by differences in electrostatic potential (Galvani potential), but this is not exactly true.[2] As a counterexample, multimaterial devices such as p–n junctions contain internal electrostatic potential differences at equilibrium, yet without any accompanying net current; if a voltmeter is attached to the junction, one simply measures zero volts.[3] Clearly, the electrostatic potential is not the only factor influencing the flow of charge in a material—Pauli repulsion, carrier concentration gradients, electromagnetic induction, and thermal effects also play an important role.
In fact, the quantity called voltage as measured in an electronic circuit has a simple relationship to the chemical potential for electrons (Fermi level). When the leads of a voltmeter are attached to two points in a circuit, the displayed voltage is a measure of the total work transferred when a unit charge is allowed to move from one point to the other. If a simple wire is connected between two points of differing voltage (forming a short circuit), current will flow from positive to negative voltage, converting the available work into heat...
Maybe this is straying too far off topic. The point was supposed to be that a voltmeter doesn't measure electrostatic potential, and what a voltmeter actually measures and what is the definition of potential and voltage are more complicated than we usually think.

The reason for that is that to connect to the silicon you have to create ohmic contacts (nonrectifying contacts) and...
Nah, I'll use the first link.
https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction (https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction)
Don't believe everything you read on the internet.
The voltmeter reads the difference in Fermi levels between the two contacts:
https://en.wikipedia.org/wiki/Fermi_level (https://en.wikipedia.org/wiki/Fermi_level)
Well, wikipedia is on the Internet, so I shouldn't believe it. But maybe you misquoted it.
Besides, the difference in Fermi levels is the barrier potential (if we agree on how to treat the sign). I guess you were the one saying that you cannot read it with a voltmeter.
But if you want a reference that is not on the Internet, you might want to read page 242 of "Semiconductor Physics and Devices" by Donald Neamen.
"This potential difference across the junction cannot be measured with a voltmeter because new potential barriers will be formed between the probes and the semiconductor that will cancel V_bi"
This is the first book I took off my shelf, but I'm pretty sure I could find something along the same line on Sze, or on Streetman, or on Muller Kamins.
Oh my.

The reason for that is that to connect to the silicon you have to create ohmic contacts (nonrectifying contacts) and...
Nah, I'll use the first link.
https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction (https://www.quora.com/Whywecantmeasurethebarrierpotentialexistingacrossapnjunctionbyconnectingvoltmeteracrossthepnjunction)
Don't believe everything you read on the internet.
The voltmeter reads the difference in Fermi levels between the two contacts:
https://en.wikipedia.org/wiki/Fermi_level (https://en.wikipedia.org/wiki/Fermi_level)
Well, wikipedia is on the Internet, so I shouldn't believe it. But maybe you misquoted it.
Besides, the difference in Fermi levels is the barrier potential (if we agree on how to treat the sign). I guess you were the one saying that you cannot read it with a voltmeter.
With no bias, in equilibrium, the Fermi levels on both terminals are equal, so zero voltage. Refer to figure 7.3 of Neamen.
But if you want a reference that is not on the Internet, you might want to read page 242 of "Semiconductor Physics and Devices" by Donald Neamen.
"This potential difference across the junction cannot be measured with a voltmeter because new potential barriers will be formed between the probes and the semiconductor that will cancel V_bi"
You have to wonder if "potential barrier" is the right phrase for an ohmic contact, which should have little or no barrier.
This is the first book I took off my shelf, but I'm pretty sure I could find something along the same line on Sze, or on Streetman, or on Muller Kamins.
Oh my.
So what's your point? Are you saying that there is no net electrostatic potential across the diode terminals?

"This potential difference across the junction cannot be measured with a voltmeter because new potential barriers will be formed between the probes and the semiconductor that will cancel V_bi"
Right. This is where I fully agree with you :)
So what's your point?
What's *your* point to talk about semiconductors in discussion about Dr.Lewin's lecture explaining electromagnetism?
Observer effect of quantum theory while looking at bare PN junction is way too huge stretch off the rails of said discussion. We shall stick to Dr.Lewin's original experiment conditions where circuit element terminals/lugs are made out of conductor (not semiconductor) and voltmeter measures potential difference using Ohms law  by running current through it's internal resistance.
So if such "voltmeter vulgaris" measure 0V on lumped element terminals, we say it's E dot dl is zero and disregard quantum or chemical or whatever phenomena inside it.

I'm not clear what you are talking about. So the two voltmeters in this experiment are not affected by the EMF? Then why do they read different voltages?
Anyway, voltmeters don't read the field caused by electron density. They don't read the electrostatic potential. Take the example of a PN junction diode. It clearly has different electron densities in the P and N depletion region. There is an electrostatic potential difference due to the charge separation. But a voltmeter measures zero volts when connected to the leads of the diode.
If you integrate E dot dl through an unbiased diode, you get a voltage! Diodes violate KVL!
(https://i.stack.imgur.com/SaSH6.jpg)
Obviously using integral of E dot dl has a problem. Circuits with diodes would be another KVL fail according to Dr. Lewin's definition.
This diagram shows a diode with a current flowing trough it. In such a case all semiconductors show a voltage drop that can indeed be measured with a voltmeter.
In a rest state any voltage created on the junction is subtracted back out once the semiconductor connects to the copper pins. If a diode was to create a voltage in such a conduction this would mean i will also have to be capable of pushing current in that direction of voltage. Once you have both you have power being output from the diode and this would violate conservation of energy. That being said it is possible to use a diode to generate a voltage. If you are to heat up one end of a diode and cool the other you can get a strong thermocouple effect that converts some of that heat into output power on the pins. Additionally if this is a glass encapsulated diode or a LED then shining the right wavelengths of light on the diodes junction will also cause it to operate like a solar cell and produce power. In all of these cases external energy had to be put in to make it do that.
Again KVL has no way of dealing with diodes as that's not part of its job. But circuit analysis theory makes it work by having lumped models for all these semiconductor devices (Diodes, BJTs, FETs, IGBTs, SCRs...). There lumped models often contain parametric current sources and volt/amp meters inside of them and they vary in complexity depending on how accurate you need it to be. This allows for circuit analysis to be used on circuits with active components without any issues.
So what does a voltmeter measure? Well it actually measures the current trough its internal resistance and then displays what voltage it takes to push such a current. Notice how in Dr. Lewins example the voltage across the resistors is always defined as a single value. In the same way it is defined to have a single value across the terminals of a voltmeter. Since an ideal resistor has zero physical dimension, means that it is impossible to generate any magnetic EMF across it (It can't be part of a surface area edge as it has no length) and a external electrostatic field can't produce a gradient sharp enough to pull electrons along. So the only "electron pusher" that remains to convince electrons to flow trough the resistor is the difference in charge density on the resistors terminals. The crowded electrons on one end want to get trough to the not as crowded electrons on the other end. Hence why the voltmeter ends up showing a difference in charge density across its terminals.
But it is possible to have EMF generated on a resistor that has physical length. Its basically the combination of a wire and a resistor (And can be lump modeled as such if desired). In the same way a voltmeter that's longer than zero will read EMF across itself. But its only the EMF induced in the section that the voltmeters size occupies. So the larger the voltmeter the more EMF it will show on the display. This just makes things more confusing so we say voltmeters have zero size so they don't read any EMF.

This diagram shows a diode with a current flowing trough it. In such a case all semiconductors show a voltage drop that can indeed be measured with a voltmeter.
In a rest state any voltage created on the junction is subtracted back out once the semiconductor connects to the copper pins. If a diode was to create a voltage in such a conduction this would mean i will also have to be capable of pushing current in that direction of voltage.
Actually, the diagram is in equilibrium, meaning no net current is flowing.
I fully agree that the diode contacts, which are not shown on the diagram, will have their own potential difference, Efield and charge that compensates for the voltage across the diode junction. Maxwell's equations still work.
So I guess the only point of bringing up the diode is to point out that E field is not the only "pusher" of charge. The concentration gradient at the diode junction is another. You have electrochemical potential as well as electrostatic potential and induced EMF that can all move charge. The voltmeter can't tell the difference between them.
So what does a voltmeter measure? Well it actually measures the current trough its internal resistance and then displays what voltage it takes to push such a current. Notice how in Dr. Lewins example the voltage across the resistors is always defined as a single value. In the same way it is defined to have a single value across the terminals of a voltmeter. Since an ideal resistor has zero physical dimension, means that it is impossible to generate any magnetic EMF across it (It can't be part of a surface area edge as it has no length) and a external electrostatic field can't produce a gradient sharp enough to pull electrons along. So the only "electron pusher" that remains to convince electrons to flow trough the resistor is the difference in charge density on the resistors terminals. The crowded electrons on one end want to get trough to the not as crowded electrons on the other end. Hence why the voltmeter ends up showing a difference in charge density across its terminals.
But it is possible to have EMF generated on a resistor that has physical length. Its basically the combination of a wire and a resistor (And can be lump modeled as such if desired). In the same way a voltmeter that's longer than zero will read EMF across itself. But its only the EMF induced in the section that the voltmeters size occupies. So the larger the voltmeter the more EMF it will show on the display. This just makes things more confusing so we say voltmeters have zero size so they don't read any EMF.
So you are still saying that EMF is located at specific segments of the loop. A zero length voltmeter won't show any EMF on the display? I thought it would show the EMF of the whole loop that includes the voltmeter and the test leads and the path connecting the two points you are measuring.
We're all just stuck in an endless loop now. break;

You have electrochemical potential as well as electrostatic potential and induced EMF that can all move charge. The voltmeter can't tell the difference between them.
What does it prove?  That all electrons are equal and you can't mark them?
So you are still saying that EMF is located at specific segments of the loop.
Seems, you are alone denying this here. Remember time when this thread talked about resistive ring (introduced by you BTW)?
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348)

I probably shouldn't dig this thread back up, but wanted to (humbly) share the sim that I worked on such as it is. I've seen some of the comments referring indirectly to my previous posts as trolls, idiot, etc. First off, let me start by saying that I'm not trying to *prove* anything here. I don't care who is right or wrong. I'm just someone who had some time recently to play with openEMS and see if I could reproduce something similar to the Romer experiment and thought I would share it in case someone else might see how cool FDTD sims are. I feel bad for screwing up the initial sims and posting them. It may still have issues, but I think I figured out what was wrong in the first couple of posts. The mesh you see in the geometry viewer is not necessarily how the materials get discretized before being passed on to the FDTD engine (I had forgotten about this). It is really important to use the debugPEC option to view the mesh in Paraview in order to verify materials didn't disappear too much after the engine matches materials up on the mesh subvolumes. This sim is still not the right scale for Romer because it is just too much to discretize a meshed coil with submm wire radius. I still think it is worth sharing. If for no other reason, then just to give some more exposure to the really nice open/free software called openEMS http://www.openems.de/start/index.php (http://www.openems.de/start/index.php)
As for the crazy voltages / currents in my previous post that some obviously found funny, I should have explained more on that. I was testing several different voltages for the excitation with highly scaled up geometry to try and see if I got a log response (I did). I noticed the thing with the feed coil and posted some images while the voltage was something like 10e6 or something crazy like that while trying to make an unrelated point (unconvincingly). Part of the issue may have been with the mesh on that one... or it may have been find at that point... not sure. Anyway, hopefully that makes sense. I understand some of the comments. Sorry if I wasted your time or offended in previous posts.
The images and videos are from a sim with a triangular waveform (like Romer), but with a DC bias (not like Romer). This gives a slow rise DC component in the beginning of the excitation. Note that due to the time it takes to simulate a complex geometry like this, the excitation is at a higher frequency (above SRF and much higher than Romer). I also ran the sim for 1 cycle below SRF (still much shorter wavelength than Romer) and will post voltage measurements for that. The videos are generated with Paraview. Also another very nice free software.
SRF of the coil was determined by excitation with a bandwidthlimited Gaussian pulse which generates a nice flat stimulus in the frequency domain (think using a wideband noise source with an FFT spectrum analyzer). The simulation generates time domain voltages / currents in a text file. If you process that with FFT, then you can analyze arbitrary materials / structures in the frequency domain.
Another mucheasiertosimulatewithamazingaccuracy example would be a planar microstrip filter made of copper, vias, dielectric, airbox, etc.
Time steps in the videos should match time steps in the plots.
https://www.youtube.com/watch?v=84wCYzqA5a8 (https://www.youtube.com/watch?v=84wCYzqA5a8)
https://www.youtube.com/watch?v=Y57rDnQfjlw (https://www.youtube.com/watch?v=Y57rDnQfjlw)
Another thing that someone might find interesting... was talking to a guy who does almost nothing but RF sims. He told me about another method. MoM (method of moments) that can be used to mesh geometries and convert them to equivalent reactive components for simulating in a standard analytical circuit simulator (e.g. Spice). I couldn't find any opensource projects that looked like something worth investigating. Would be very interested this if someone is aware of any.

radioactive, I wanted to double check your previous simulation and posts  they all gone, deleted. This is disrespect to people who spent their time answering.
I'm just someone who had some time recently to play with openEMS and see if I could reproduce something similar to the Romer experiment
Thank you for investing your time trying. You shall show time and voltage units used in X&Y scales. Now we can only guess  excitation pulse period is 100 seconds, 100 femtoseconds or what? It is very important to simulate experiment as close as possible to the original which is pure electromagnetism because of huge solenoid and comparably slow impulse where electric fields and antenna effects can be ignored. Your simulations seems far from that. Besides my suggestion to add core material to form solenoid, I would like to remind following comment as well:
So you need to apply a similar voltage step response across your solenoid coil (Not just a pulse). Also your time scale appears to be very short in the simulation. The pulse you applied seams to last only a few picoseconds, this gives it a bandwidth of >100GHz and hence why you get funny behavior as you are mostly simulating radio waves traveling around your scene. The whole simulation only lasting what appear to be around half a nanosecond. My experiment had the pulse last 500 microseconds so about 1 000 000 times longer than your simulation time.

Ogden,
Besides my suggestion to add core material to form solenoid,
See the Romer paper where "iron core" is specifically mentioned (and not used).
As for the instantaneous step, I think this would be a good simulation for you to try now that you have the source. You might be surprised at the results.

Besides my suggestion to add core material to form solenoid,
See the Romer paper where "iron core" is specifically mentioned (and not used).
I did miss that, apologies. Actually no big deal because see the Romer's paper where it is said that solenoid is wound with 444 turns of wire, it's inductance is 1.8 mH (quite big number) and test frequency is 300 Hz. What is inductance of your "solenoid"? What is frequency of your signal?
I think this would be a good simulation for you to try now that you have the source.
You are so kind, but thank you. I think would be good if you fix/update your simulation. First thing you shall fix is presentation of your waveform graphs:
You shall show time and voltage units used in X&Y scales. Now we can only guess  excitation pulse period is 100 seconds, 100 femtoseconds or what?

<Knock knock>
Is this thing still on?
The super demo has long bothered me since I first watched it back in 2004 or so (when I was first learning Physics). I recently came back to it a few months ago and spent many late nights reading physicsforums threads of people arguing over it. Even though Mehdi (and Mabilde) are ultimately wrong and misleading many people, I'm really happy about all the drama surrounding this because it surfaced up all the extra pieces I needed to understand (I feel like I'm at maybe 80~90 % comfortability with this now), namely Lewin's response videos (which included the crucial mesh analysis), the Romer paper, the McDonald paper (which admittedly includes some Physics concepts beyond my current level but includes crucial footnotes and KVL history), the Feynman chapter, and finally the Belcher writeup.
I spent a lot of time working on this by myself and then found this thread fearing it would be more of the same in Electroboom's comment section but I was happy to find some voices of reason that supported my conclusions in sredni and bsfeechannel. Thank you for your patience in these past 19 pages of threads.
I tried to organize my thoughts about the whole thing here https://grumpyengineering.wordpress.com/ (only one post there for now) if you want to read them.

I tried to organize my thoughts about the whole thing here https://grumpyengineering.wordpress.com/ (only one post there for now) if you want to read them.
I'm looking forward to reading more of your thoughts if you continue. Very easy to read. I also echo your thanks to sredni and bsfeechannel, and especially Lewin for their responses/patience to the challenge put forth. Combing those responses with working on an EM sim and being able to see the mag/dir of the fields over time/space definitely gave me a much better intuitive feel for it.

I tried to organize my thoughts about the whole thing here https://grumpyengineering.wordpress.com/ (https://grumpyengineering.wordpress.com/) (only one post there for now) if you want to read them.
When you talk about advanced stuff like Faraday's law, you shall not ignore other laws like law of conservation of energy (https://en.wikipedia.org/wiki/Conservation_of_energy).
Pay close attention to following post made by proponent of Dr.Lewin (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348) to see where exactly you and Dr.Lewin made mistake.

I tried to organize my thoughts about the whole thing here https://grumpyengineering.wordpress.com/ (https://grumpyengineering.wordpress.com/) (only one post there for now) if you want to read them.
When you talk about advanced stuff like Faraday's law, you shall not ignore other laws like law of conservation of energy (https://en.wikipedia.org/wiki/Conservation_of_energy).
I agree.
Pay close attention to following post made by proponent of Dr.Lewin (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348) to see where exactly you and Dr.Lewin made mistake.
I don't see an issue here, but feel free to point it out if you like.

Pay close attention to following post made by proponent of Dr.Lewin (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348) to see where exactly you and Dr.Lewin made mistake.
I don't see an issue here, but feel free to point it out if you like.
Your (and Dr.Lewin's) equation does not separate EMF (energy) source from load, incorrectly and blatantly saying that KVL is as follows:
(https://s0.wp.com/latex.php?latex=%5Coint+%5Cvec+E+%5Ccdot+d%5Cvec+l+%3D+0&bg=ffffff&fg=333333&s=4)
Kirchsoffs CIRCUIT law requires circuit consisting of energy source and load. Correct equation would be:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570254;imag)

Pay close attention to following post made by proponent of Dr.Lewin (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1961348/#msg1961348) to see where exactly you and Dr.Lewin made mistake.
I don't see an issue here, but feel free to point it out if you like.
Your (and Dr.Lewin's) equation does not separate EMF (energy) source from load, incorrectly and blatantly saying that KVL is as follows:
(https://s0.wp.com/latex.php?latex=%5Coint+%5Cvec+E+%5Ccdot+d%5Cvec+l+%3D+0&bg=ffffff&fg=333333&s=4)
It's not "my" equation. It's how Lewin defines KVL. I'm not sure why you think it can't be rewritten to explicitly show sources and loads. It would look like this.
(https://s0.wp.com/latex.php?latex=%5Coint+_%7Bsources%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl+%2B+%5Coint+_%7Bloads%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl%3D+0+&bg=ffffff&fg=333333&zoom=2)
Kirchsoffs CIRCUIT law requires circuit consisting of energy source and load.
Not really. I can apply KVL just fine to a trivial network of resistors with no energy source and still get the correct answers.
Correct equation would be:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=570254;imag)
Actually, I think there's a minus sign missing on the right side of the above equation, due to Lenz law, but I'm not really sure what you're arguing here. Are you saying that Lewin's definition of KVL doesn't work in this circuit? If so then yes, I agree, that's just about his entire point!

It's not "my" equation. It's how Lewin defines KVL. I'm not sure why you think it can't be rewritten to explicitly show sources and loads. It would look like this.
(https://s0.wp.com/latex.php?latex=%5Coint+_%7Bsources%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl+%2B+%5Coint+_%7Bloads%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl%3D+0+&bg=ffffff&fg=333333&zoom=2)
Right. BTW where I did say that I think it can't be rewritten? Look, whole idea of "KVL does not work" proof is based on statement that integral of E.dl for the loop equals zero, thus EMF equals zero which is as Dr.Lewin say impossible. Indeed it is impossible  because equation is incomplete, thus statement is futile. You just corrected it by writing EMF + ( I*R ) = 0. If you agree then we are done. You disproved Dr.Lewin.

It's not "my" equation. It's how Lewin defines KVL. I'm not sure why you think it can't be rewritten to explicitly show sources and loads. It would look like this.
(https://s0.wp.com/latex.php?latex=%5Coint+_%7Bsources%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl+%2B+%5Coint+_%7Bloads%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl%3D+0+&bg=ffffff&fg=333333&zoom=2)
Right. BTW where I did say that I think it can't be rewritten?
When you said "Your (and Dr.Lewin's) equation does not separate EMF (energy) source from load". I suppose you didn't explicitly say it can't be rewritten, but you seemed to be implying that for some reason it couldn't. Anyways, I'm glad we agree on this.
Look, whole idea of "KVL does not work" proof is based on statement that integral of E.dl for the loop equals zero, thus EMF equals zero which is as Dr.Lewin say impossible.
In a typical batteries+resistors type circuit, the EMF is the batteries, and they are included in the E•dl integration. I wrote this out explicitly in my last post where the source and loads were specified in separate integrations (i'm not even sure if this is proper notation but I think you get the point). Saying that E•dl equals zero means the EMF must equal zero is not correct, and I don't believe Lewin ever said that (please link with timestamp if he did). Rather, the point is that using KVL (as defined by Lewin as E•dl = 0) will yield the wrong answer in the presence of time varying magnetic flux, and the reason it yields the wrong answer is that now we have an EMF that doesn't come from an electric field.
Indeed it is impossible  because equation is incomplete, thus statement is futile.
Of course it's incomplete, that's Lewin's point. And the way to complete it is to update it to Faraday's law. If you disagree I'd ask you how you would complete it.
You just corrected it by writing EMF + ( I*R ) = 0. If you agree then we are done. You disproved Dr.Lewin.
As I mentioned in the previous post, there was a minus sign missing. In the drawing, the assumption is we're looking at a specific point in time where the emf from the solenoid is 1V. The value of the evenly distributed resistance will determine the value of the current (if it's total 1ohm, we get 1A, etc.). Either way, if you start from Faraday's law, you have 1V on both sides of the equation (both sides better be the same value otherwise we either screwed up or Faraday's law is somehow wrong). If you move that 1V over to the left then you're effectively saying 1V  1V = 0V. Not a very enlightening statement and the spirit behind Lewin's "5 + 3  8 = 0" video.
I'm wondering if maybe this will help. Here I've rearranged Faraday's law for the bseechannel example to have the emf on left side (the source), and the load on the right side. Note both sides are still equal to E•dl and nonzero, and as always you can subtract the RHS side from both sides if you want to see zero there.
(https://ibin.co/w800/4RCvdo3HWTGP.png)
In addition to asking how you would complete Lewin's KVL (Int E•dl = 0) to make it correct (I agree that it is not universally correct), I think I should ask you to clarify exactly what it is that you think Lewin has done incorrectly so we can make some progress in understanding each other.

Of course it's incomplete, that's Lewin's point. And the way to complete it is to update it to Faraday's law. If you disagree I'd ask you how you would complete it.
That's the whole point  you cannot use incomplete equation to prove anything! Integral E.dl = 0 of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*. You completed it for me:
(https://ibin.co/w800/4RCvdo3HWTGP.png)
In addition to asking how you would complete Lewin's KVL (Int E•dl = 0) to make it correct (I agree that it is not universally correct), I think I should ask you to clarify exactly what it is that you think Lewin has done incorrectly so we can make some progress in understanding each other.
Move right side (load) of equation you just completed to left side and I am done showing where Dr.Lewin was wrong. It will be in front of your eyes contradicting with what you say in your blog:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=605005;image)

Of course it's incomplete, that's Lewin's point. And the way to complete it is to update it to Faraday's law. If you disagree I'd ask you how you would complete it.
That's the whole point  you cannot use incomplete equation to prove anything! Integral E.dl = 0 of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*. You completed it for me:
(https://ibin.co/w800/4RCvdo3HWTGP.png)
In addition to asking how you would complete Lewin's KVL (Int E•dl = 0) to make it correct (I agree that it is not universally correct), I think I should ask you to clarify exactly what it is that you think Lewin has done incorrectly so we can make some progress in understanding each other.
Move right side (load) of equation you just completed to left side and I am done showing where Dr.Lewin was wrong. It will be in front of your eyes contradicting with what you say in your blog:
If I move the right side of the equation to the left hand side, it will look like this:
(https://ibin.co/w800/4RDW0KhA0NN6.png)
So what?
It doesn't contradict anything I wrote in that blog. The point there is that something can't be simultaneously zero and non zero. This is how Lewin points out that EMFs don't have to come from batteries and then introduces Faraday's law. Maybe it will help if you look at this to get the full picture:
(https://ibin.co/w800/4RDKta0bGGlv.png)
I feel like perhaps your disconnect is that you feel that the EMF in the Lewin circuit must be able to be part of the int E•dl term, but it never will be because it comes from a time varying magnetic flux. int E•dl is *not* (necessarily) the same thing as the sum of all EMFs and voltage drops in the loop! It is however *always* equal to the negative time rate of change of the magnetic flux, which in this demo is the *only* emf, i.e. the only thing causing anything to happen (this is Faraday's law, and I am just assuming all this time that you agree with Faraday's law, please let me know if this is not the case). Think of the changing magnetic flux as the source, and int E•dl as the way you can figure out what is happening in the load. In this circuit we've been talking about int E•dl is nothing but currents through resistors. You can add a real battery in there and then you'll have two different kinds of EMF but that's not what we've been talking about up til now.
I'll ask once more for you to clearly articulate what it is that you think that Lewin got wrong. Please don't just respond to something I said here, state your objection clearly so that I can respond to it (tomorrow, we're in very different time zones). I'm still not totally clear on what your objection is but it feels like we might be able to come to an understanding.

The point there is that something can't be simultaneously zero and non zero.
It can  when "something" is one thing in one case and completely different in another.
Take following as my objection you asked for: you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's.
Shall I repeat & emphasize : Integral E.dl part of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*. You simply can't equal two (integrals), because they "look the same" (your words BTW). Following equation describes circuit of Dr.Lewin's experiment inner loop:
(https://ibin.co/w800/4RDW0KhA0NN6.png)
Don't you find it similar to equation of KVL you wrote?
(https://s0.wp.com/latex.php?latex=%5Coint+_%7Bsources%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl+%2B+%5Coint+_%7Bloads%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl%3D+0+&bg=ffffff&fg=333333&zoom=2)
I assume you agree to both. Me too.

OK now we're getting somewhere, i think (i hope!). If I understand you correctly, you believe that Faraday's law implies a violation of conservation of energy!
"you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's." I would call this a strawman, unless you can point me to where Lewin said that Maxwell's equations require ignoring conservation of energy.
It's his KVL that violates conservation of energy in his experiment because it can't possibly account for the source of energy as it knows nothing about magnetic flux!
I'm not sure I'm going to be able to bring you over without repeating things I've already said in the past few posts, but I'll try.
The point there is that something can't be simultaneously zero and non zero.
It can  when "something" is one thing in one case and completely different in another.
but.. it's not. int E•dl is int E•dl is int Ed•dl. It has the same meaning in both Lewin's KVL and Faraday's law. It means you go around a loop adding up each incremental bit of E field you encounter along your path. It doesn't matter whether it's an E field from a battery or an E field in a resistor or an E field arising from a changing magnetic flux. Do you believe that int E•dl has somehow a different meaning in the two equations?
Take following as my objection you asked for: you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's.
Shall I repeat & emphasize : Integral E.dl part of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*.
I would say that as applied to this experiment, Faraday's law equates Int E•dl with the source (negative time rate of change of magnetic flux through the loop) of energy. It seems like you are unwilling to accept an EMF that doesn't arise from a source that is clearly related to an E field being maintained between two points, and that's what's causing you trouble, but that's the reality that Faraday describes.
You simply can't equal two (integrals), because they "look the same" (your words BTW).
I think you are misunderstanding my point. Let's use completely different symbols to hopefully make it clear. Let's look at two equations:
Y = 0
Y = F(x)
In equation one, we are saying that Y = 0. In equation two we are saying Y is equal to some function of x. There is only one way both can be valid and that is the case where F(x) = 0 for any value of x. But we are asserting that F(x) also takes on nonzero values. Therefore Y = 0 is not a universal relation but just one possible point on the real general case of Y = F(x). 0 is just one possible value in the range of the function.
If it helps, think of Y as your height above the ground, and F(x) as a function that gives your current height above the ground. You might spend days, weeks or months walking around thinking that F(x) always equals 0 because you're always firmly on the ground. Then you get in an elevator, or an airplane for the first time. F(x) is no longer zero, and you must conclude that Y = 0 is a special case and not a general relation. This is mathematically, logically the same argument with different symbols.
Following equation describes circuit of Dr.Lewin's experiment inner loop:
(https://ibin.co/w800/4RDW0KhA0NN6.png)
Don't you find it similar to equation of KVL you wrote?
(https://s0.wp.com/latex.php?latex=%5Coint+_%7Bsources%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl+%2B+%5Coint+_%7Bloads%7D+%5Cvec+E+%5Ccdot+%5Cvec+dl%3D+0+&bg=ffffff&fg=333333&zoom=2)
I assume you agree to both. Me too.
Yes, and I had to use Faraday's law to get there. Lewin's KVL could not have done it. That is one of his points.
[Edit: few clarifying words]
[Edit2: fix broken quoting]

OK now we're getting somewhere, i think (i hope!). If I understand you correctly, you believe that Faraday's law implies a violation of conservation of energy!
"you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's." I would call this a strawman, unless you can point me to where Lewin said that Maxwell's equations require ignoring conservation of energy.
It's his KVL that violates conservation of energy in his experiment because it can't possibly account for the source of energy as it knows nothing about magnetic flux!
Seems, you did not get it or just pretend that you do not understand what I did mean with that sentence.
Ok. Next try. I do not talk about abstract KVL and Maxwell equation "cases". I talk about equations that describes circuit of experiment. Everything seemingly is ok with KVL simple int E.dl = 0, yet I would prefer to split it into EMF source and load, as you already did  thank you for that. Problem arises when Dr.Lewin use plain Maxwell's equation and say that it miraculously tells everything about inner loop of his experiment. I disagree. Maxwell's equation is just EMF source part! Where's physics of load (resistors) in Maxwells equation? If you leave it like that, then it is indeed violation of conservation of energy. Plain Maxwell's equation can be used only to describe superconductive ring (w/o embedded resistors) placed in changing magnetic flux.
I would say that as applied to this experiment, Faraday's law equates Int E•dl with the source (negative time rate of change of magnetic flux through the loop) of energy. It seems like you are unwilling to accept an EMF that doesn't arise from a source that is clearly related to an E field being maintained between two points, and that's what's causing you trouble, but that's the reality that Faraday describes.
Oh my. You better take care of your own troubles first, ok? Seems, you are unwilling to accept that EMF energy is dissipated in the embedded resistors of the inner loop.

If you don't believe Maxwell's equations always apply, or you think they violate conservation of energy, then I'm afraid we can't go anywhere from there. Maxwell's equations are axiomatic to any discussion about electricity and magnetism regardless of circuit configuration (regardless of whether the elements of the circuit can be represented as lumped elements or not) and they always hold[1].
Still, thank you for the conversation. It's been helpful to me.
[edit: added bit in the parenthesis]
[edit2: minor clarifying edit]
[edit3: add bit about QED]
[1] Except, apparently in the domain of Quantum Electrodynamics, which is not what we're talking about here.

If you don't believe Maxwell's equations always apply, or you think they violate conservation of energy, then I'm afraid we can't go anywhere from there.
LOL. Here we go. Again. When out of arguments  just state that debate opponent does not understand Maxwell's equations. :horse:
I never said or implied that I do not believe Maxwell's equations. Also I never said that they violate law of conservation energy. What I did say that you can't use EMF source equation alone to describe system of EMF source and load. If you cannot comprehend such a simple concept then further discussion indeed is pointless. Funny that you even did write proper equation which shall be used to describe/analyze circuit of experiment against "KVL apply to circuit or not", but when you most likely realized that it would destroy your whole system of beliefs/reasoning, you decided to completely ignore everything about it:
(https://ibin.co/w800/4RDW0KhA0NN6.png)

LOL. Here we go. Again. When out of arguments  just state that debate opponent does not understand Maxwell's equations. :horse:
I never said or implied that I do not believe Maxwell's equations. Also I never said that they violate law of conservation energy.
You said:
"Maxwell's equation is just EMF source part! Where's physics of load (resistors) in Maxwells equation? If you leave it like that, then it is indeed violation of conservation of energy. Plain Maxwell's equation can be used only to describe superconductive ring (w/o embedded resistors) placed in changing magnetic flux."
I can't go anywhere from there. If you think that you can write something like "Plain Maxwell's equation can be used only to describe ..." then either you think that there are more fundamental equations or you simply don't understand how they work. Maxwell's equations are the starting point. Everything else can be derived and approximated from them. This is accepted science for the last 100+ years.
It's clear that you disagree with me and that's fine. I'm willing to end this discussion in disagreement. I don't think there's anything left for me to say, but as I said I appreciate the discussion.
p.s. the load (resistors) are in the int E•dl. it's all up there in the equations i've already posted.
[edit: p.p.s. i'd been waiting for the emoticons to come out. not a device i'd employ if I wanted to be taken seriously]

I can't go anywhere from there.
Yes. Please. Stop this :blah: nonsense of pretending that you do not understand what I mean. Our discussion looks like broken record.

LOL. Here we go. Again. When out of arguments  just state that debate opponent does not understand Maxwell's equations. :horse:
You don't. But that's not your fault. Maxwell's equations show how Nature is much weirder than we may conceive. You'll have to reboot your brain to understand it. Just give it time. We all had our Maxwell crisis.
You're just having yours in public.

LOL. Here we go. Again. When out of arguments  just state that debate opponent does not understand Maxwell's equations. :horse:
You don't. But that's not your fault. Maxwell's equations show how Nature is much weirder than we may conceive. You'll have to reboot your brain to understand it...
Or in my case literally spend a few months of sleepless nights reading/watching everything on the topic. There's still a gremlin in my understanding but I'll start a different thread for that one.
I can't help but feel all of the drama around this could have been avoided if electronics educators did a better job of adding caveats and asterisks to their materials and explanations. I went to UC Berkeley and I'm pretty sure not a single professor ever uttered the words "lumped circuit abstraction" in my entire undergrad career. Agarwal is doing God's (or rather Feynman's) work.

I can't go anywhere from there.
Yes. Please. Stop this :blah: nonsense of pretending that you do not understand what I mean. Our discussion looks like broken record.
Do not waste your time.

I can't help but feel all of the drama around this could have been avoided if electronics educators did a better job of adding caveats and asterisks to their materials and explanations. I went to UC Berkeley and I'm pretty sure not a single professor ever uttered the words "lumped circuit abstraction" in my entire undergrad career. Agarwal is doing God's (or rather Feynman's) work.
Exactly.
Kirchhoff is normally taught in high school. Maxwell is mentioned only en passant. No one says that Maxwell is the theory underlying Kirchhoff's laws. When you get to college, you are taught a lot of apparently meaningless and complicated math. No one says that this will be in preparation for Maxwell and other theories. Then they teach you electromagnetism mercilessly without explaining that the fluxing Kirchhoff is a special case of Maxwell.
Lewin is a critic of that way of teaching, given how that cripples understanding the basic concepts.
We could suggest a change. Teach a simplified version of calculus and vector analysis in high school. This is perfectly possible. My video "Calculus for young players" is aimed at highschoolers. Then teach the basics of Maxwell, explaining that Kirchhoff is a special case of that theory.
When at college, they should say, now that you are going to be an engineer, you will be responsible for designing serious things. So you are going to learn this stuff with all the rigor these theories require. You'll also learn circuit analysis with even more detail and rigor, always having in mind that it is a special case of electromagnetism.
That would avoid the anger everybody feels when they discover the truth years later.

This is proabobly the most important realization you made Mhz:
https://grumpyengineering.wordpress.com/
If you still disagree with the above I would love to hear from you, but I believe, most of the confusion results from disagreements about what KVL is.
Nobody in this thread is trying to prove that Maxwells equations are wrong, stop blaming people for that.
Most of the arguing between the "Kirchoff" and "Maxwell" sides is due to both sides having a different idea of what KVL is. I fully agree that if KVL is what Dr. Lewin explains it as being then its garbage as soon as you have changing magnetic fields. I have no idea where he got that definition of KVL, everywhere i see it defined as the flowing:
The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero
It explicitly mentions all voltages, this includes the electric field as well as the EMF (I think we all agree EMF is a voltage). Also notice that it mentions an algebraic sum (This is not an integral!) since KVL is not a law of the universe but a tool for analyzing circuit mesh models.
Both the "Kirchoff" and "Maxwell" sides are correct! The only only reason that we are arguing is because the so called "Maxwell" side is using a less useful interpretation of KVL. The people on the "Kirchoff" side are not denying anything about Maxwells equations, the only thing this side is trying to say is that you can use KVL to solve Lewins paradoxic circuit just fine i you use KVL correctly. You indeed CAN NOT USE Kirhoffs laws for everything, but this particular circuit is not such a case.
The "Kirchoff" side should actually be named "Kirchoff and Maxwell" side. We are happy to use one or the other rather than swear by Maxwell only, just a matter of the right tool for the job. Is there something wrong with that?

Nobody in this thread is trying to prove that Maxwells equations are wrong
But that is exactly what you do when you say that you can solve Lewin's circuit with Kirchhoff. Which, by the way, is not Lewin's. You find that circuit anywhere because it defines the phenomenon of induction.
Your claims lead immediately to a logical contradiction which indicates that your reasoning is false. And that's why people keep "blaming" you, or better, warning you.

Circuit analysis makes use of equations derivated from Maxwells equations in order to make inductors and capacitors work with Kirchoffs circuit laws. Is there some law that forbids the use of Maxwells equations in anything else but there raw form? Somehow making anything they are used in automatically wrong even if it gives the same result?
So is it a problem that Kirhhoffs cirucit laws work in lumped circuit meshes? Or is it a problem that circuit modeling has to be used to link the real world with circuit meshes?

This is proabobly the most important realization you made Mhz:
https://grumpyengineering.wordpress.com/
Quote
If you still disagree with the above I would love to hear from you, but I believe, most of the confusion results from disagreements about what KVL is.
Nobody in this thread is trying to prove that Maxwells equations are wrong, stop blaming people for that.
On the contrary, that's exactly where the previous discussion with ogden led, with them concluding that Maxwell's equations are only correct in specific situations (superconducting rings, I believe is what was said). That's another way of saying that sometimes they are wrong.
Most of the arguing between the "Kirchoff" and "Maxwell" sides is due to both sides having a different idea of what KVL is. I fully agree that if KVL is what Dr. Lewin explains it as being then its garbage as soon as you have changing magnetic fields. I have no idea where he got that definition of KVL, everywhere i see it defined as the flowing:
Quote
The algebraic sum of all the voltages around any closed loop in a circuit is equal to zero
the problem with this definition, what I keep calling the "modified" KVL, which is what I think most of us think of as the "real" KVL, is it starts to break down in situations where you're dealing with nonlumped elements. As I mentioned in the blog post, there is nothing keeping us from modeling things with lumped elements (we'd have to add a mutual conductance in the inner loop) to get thngs to sum to zero in a nice KVL way but at the expense of incorrectly localizing the effect.
It explicitly mentions all voltages, this includes the electric field as well as the EMF (I think we all agree EMF is a voltage). Also notice that it mentions an algebraic sum (This is not an integral!) since KVL is not a law of the universe but a tool for analyzing circuit mesh models.
right! the algebraic sum is the key to pointing out that it only works with lumped circuits, or circuits modeled with lumped elements.
Both the "Kirchoff" and "Maxwell" sides are correct! The only only reason that we are arguing is because the so called "Maxwell" side is using a less useful interpretation of KVL. The people on the "Kirchoff" side are not denying anything about Maxwells equations, the only thing this side is trying to say is that you can use KVL to solve Lewins paradoxic circuit just fine i you use KVL correctly. You indeed CAN NOT USE Kirhoffs laws for everything, but this particular circuit is not such a case.
I'd invite you to redraw the diagram and use the "modified" KVL on this circuit. See if you can model it in a way that doesn't falsely localize the effect of the mutual inductance but that allows you to get the correct answer with the "modified" KVL. It would help if you post the drawing of the updated model for us.
The "Kirchoff" side should actually be named "Kirchoff and Maxwell" side. We are happy to use one or the other rather than swear by Maxwell only, just a matter of the right tool for the job. Is there something wrong with that?
Nothing wrong with that at all. The real lesson of all this, to me at least, is that the "modified" KVL only works with lumped circuits. If Lewin had introduced the concept of lumped circuit analysis (as described expertly by Feynman and Agarwal) explicitly after the super demo I think there would be probably be a lot less confusion.

I'd invite you to redraw the diagram and use the "modified" KVL on this circuit. See if you can model it in a way that doesn't falsely localize the effect of the mutual inductance but that allows you to get the correct answer with the "modified" KVL. It would help if you post the drawing of the updated model for us.
I already did that in the very first few posts on this thread:
https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312 (https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/msg1945312/#msg1945312)
You simply calculate the contributions each wire segment is providing and distribute the inductance accordingly (Note these are all coupled inductors since the all interact with the same flux). This way only parts of the circuit that are not interesting get lumped up while preserving all the points of interest along with there voltages. If you suddenly want to know whats happening half way along a wire you simply represent it as two lumps with correct proportions to expose the point we want.
Calculating the inductance is easy in this case because the circuit is very symmetrical and there is high coupling between the wires due to them flowing the same path. Had the wires followed arbitrary complex 3D paths trough space it would have been much harder to model. We would need to go trough Maxwell with fancy convoluted 3D space intergals in order to get the magical inductance values for the equivalent circuit. Or if we have access to the physical circuit simply measure them with a impedance analyzer and plonk the numbers into the equivalent circuit. No matter what the process is you end up with a cirucit mesh that acts like the real cirucit, but can be used with KVL just fine since its a lumped circuit mesh.
Modeling has nothing to do with KVL or even electronics. Its simply a process of turning a real thing into math that acts like the real thing so that we can run calculations or simulations on it. Its done with all sorts of things, be it mechanical, structural, thermal etc. These models all have there limitations. Just as a thermal model of a house will not be accurate if you try to simulate ambient being 10 000 °C in the same way your equivalent circuit will not be accurate at RF frequencies unless specifically modeled for it.

On the contrary, that's exactly where the previous discussion with ogden led, with them concluding that Maxwell's equations are only correct in specific situations (superconducting rings, I believe is what was said). That's another way of saying that sometimes they are wrong.
Typical strategy of forum trolls and "sofa experts" BTW  take just single sentence out of context, twist it as much as possible, draw conclusions out of this new "twisted meaning" to prove own agenda.
For those unaware this is what I ACTUALLY said:
I do not talk about abstract KVL and Maxwell equation "cases". I talk about equations that describes circuit of experiment. Everything seemingly is ok with KVL simple int E.dl = 0, yet I would prefer to split it into EMF source and load, as you already did  thank you for that. Problem arises when Dr.Lewin use plain Maxwell's equation and say that it miraculously tells everything about inner loop of his experiment. I disagree. Maxwell's equation is just EMF source part! Where's physics of load (resistors) in Maxwells equation? If you leave it like that, then it is indeed violation of conservation of energy. Plain Maxwell's equation can be used only to describe superconductive ring (w/o embedded resistors) placed in changing magnetic flux.

I disagree with the thread title.
Walter Lewin used to be a master. Then he started flinging poo at good people.
So i vote we take Master status from him. :DD

I disagree with the thread title.
Walter Lewin used to be a master. Then he started flinging poo at good people.
So i vote we take Master status from him. :DD
So is that why this thread travels toward flinging poo AGAIN emulating the Master? :palm:
The last few pages and a lot of the thread have been really interesting and in between the poo this thread is more informative than my Uni lecturers way back in the dim dark past ever were.

@berni Ah, perfect. Ok so my point is this, you've modeled the circuit with lumped elements and that gives something that looks correct, but if you set this experiment up in real life, do you really think you'll measure any significant voltage across any of L2, L3, L4 or L5 like spice would tell you is there? The coupled flux isn't confined in those points so you won't. This is where our "modified" KVL breaks down.
We saw Mehdi struggle with this in his first video. This is one of the biggest points of confusion, that there must be "voltage in the wire". I don't remember who, bsfeechannel?, was earlier arguing that this can't be modeled 100% correctly in spice because spice only knows about lumped elements. No matter how many inductors you split the mutual inductance into in spice, it will give an incorrect answer if you use it try to use it to measure a voltage along the wire. The reason is that in the actual experiment, there aren't any lumped inductors, the linked flux in the secondary is not confined to any specific two terminals.
Also, I'd argue that the leads should not be modeled as mutual inductance as they aren't supposed to link any of the flux in the center loop. (This is how Romer defines the experiment).
p.s. I'm not going to be bothering to respond to others that aren't attempting to have a productive conversation
[edit: clarify who I'm talking to since a few posts happened in the interim]

Ok so my point is this, you've modeled the circuit with lumped elements and that gives something that looks correct, but if you set this experiment up in real life, do you really think you'll measure any significant voltage across any of L2, L3, L4 or L5 like spice would tell you is there? The coupled flux isn't confined in those points so you won't.
So you say that Kirk T. McDonald is wrong in chapter "2.3 Comments" (page 10) (http://www.physics.princeton.edu/~mcdonald/examples/lewin.pdf)? Please tell where and why he is wrong. Prove him wrong.
Excerpt:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=605980;image)

Ok so my point is this, you've modeled the circuit with lumped elements and that gives something that looks correct, but if you set this experiment up in real life, do you really think you'll measure any significant voltage across any of L2, L3, L4 or L5 like spice would tell you is there? The coupled flux isn't confined in those points so you won't.
So you say that Kirk T. McDonald is wrong in chapter "2.3 Comments" (page 10) (http://www.physics.princeton.edu/~mcdonald/examples/lewin.pdf)? Please tell where and why he is wrong. Prove him wrong.
Excerpt:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=605980;image)
Did you even read that section?
Suppose a voltmeter were connected to two points on the upper wire between resistors 1
and 2, as shown in the sketch below. The voltmeter loop is not coupled to the solenoid, so
there is no (or extremely little) EMF induced in this loop, and hence I1 = 0, and the meter
reading would be Vmeter = 0.
This agrees with what @mhz said.
In that section, Dr. McDonald is pointing out that a voltmeter does not read the difference in scalar potential. He is making up his own definitions of "voltage drop" and "EMF" in the presence of a changing magnetic field.

Do you see the above two equations as equivalent term by term?
I did say "Don't you find it similar". I did not say equivalent, especially term by term. One more illustration of troll & "coach expert" tactics. You just cherrypick out of context whatever you find convenient for you, ignoring what I was ACTUALLY talking about: circuit that has EMF source and load, that both equations describes such and are similar in such sense.

Besides, the difference in Fermi levels is the barrier potential (if we agree on how to treat the sign). I guess [NOTE: I should have written 'thought', instead of 'guessed') you were the one saying that you cannot read it with a voltmeter.
With no bias, in equilibrium, the Fermi levels on both terminals are equal, so zero voltage. Refer to figure 7.3 of Neamen.
I was talking about the Fermi levels of the separated materials, what Neamen call 'intrinsic Fermi levels' when referring to the compound structure. At thermodynamic equilibrium there are no longer Fermi levelS. But yes, out of equilibrium the one Fermi level of the structure splits in separate levels and the voltage corresponding to that difference is what is measured.
You have to wonder if "potential barrier" is the right phrase for an ohmic contact, which should have little or no barrier.
I guess it is the right denomination, since there are potential barriers nonetheless. In some cases they are not very hard to overcome thanks to the field associated with the charge developed at the contact surface , in others they are very high and steep, but electrons can easily tunnel through them. See Muller and Kamins for an explanation of both versions (section 3.4 in the second edition).
So what's your point? Are you saying that there is no net electrostatic potential across the diode terminals?
I am saying that whatever potential is there, it will be canceled by the contact potentials created by the placement of the probes.
But anyway, by putting the limelight on other sources of emf, you raised an interesting point that might benefit the original discussion: could it be that the emf due to changing dB/dt is different from all other emfs? Faraday's law seems to point there.

Did you even read that section?
Did you? Carefully enough?
Suppose a voltmeter were connected to two points on the upper wire between resistors 1
and 2, as shown in the sketch below. The voltmeter loop is not coupled to the solenoid, so
there is no (or extremely little) EMF induced in this loop, and hence I1 = 0, and the meter
reading would be Vmeter = 0.
This agrees with what @mhz said.
In that section, Dr. McDonald is pointing out that a voltmeter does not read the difference in scalar potential.
From which planet did you just arrive? We are not talking about scalar potentials but EMF. @mhz said that voltmeter will not measure any EMF as Spice do.

To not repeat a certain arrangement i will also answer this for both definitions of voltage:
A) For definition "Voltage is the integral of all forces pushing on electrons along a given path connecting two points":
The inductors L2 L3 L4 L5 have zero voltage across them at all times (Zero resistance). Any EMF voltage induced in the wire by the magnetic field is instantly countered by the charge separation of electrons.
B) For definition "Voltage is the difference in charge density between two points" (This is what real life voltmeters show)
The inductors L2 L3 L4 L5 have a voltage drop that sums up to the same voltage as the total voltage drop on the resistors. This voltage in the wire is caused by charge separation pushing electrons towards one end of a wire, resulting in more electrons on one end hence higher voltage on one end.
The proper textbook definition (A) is the one that is used in Dr. Lewins example where he gets two different voltages across the same two points. This is fully correct and there are indeed two voltages there. The reason for the two solutions is that this voltage is including the EMF voltage from the magnetic field, yet the loop is not closed yet as the two points are in different locations in space. Depending on how this path is closed results in a different solution for the EMF voltage and this changes the result. Hence why voltage is path dependent.
So why are we using the other definition (B) if its clearly wrong? Well turns out in real life its rather tricky to measure the voltage according to that definition. Electrical components (such as resistors) represent only a small part of the path around the magnetic fields loop area, because of this all of the electron pushing work is done by the electrical field (caused by charge seperation). Turns out all the voltmeters are actually devices that measure current trough the internal resistance and display the voltage required to push that current. The density of electrons at a point in space can only have 1 single defined value hence why these voltages always have one value rather than multiple. All of this simply makes this definition (B) more useful and as such is used in circuit analysis and spice simulations. Since circuit analysis uses it that forces KVL to use it too.
In the absence of a changing magnetic field around the circuit both definitions of voltage have the same value so it doesn't matter what you use. But in a magnetic field it does matter a lot.
As for the lumped model, it only hides what you want it to hide. Many many tiny inductors in series act the same as one big inductor, so it makes it easier to use a lumped version. Once you lump a segment of a circuit all voltages within the lumped part become meaningless, this is why lumping the inductor as a single one causes problems in this example. The lumping procedure also lumped all our points of interest and messed them up, they no longer show true voltages. However anything outside the area we just lumped is preserved. The rest of the circuit doesn't care how many inductors there are, it just sees a set inductance value across the points. So by only lumping sections of the wire that have no points of interest we preserve all the points we want to measure. Hence why all the points on the ends of the inductors have the correct voltage values.
All wires have some amount of mutual inductance to each other as long as they are not placed at perfect right angles. In this case there is more to it however. The inductors L2 L3 L4 L5 are actually a single inductor (single whole turn of the loop) that has been sliced up in to 4 parts. Because they are part of the same inductors means they share the same magnetic flux and hence are highly coupled inductors. The inductors L6 L7 L8 L9 are another inductor that has been sliced up in to quarters, but since the wire follows the same path as the inner cirucit means that any flux passing trough that loop passes trough this one too. This means all of them are coupled to each other (aka a transformer). The solenoid coil in the middle is also having the same magnetic flux pass trough it hence why its also coupled. In my simulation it has a ideal coupling coefficient of 1, but in reality it would be lower because solenoid is smaller than the loop so some of the flux escapes.
So yeah we are mostly looking at two sides of the same coin here. Its two different ways of explaining the same thing.

Do you see the above two equations as equivalent term by term?
I did say "Don't you find it similar". I did not say equivalent, especially term by term. One more illustration of troll & "coach expert" tactics. You just cherrypick out of context whatever you find convenient for you, ignoring what I was ACTUALLY talking about: circuit that has EMF source and load, that both equations describes such and are similar in such sense.
I am just trying to pinpoint what I believe to be the origin of your misconception.
Back in one of your exchanges with MHz, you wrote:
Integral E.dl = 0 of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*.
Have you ever tried to compute the integral of E.dl of a RLC circuit with a generator  a lumped circuit, just to see that Kirchhoff and field theory can agree if there is no dB/dt area enclosed by the circuit path? It might clear a lot of things up before trying to attack a nonlumped circuit such as Lewin's.

Have you ever tried to compute the integral of E.dl of a RLC circuit with a generator
No. Have you?
I use L(di/dt) with real inductors/transformers having inductance and saturation current specs. Works for me well.

Ok so my point is this, you've modeled the circuit with lumped elements and that gives something that looks correct, but if you set this experiment up in real life, do you really think you'll measure any significant voltage across any of L2, L3, L4 or L5 like spice would tell you is there? The coupled flux isn't confined in those points so you won't.
So you say that Kirk T. McDonald is wrong in chapter "2.3 Comments" (page 10) (http://www.physics.princeton.edu/~mcdonald/examples/lewin.pdf)? Please tell where and why he is wrong. Prove him wrong.
Excerpt:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=605980;image)
I didn't say that I disagree with McDonald. Unlike many of us here, I'm not generally inclined to disagree with Physics professors. As rfeecs pointed out, McDonald echoes what I said to Berni, that the voltmeter will measure zero (whereas in his spice model, with the loop inductance split up into four lumped inductors, measuring across the inductor will give a nonzero value).
To be honest, some of McDonald's writing is presented at a level beyond the one I'm at. I'm going to work through Griffiths and hopefully come back to it able to fully digest what he has to say. That said, his footnote number 8 in http://physics.princeton.edu/~mcdonald/examples/voltage.pdf (http://physics.princeton.edu/~mcdonald/examples/voltage.pdf) seems to be expressing what I've been trying to get across in my discussion with Berni.

As rfeecs pointed out, McDonald echoes what I said to Berni, that the voltmeter will measure zero
He says exactly opposite: "the result Vmeter = 0 is appealing in that we might naïvely expect the “voltage drop” to be zero between points along a good/perfect conductor.".
You really shall read last paragraph of mentioned chapter carefully.

Have you ever tried to compute the integral of E.dl of a RLC circuit with a generator
No. Have you?
Yes. It clears things up. A lot.
You should too, before embarking in discussions such as this.
Luckily for you, you can find a well presented walkthrough in Ramo, Whinnery and VanDuzer "Fields and Waves in Communication Electronics". Chapter 4, "The electromagnetics of circuits".
Find a library that has this book, and read the first few pages of chapter 4.
I use L(di/dt) with real inductors/transformers having inductance and saturation current specs.
You should try to see where that expression comes from.
Works for me well.
Does not look like that, from this side of the monitor.

Does not look like that, from this side of the monitor.
You shall visit optometrist then. Thank you for suggestions anyway ;)

To not repeat a certain arrangement i will also answer this for both definitions of voltage:
A) For definition "Voltage is the integral of all forces pushing on electrons along a given path connecting two points":
The inductors L2 L3 L4 L5 have zero voltage across them at all times (Zero resistance). Any EMF voltage induced in the wire by the magnetic field is instantly countered by the charge separation of electrons.
B) For definition "Voltage is the difference in charge density between two points" (This is what real life voltmeters show)
The inductors L2 L3 L4 L5 have a voltage drop that sums up to the same voltage as the total voltage drop on the resistors. This voltage in the wire is caused by charge separation pushing electrons towards one end of a wire, resulting in more electrons on one end hence higher voltage on one end.
Where does definition B come from? Charge density and Voltage don't even have the same units. [C/m^{3}] vs [J/C]
The proper textbook definition (A) is the one that is used in Dr. Lewins example where he gets two different voltages across the same two points. This is fully correct and there are indeed two voltages there. The reason for the two solutions is that this voltage is including the EMF voltage from the magnetic field, yet the loop is not closed yet as the two points are in different locations in space. Depending on how this path is closed results in a different solution for the EMF voltage and this changes the result. Hence why voltage is path dependent.
So why are we using the other definition (B) if its clearly wrong? Well turns out in real life its rather tricky to measure the voltage according to that definition. Electrical components (such as resistors) represent only a small part of the path around the magnetic fields loop area, because of this all of the electron pushing work is done by the electrical field (caused by charge seperation). Turns out all the voltmeters are actually devices that measure current trough the internal resistance and display the voltage required to push that current. The density of electrons at a point in space can only have 1 single defined value hence why these voltages always have one value rather than multiple. All of this simply makes this definition (B) more useful and as such is used in circuit analysis and spice simulations. Since circuit analysis uses it that forces KVL to use it too.
In the absence of a changing magnetic field around the circuit both definitions of voltage have the same value so it doesn't matter what you use. But in a magnetic field it does matter a lot.
As for the lumped model, it only hides what you want it to hide. Many many tiny inductors in series act the same as one big inductor, so it makes it easier to use a lumped version. Once you lump a segment of a circuit all voltages within the lumped part become meaningless, this is why lumping the inductor as a single one causes problems in this example. The lumping procedure also lumped all our points of interest and messed them up, they no longer show true voltages. However anything outside the area we just lumped is preserved. The rest of the circuit doesn't care how many inductors there are, it just sees a set inductance value across the points. So by only lumping sections of the wire that have no points of interest we preserve all the points we want to measure. Hence why all the points on the ends of the inductors have the correct voltage values.
I disagree. You can split the total mutual inductance M of the loop into two strings of as many inductors as you want in spice. The value you measure in spice will not be the actual scalar voltage potential between the ends of the resistors (which is approximately zero as measured by the voltmeter). Lumping can't be done in this kind of circuit in spice without creating false outcomes.
All wires have some amount of mutual inductance to each other as long as they are not placed at perfect right angles. In this case there is more to it however. The inductors L2 L3 L4 L5 are actually a single inductor (single whole turn of the loop) that has been sliced up in to 4 parts. Because they are part of the same inductors means they share the same magnetic flux and hence are highly coupled inductors. The inductors L6 L7 L8 L9 are another inductor that has been sliced up in to quarters, but since the wire follows the same path as the inner cirucit means that any flux passing trough that loop passes trough this one too. This means all of them are coupled to each other (aka a transformer). The solenoid coil in the middle is also having the same magnetic flux pass trough it hence why its also coupled. In my simulation it has a ideal coupling coefficient of 1, but in reality it would be lower because solenoid is smaller than the loop so some of the flux escapes.
I see now that you're trying to model the mutual inductance of the "outer loop" i.e. the path formed by the two measurement loops, but not going through R1 and R2. You've arranged the coupling dots in a way that the inner inductors and outer inductors cancel each other out in a way that satisfies there being no flux coupling in the two measurement loops.
So yeah we are mostly looking at two sides of the same coin here. Its two different ways of explaining the same thing.
Mostly, with perhaps some disagreements on how far you can go with lumped models of inherently nonlumped reality, and the part I'm not following up there about charge density.
[Edit1: fix quoting]

As rfeecs pointed out, McDonald echoes what I said to Berni, that the voltmeter will measure zero
He says exactly opposite: "the result Vmeter = 0 is appealing in that we might naïvely expect the “voltage drop” to be zero between points along a good/perfect conductor.".
You really shall read last paragraph of mentioned chapter carefully.
I have been, and I have to admit I'm quite perplexed with it. In particular equation 35 doesn't seem correct to me. For example, if we assume a point in time where I = 1mA, R1 = 100ohm, R2 = 900ohm, R = 1Mohm and I1 ≈ 0 (as he states) then he seems to be saying 0V = 1V. If someone can help clear this up for me I'd appreciate it.
(https://ibin.co/4ROe8sZbEx99.png)
[Edit 1: fix typos]

I have been, and I have to admit I'm quite perplexed with it. In particular equation 35 doesn't seem correct to me. For example, if we assume a point in time where I = 1mA, R1 = 100ohm, R2 = 900ohm, R = 1Mohm and I1 ≈ 0 (as he states) then he seems to be saying 0V = 1V. If someone can help clear this up for me I'd appreciate it.
Equation is correct indeed. Thou it is counterintuitive. Wire segment "ab" is part of *both* loops  loop of leads and loop containing R1 and R2. Leads loop does not have any EMF induced, source of "voltage drop" in particular wire segment is EMF generated only in the loop containing resistors and it is obviously mirrored in the ab segment of the leads loop. All this is not that important. Important part is: voltage will be observed which is contrary to your statement.
[edit] No, you dont'use Ohms law here. You shall use Maxwell's equation to calculate EMF generated in wire segment "ab"
[edit1] Seems, I know where your frustration comes from. By saying I1=0 he means that current induced by EMF is zero because there is no EMF in the voltmeter leads. On the other hand current will be flowing through voltmeter due to potential difference "voltage drop" between points a & b. This is my explanation. Hope it helps.
[edit2] Obviously I agree that it is kinda incorrect to indicate I1=0, at the same time saying that voltmeter having finite resistance measures something that differs from 0V.

I have been, and I have to admit I'm quite perplexed with it. In particular equation 35 doesn't seem correct to me. For example, if we assume a point in time where I = 1mA, R1 = 100ohm, R2 = 900ohm, R = 1Mohm and I1 ≈ 0 (as he states) then he seems to be saying 0V = 1V. If someone can help clear this up for me I'd appreciate it.
Equation is correct indeed. Thou it is counterintuitive. Wire segment "ab" is part of *both* loops  loop of leads and loop containing R1 and R2. Leads loop does not have any EMF induced, source of "voltage drop" in particular wire segment is EMF generated only in the loop containing resistors. All this is not that important. Important part is: voltage will be observed which is contrary to your statement.
[edit] No, you dont'use Ohms law here. You shall use Maxwell's equation to calculate EMF generated in wire segment "ab"
[edit1] Seems, I know where your frustration comes from. By saying I1=0 he means that current induced by EMF is zero because there is no EMF in the voltmeter leads. On the other hand current will be flowing through voltmeter due to potential difference "voltage drop" between points a & b. This is my explanation. Hope it helps.
Thanks for the reply. I annotated his drawing to make my confusion clearer (heh).
(https://ibin.co/4ROonqRN5Cu3.png)
The equation in question, repeated is
(https://ibin.co/4ROe8sZbEx99.png)
Green is the path integral on the left side of the equation and red is the path integral on the right side of the equation. Would be great if you can fix it so that the equation balances. By all means use Maxwell's equations to get there.
I suspect I'm not going to fully understand McDonald until I've completely grokked his discussions on vector potential.

The most confusing thing about this is that he seems to be suggesting that there is a scalar potential here that is independent of the path, despite that pesky time varying B field.
I have been, and I have to admit I'm quite perplexed with it. In particular equation 35 doesn't seem correct to me. For example, if we assume a point in time where I = 1mA, R1 = 100ohm, R2 = 900ohm, R = 1Mohm and I1 ≈ 0 (as he states) then he seems to be saying 0V = 1V. If someone can help clear this up for me I'd appreciate it.
Equation is correct indeed. Thou it is counterintuitive. Wire segment "ab" is part of *both* loops  loop of leads and loop containing R1 and R2. Leads loop does not have any EMF induced, source of "voltage drop" in particular wire segment is EMF generated only in the loop containing resistors. All this is not that important. Important part is: voltage will be observed which is contrary to your statement.
[edit] No, you dont'use Ohms law here. You shall use Maxwell's equation to calculate EMF generated in wire segment "ab"
[edit1] Seems, I know where your frustration comes from. By saying I1=0 he means that current induced by EMF is zero because there is no EMF in the voltmeter leads. On the other hand current will be flowing through voltmeter due to potential difference "voltage drop" between points a & b. This is my explanation. Hope it helps.
Thanks for the reply. I annotated his drawing to make my confusion clearer (heh).
(https://ibin.co/4ROonqRN5Cu3.png)
The equation in question, repeated is
(https://ibin.co/4ROe8sZbEx99.png)
Green is the path integral on the left side of the equation and red is the path integral on the right side of the equation. Would be great if you can fix it so that the equation balances. By all means use Maxwell's equations to get there.
I suspect I'm not going to fully understand McDonald until I've completely grokked his discussions on vector potential.

I suspect I'm not going to fully understand McDonald until I've completely grokked his discussions on vector potential.
(https://ibin.co/4ROonqRN5Cu3.png)
Oh, my... You use Ohms law to claim that voltage between ab is 1V? :palm:
I don't even know what to say. How dare you pretend that you mastered Maxwell's equations?!
First, you have to know azimuthal angle between two points, a & b. Let's assume it is PI/4 (45 degrees). According to your data EMF of the resistor loop is 1V. We put 1V and Pi/4 into equation (34): 1V*(Pi/4)/(2*Pi) = 1/8 V. Voltmeter shall show 0.125V in such case (when angle is 45 degrees).
[edit] Forget about "I1=0". It is misleading or even incorrect. All you shall know  there's no EMF induced in the voltmeter leads.

I suspect I'm not going to fully understand McDonald until I've completely grokked his discussions on vector potential.
(https://ibin.co/4ROonqRN5Cu3.png)
Oh, my... You use Ohms law to claim that voltage between ab is 1V? :palm:
I don't even know what to say. How dare you pretend that you mastered Maxwell's equations?!
First, you have to know azimuthal angle between two points, a & b. Let's assume it is PI/4 (45 degrees). According to your data EMF of the resistor loop is 1V. We put 1V and Pi/4 into equation (34): 1V*(Pi/4)/(2*Pi) = 1/8 V. Voltmeter shall show 0.125V in such case (when angle is 45 degrees).
[edit] Forget about "I1=0". It is misleading or even incorrect.
I don't pretend anything, and if you continue using these emoticons or abusive/patronizing language I will just start ignoring you again. Please drop them if you want to continue discussing like adults.
Int E•dl in the wires is 0V (no E fields in perfect conductors, or next to none in real conductors in which case we approximate to 0) and in the resistor is equivalent to I*R (if not then what do you think the contribution of Int E•dl through the resistor is?).
Your response contradicts several of the things McDonald says in his paper, namely that the voltmeter will read 0V (not 0.125V) and that I1 = 0 is misleading/incorrect. So now who should I believe, you or McDonald?
Anybody else wanna take a crack at this?

Have you ever tried to compute the integral of E.dl of a RLC circuit with a generator  a lumped circuit, just to see that Kirchhoff and field theory can agree if there is no dB/dt area enclosed by the circuit path? It might clear a lot of things up before trying to attack a nonlumped circuit such as Lewin's.
See discussion above about McDonald's paper, then think again how nonlumped circuit is Dr.Lewin's experiment.

Int E•dl in the wires is 0V (no E fields in perfect conductors, or next to none in real conductors in which case we approximate to 0) and in the resistor is equivalent to I*R (if not then what do you think the contribution of Int E•dl through the resistor is?).
Faradays law? ... Maybe? From your blog BTW:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=606070;image)
Your response contradicts several of the things McDonald says in his paper, namely that the voltmeter will read 0V (not 0.125V) and that I1 = 0 is misleading/incorrect. So now who should I believe, you or McDonald?
Anybody else wanna take a crack at this?
I do not contradict with McDonald. You do. I will repeat again what he says: "the result Vmeter = 0 is appealing in that we might naïvely expect the “voltage drop” to be zero between points along a good/perfect conductor." He even shows equation (34) how to calculate voltage between ab points.
I already explained what I think about I1=0:
[edit1] Seems, I know where your frustration comes from. By saying I1=0 he means that current induced by EMF is zero because there is no EMF in the voltmeter leads. On the other hand current will be flowing through voltmeter due to potential difference "voltage drop" between points a & b. This is my explanation. Hope it helps.

I have been, and I have to admit I'm quite perplexed with it. In particular equation 35 doesn't seem correct to me. For example, if we assume a point in time where I = 1mA, R1 = 100ohm, R2 = 900ohm, R = 1Mohm and I1 ≈ 0 (as he states) then he seems to be saying 0V = 1V. If someone can help clear this up for me I'd appreciate it.
(https://ibin.co/4ROe8sZbEx99.png)
[Edit 1: fix typos]
I agree equation 35 does not look correct, maybe it is a typo. He seems to have left out the EMF term. Perhaps by E he is refering to E_{V} as in equation 18.

I agree equation 35 does not look correct, maybe it is a typo. He seems to have left out the EMF term.
It's not a crime and it does not make it a typo. Dr.Lewin omits EMF vector potential terms all the time. Everybody does. Even mhz himself:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=606070;image)

Int E•dl in the wires is 0V (no E fields in perfect conductors, or next to none in real conductors in which case we approximate to 0) and in the resistor is equivalent to I*R (if not then what do you think the contribution of Int E•dl through the resistor is?).
Faradays law? ... Maybe? From your blog BTW:
(https://www.eevblog.com/forum/chat/doeskirchhoffslawholddisagreeingwithamaster/?action=dlattach;attach=606070;image)
That is Faraday's law yes, how would you use it to calculate the contribution of the line integral of E•dl through the resistor?
Your response contradicts several of the things McDonald says in his paper, namely that the voltmeter will read 0V (not 0.125V) and that I1 = 0 is misleading/incorrect. So now who should I believe, you or McDonald?
Anybody else wanna take a crack at this?
I do not contradict with McDonald. You do. I will repeat again what he says: "the result Vmeter = 0 is appealing in that we might naïvely expect the “voltage drop” to be zero between points along a good/perfect conductor." He even shows equation (34) how to calculate voltage between ab points.
You said "Voltmeter shall show 0.125V."
McDonald said "the result Vmeter = 0 ..."
I believe what you meant to say is that Vab = 0.125V (based on your use of equation 34), despite the fact that the Voltmeter shows 0V.
At any rate, I'm asking about equation 35 not 34*. You're fixating on the arc ab when equation 35 doesn't include that arc in either of its path integrals (as shown in my color coded annotation).
I asked a question in the previous post. "what do you think the contribution of Int E•dl through the resistor is?" You seemed to disagree with me that it is equal to I*R.
*admittedly, equation 34 is confusing to me as well but I suspect I'm not going to follow McDonald there without a much deeper reading of this paper, rather than having it explained to me here.
Edit1: attempt at fix quotesing

That is Faraday's law yes, how would you use it to calculate the contribution of the line integral of E•dl through the resistor?
Why you suddenly introduce resistor here? We talk about Maxwell's equations and Faradays law. Note that wire segment ab does not contain any resistor.
You said "Voltmeter shall show 0.125V."
Yes. I demonstrated you how to calculate voltage between ab in case angle is 45 degrees. McDonald provides only formula, not actual calculation. Where's your problem to understand that?
McDonald said "the result Vmeter = 0 ..."
If you cannot comprehend that McDonald says that it is naïve to expect that voltmeter will show 0V, then our discussion is finished here and now. When you confirm that you can read  we may continue.

That is Faraday's law yes, how would you use it to calculate the contribution of the line integral of E•dl through the resistor?
Why you suddenly introduce resistor here? We talk about Maxwell's equations and Faradays law. Note that wire segment ab does not contain any resistor.
I didn't suddenly introduce it. It's inside one of the path integrals in equation 35 which is what I've been talking with you about for these past several posts. I now see that you were still referring to the arc ab and using equation 34 when you said "Oh, my... You use Ohms law to claim that voltage between ab is 1V? :palm:"
I'm fully able to plug the same numbers into equation 34 as you are. You keep responding to my questions about equation 35 with equation 34. I've already conceded that I don't understand McDonald's development to arriving at that equation, and I'm not particularly interested in discussing it here without a chance to do a deeper read of his paper. I have been talking about equation 35 for these past several posts and it's now clear that you've been ignoring them and persisting at talking about equation 34. We're not even talking about the same thing.