#562 – Electroboom!

[Jesse Gordon]

Dr. McDonald said "Lewin's circuit is within the range of applicability of Kirchhoff's loop equations, which can be used to predict measurements by the 'voltmeters' in the experiment. "

You said you have no degrees and you're no math wiz.

At least I admit it.

Probably you didn't read the entire paper by McDonald, or if you did, you didn't understand it.

I did read and did my best to understand it.

What he says is that, specifically for Lewin's circuit, it is possible to consider the EMF as a generator element of an equivalent circuit and still apply KVL EQUATIONS. Which is true.

Note, by the way, I don't think McDonald used the term "KVL Equations." I think he seems to be saying "Kirchhoff's  loop equations." That sounds to me like the equations which define KVL.

So we can apply Kirchoff's Loop equations just not KVL itself? Hmmmm. What's left beyond the equations?  What are the Kirchhoff's loop equations, if not the heart of KVL itself?

Isn't the Kirchhoff's loop equation Σ(V1,V2,...,Vn) = 0 ?

What Dr. McDonald actually said is "Lewin’s circuit is within the range of applicability of Kirchhoff’s loop equations, which can be used to predict measurements by the 'voltmeters' in the experiment."

So isn't he saying that we can use Kirchhoff's loop equations to predict the measurements by the volt meters?

But he stresses that this EMF is nowhere to be found with voltmeters in the circuit.

In Lewin’s example, the magnetic flux in the primary solenoid may well be within a small coil, but the secondary consists of only a single “turn”, so the associated inductive EMF is not well localized, but rather is distributed around the entire secondary loop. Then, since inductive EMF’s are associated with a vector potential, rather than a scalar potential, it can be misleading to interpret the inductive EMF as related to a “voltage”.

Wait a second. Where does he stress that the EMF is no where to be found with the voltmeters in the circuit? He specifically says that the EMF, which by Faradays law is -L(dI/dt), is read by the volt meter.

The part you are quoting simply says that the inductive EMF is not well localized, and that it can be misleading to interpret the inductive EMF as related to "Voltage."

He didn't say it IS misleading, but that it CAN be misleading.

Of course it can be misleading because if you are sloppy how you run your probes you may get an ambiguous reading, which is no reading at all. If you are measuring two  unknowns, you are measuring neither.

But it doesn't have to be misleading, according to him.

How did you get from "can be misleading" to "EMF is nowhere to be found with the voltmeters in the circuit?"

Lewin's beef is that people read that you can use KVL EQUATIONS to calculate the voltage across the resistors and try to find this EMF with voltmeters. You'll never find it.

But I do find that voltage with volt meters.

People say that the voltages are in the wires. McDonald denies that. It's all over the circuit, and it is not a voltage. So voltmeters won't measure it. (In other words, this circuit is "unlumpable", and modeling it so as to make KVL work is just a math trick).

I never said "the voltage was in the wires."

If it's unlumpable, then why did McDonald say that it was within the range of applicability or Kirchhoff's loop equations? Is not that equation Σ(V1,V2,...,Vn) = 0 ?

Regardless of the dB field distribution, at the end of the day, a transformer's wires emerge far from within the influence of the dB and run out to power loads, where they do have an unambiguous voltage which can be unambiguously measured with a volt meter and used to power energy consumers.

MacDonald says more.

Kirchhoff’s (extended) loop equation (1) does not apply to all possible circuits, and gives a poor description of circuits whose size is not small compared to relevant wavelengths, in which effects of radiation and retardation can be important. Examples such as Lewin’s in which the self inductance of the entire loop could be important must be treated with care.

So Kirchhoff's law doesn't always hold, does it?

I never said that there aren't cases where KVL fails, but.....

  Woah, is this what I've been overlooking? 

Were the wavelengths in Lewin's loop or in my shortwave transmitter (Lewin Clock) experiment small compared to the test apparatus?

  That's something... wow.. Is that what I've been overlooking this whole time? 

He calculates and confirm that the two voltmeters in Lewin's experiment will show two different voltages even though connected to the same points in the circuit and then declares:

These results were validated by experiment during Lewin’s lecture demonstration.

Of course, I myself verified that if I ran my volt meter leads through the core of the transformer I could get all sorts of errors too.

"In this sense, KVL holds, as argued by Mehdi Sadaghdar ..."

In what sense? Have you read the whole paper? He explicitly said that the voltage through an inductor is zero. Of course it is! It's just a piece of wire! But across the terminals of the inductor it is defined by its inductance (path dependence of voltage). And IN THIS SENSE, KVL holds. Which is true.

Wait, if the voltage across the winding is zero, and the voltage across the resistors is non-zero, then how the tarzan can the sum be zero?

It looks to me like he's saying that -L(dI/dt) does not represent -∫E.dl

(NOTE: I copy pasted integral and close loop/contour integral symbols. If you don't see one of the two before occurrences of "E.dl" then it didn't paste correctly.Let me know. Looks fine to me.)

It looks to me like he's saying that Feynman stated explicitly that -∫E.dl is through an inductor, but that the voltage difference across the inductor, which they correctly identify as EMF, is ∮E.dl, which by Faraday's Law is -L(dI/dt).

He goes on to state that this quantity  ∮E.dl or -L(dI/dt) has NOTHING to do with -∫E.d, even though the latter does have the unit volts.

In summary, what I take this to mean:

1:  -∫E.dl  through an inductor is zero for a super conductor.

2: ∮E.dl is the voltage difference across the inductor, and is equal to Faraday's law -L(dI/dt), and can be measured with a volt meter.

3: -∫E.dl has nothing to do with ∮E.dl

Do you agree that Dr. Belcher stated the above 3 numbered points?

It sure looks to me like he's saying that the ∮E.dl of the windings will have a voltage differential which, when algebraically summed with the voltages across the resistors, will equal zero, and that KVL thus holds true.

"In this sense, KVL holds, as argued by Mehdi Sadaghdar ..."

...
He explicitly said that the voltage through an inductor is zero.
...

No, he said that the -∫E.dl (which has the unit of volts) is zero, but that the ∮E.dl (which also has the unit of volts) is the volts that the volt meter reads.

Is this what the whole shebang is about? ∮E.dl vs -∫E.dl? Two different unrelated quantities, both of unit type volts?

Are you saying that KVL must only be used with -∫E.dl and not ∮E.dl?

And here we come to the Mehdi problem.

Mehdi claims that KVL ALWAYS holds. Which is not true.

"Always" as in are you saying that he claims that there are absolutely no circumstances that KVL fails? Got a link to him saying that?

But anyway, it doesn't really matter, I'm not Mehdi, and I don't claim that there is no possible situation where KVL will fail.

He claims that Belcher agrees with him. He doesn't.

Well, did Mehdi claim that Belcher agrees with him on every single point?

Belcher sort of did agree with Mehdi on some points, otherwise he wouldn't have said "In this sense, KVL holds, as argued by Mehdi..."

That is some level of agreement. Did Mehdi overstate that? Got a link?

But it doesn't really matter, and I'm not Mehdi. I'm not stating that Belcher did or did not COMPLETELY agree with EVERYTHING Mehdi said, I'm only stating that he did agree on the point that KVL holds, as argued by Mehdi.

Belcher says KVL only holds for specific conditions. He says that Lewin is wrong and invokes McDonald. MacDonald doesn't say Lewin is wrong anywhere in his paper.

Out of professional courtesy, he may not name Lewin and say the exact words "Lewin is wrong" however Lewin said Mehdi was wrong to claim that KVL holds, and Dr. Belcher says that Mehdi was right in arguing that KVL holds, so that sort of makes Lewin wrong according to Belcher - they can't both be right.

Furthermore, Lewin stated that the voltage across the wire was zero volts. Belcher says "No, -∫E.dl is zero. But the voltage that your scopes measure is measuring  ∮E.dl which is the voltage difference across the wire, which is not zero."

So while he was polite about it, he does seem to saying that Lewin was wrong, even though he doesn't name him like  Dr. McDonald did.

His argument is because he thinks that Lewin presented his circuit as a paradox that cannot be solved in the confines of Kirchhoff's equations. He shows it actually can. But in fact there's no paradox--that's Lewin's argument--when you realize the circuit is immersed in a non-conservative field, which is a much broader concept, that allows you to understand the problems to which McDonald says Kirchhoff's equations can't be applied.

Mehdi claims the voltages are in the wires, that Lewin doesn't know how to probe his circuit and many other irrational and nonfactual assertions. We just can't accept that.

Noooo of course we can't accept any of that, nooooo!

Except those of us who aren't we. 

But maybe all of that is above my skill level.

Let's start at a very simple place where my small brain gets it. Ok?

Let's say I have two small but powerful battery operated optically synchronized DDS waveform generators each generating a 60Hz 100mV AC RMS sinewave.
Further, let's say I have a 100 ohm resistor and a 1000 ohm resistor and I use these four components to form a series loop, alternating resistors and DDS units.

If I take a four channel fully isolated input scope and connect each of my four elements to their own scope input with positive-clockwise polarity, will the sum be zero? Let's say I turn on the math channel on the scope, and sum all the inputs, will it be a straight line?

KVL will hold fine in this case, right?

[thinkfat]

Welcome to our little "Understanding Faradays' Law" support group. Please have a seat.

...
PS: this would be a brilliant experiment: Use a split core with different permeability in each of the toroids, so that the flux is no longer evenly split. I wonder if the voltages would still add up

Thank you for the invite here my friend!

And yes, the two toroids are slightly different from eachother. They actually really are two toroids in this particular transformer, each made from a looong strip of sheet metal wound up, and there are two of them in there, butted up.

And evidently, one has a little more iron to it because it has more voltage across it.

But regardless, the sum still adds up to "zero." (within the resolution limitation of my volt meter.)

However, if you would like, I would be glad to do an experiment literally with two different toroids which are of significantly different sizes, and do the same test to show you that even then, all the voltages add up to zero going clockwise around the loop.

Would that be meaningful to you? Do you think the voltage would no longer add up to zero?

The voltages would still add up, I give you that. My mistake, I wasn't thinking straight.

But doesn't it feel odd how suddenly half of the Lewin Loop in your experiment has a vastly different voltage "across" the same red wire than before? Because the Lewin Loop, and also the yellow reference loop still experience the same flux as before (of course presuming the total magnetic flux didn't change).

And I have another thought experiment for you: what if you replaced the two resistors with just wires, what would you measure around the loop?
I can actually predict it: the voltage across the two wires replacing the resistors would read "zero", while across the other two, the red wires of your original experiment, you would still read roughly 100mV.

That is a little hard to explain with your claim that none of your probing wires "cross" any magnetic flux, right?

[Jesse Gordon]

Welcome to our little "Understanding Faradays' Law" support group. Please have a seat.

...
PS: this would be a brilliant experiment: Use a split core with different permeability in each of the toroids, so that the flux is no longer evenly split. I wonder if the voltages would still add up

Thank you for the invite here my friend!

And yes, the two toroids are slightly different from eachother. They actually really are two toroids in this particular transformer, each made from a looong strip of sheet metal wound up, and there are two of them in there, butted up.

And evidently, one has a little more iron to it because it has more voltage across it.

But regardless, the sum still adds up to "zero." (within the resolution limitation of my volt meter.)

However, if you would like, I would be glad to do an experiment literally with two different toroids which are of significantly different sizes, and do the same test to show you that even then, all the voltages add up to zero going clockwise around the loop.

Would that be meaningful to you? Do you think the voltage would no longer add up to zero?

The voltages would still add up, I give you that. My mistake, I wasn't thinking straight.

That's what I'm struggling with. I have seen this forum full of small mistakes like that which tells me I ought to not just accept statements seen here without understanding them.

But doesn't it feel odd how suddenly half of the Lewin Loop in your experiment has a vastly different voltage "across" the same red wire than before? Because the Lewin Loop, and also the yellow reference loop still experience the same flux as before (of course presuming the total magnetic flux didn't change).

I'm not sure what you're asking here, please explain your setup in more detail if I misunderstand.

ASSUMING that you're talking about the "KVL holds in iron core transformer" video except with two toroids of vastly different permeability, and you're asking whether it "feels odd" how one of the red wires has less voltage on it, NO, Not at all:

Like I keep yammering on about, model reality! model reality!

The two toroids having different permeability (given the same number of primary windings) will have different inductive reactance, which is like AC-resistance. So just like two resistors of different values in series, the two toroids will have different volts/turn when unloaded or not significantly loaded.

The two toroid's primaries are electrically in series, same current flowing through both of them, and the one with more permeability will have a higher inductive reactance and more inductive voltage drop which means more unloaded volts per turn.

I keep saying unloaded because if you put a secondary winding and a load on the larger inductor, then the primary current will increase and the primary voltage on the bigger one will drop and the primary voltage on the second one will rise.

It doesn't feel weird at all to me.

Does it feel weird to you?

And I have another thought experiment for you: what if you replaced the two resistors with just wires, what would you measure around the loop?
I can actually predict it: the voltage across the two wires replacing the resistors would read "zero", while across the other two, the red wires of your original experiment, you would still read roughly 100mV.

Instead of using my little red wires, I used a single length of 14AWG  in a loop, and soldered the ends together with 3/4" overlap so I wouldn't have any contact resistance issues to worry about, like this: https://postimg.cc/nXD7ynQf

I cannot run it for very long because the wire starts getting hot.

However:
Measuring across where the red wires used to be gives about +50mv.
Measuring across where the resistors used to be gives about -50mv.

(NOTE: Signs are to indicate the phase! I was using an AC volt meter, but I also determined the phase.)

Measuring from two points exactly opposite on the copper ring gives about 0mv.

The voltage dropped on the exposed part of the wire is opposite phase as compared to the voltage developed  on the wire which passes through the core.

To determine whether the voltage drop across the place where the resistors were was resistive or inductive, I put on a twisted pair as you can see, and it read the same ~50mv that the volt meter leads do.

It looks like we basically have essentially four resistors in series, two passing through the core and 2 not passing through the core.

A total of 200mv is induced, and each of the four "resisters" drops 50mv.

There would be 100mv induced in each resistor which passes through the core, but due to the current, there is a 50mv ohmic voltage drop in the opposite direction.

And since Σ(50,50,-50,-50)=0 it looks like KVL still holds.

That is a little hard to explain with your claim that none of your probing wires "cross" any magnetic flux, right?

I don't see why. The two ends of the "resistor" that is inside the core stick out, and those are the output wires to my transformer. They have ∮E.dl voltage across the ends of the wire.
By definition, a closed path core is equivalent to an infinitely long solenoid, right? So it makes sense that if the solenoid wraps around the straight wire, the straight wire effectively does exactly one turn around the infinitely long solenoid.

For the sake of KVL, it seems to model that way just fine.

[thinkfat]

Instead of using my little red wires, I used a single length of 14AWG  in a loop, and soldered the ends together with 3/4" overlap so I wouldn't have any contact resistance issues to worry about, like this: https://postimg.cc/nXD7ynQf

I cannot run it for very long because the wire starts getting hot.

The wire getting hot means there's a significant contribution by Mr. Ohm and so we can no longer neglect him.

EDIT (sorry, I pushed the POST button to early)

However:
Measuring across where the red wires used to be gives about +50mv.
Measuring across where the resistors used to be gives about -50mv.

(NOTE: Signs are to indicate the phase! I was using an AC volt meter, but I also determined the phase.)

Measuring from two points exactly opposite on the copper ring gives about 0mv.

You get 50mV from the voltage drop due to the wire resistance, -100mV from the EMF in the volt meter loop, resulting in -50mV total.

You get 0mV across two opposite points on the loop, but only in one case, if your volt meter loop encloses a part of the core (linking the flux and having an induced EMF) and also the ohmic voltage drop exactly counters the EMF in the volt meter loop. But it will be path dependent, in any other case you will get a non-zero voltage reading.

[bsfeechannel]

Yes, it's like "Ow My Balls!"* with some wires thrown in.  But Lewin isn't any less of a showman. 

That's where the similarities between the two end. Every reputable author says the same thing about trying to apply KVL to a circuit subjected to a non-conservative field: caveat emptor, if you try to find the inductive EMF in the circuit as a voltage you'll come a gutser. But, people shrug and don't pay attention. Lewin does the same the other authors do, only that he goes one step further and asks his students to explain WHY exactly you can't find the "missing" "voltage". Wouldn't expect less from an MIT-quality lecture.

Mehdi does differently. He says that this "voltage" is really somewhere in the circuit (sometimes in the wire, sometimes in the resistors) and through some kind of clever technique you will be able to find it. Those who believe his false claims set out to devise all kinds of pseudo-scientific and contradictory explanations and "experiments" to try to confirm the word of their idol.

But Mehdi does worse. He divides the community and incites people against each other, all in the name of a polemic with the only intent of increasing his viewership.

Fortunately, there are courageous people who are turning this into an opportunity to debunk this bunk and introduce people to the tried and tested concepts behind the electromagnetic phenomenon.

[Sredni]

1. That sentence of Belcher is about the RLC lumped circuit of section 10. Read pages 15 and 16. It's not about the unlumpable Lewin ring.

That's where I was quoting from. Wouldn't you say that he clearly describes that there are two different attributes, both of which use the unit volt, but one of which is always zero across an inductor and one which is what a volt meter reads, which is how KVL holds as argued by Mehdi?
He says "Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds) "

Ok, let me join the dots for you.

About that sentence by Belcher
You already posted the two relevant pages of Belcher's note. Let me show you that the partial sentence you keep repeating ("In this sense, KVL holds as argued by Mehdi Sagadhdar, but..." - oh, no! You stop right before the 'but') is not about the unlumpable Lewin's ring, but another, lumpable, circuit. You need to read carefully, lest you mistake similar words, like "many" with "any", or something like that.
The famous sentence appears in section 11 on page 16, but it is related to a discussion that began in section 10, on page 15.

Source: Belcher's note available on Mehdi's YT channel. Let's see what section 10 is about, first.

10. Another circuit

link to image: https://i.postimg.cc/DZwxkkyJ/screenshot-3.png

The experiment above was not considered in the video, but I offer it up as an exercise for the reader. I have a “one-loop” inductor, with a capacitor and resistor, as shown, where I assume the self-magnetic field is only non-zero inside the loop. The battery is shown with the positive terminal down, which will result in a current flow counterclockwise around the circuit, giving a self-magnetic field out of the paper.

At the top of p. 15, he writes

https://i.postimg.cc/vTphV47f/screenshot-4.png

Take note of the equation, You will see it repeated shortly. For the time being, let's look at the other picture:


https://i.postimg.cc/ZqCLVPfp/screenshot-5.png

Oh, look: same circuit, same test points to which attach the probes and different voltages depending on whether the voltmeter is on the left or on the right of the loop. I wonder where I have ever seen that before.
Oh yes, Lewin's ring. There is a difference though: Lewin's ring is not lumpable, while this RLC circuit with lumped R, L and C component is lumpable.

How so? What you need to do to consider it lumped is to devise a circuit path that DOES NOT CONTAIN the changing magnetic flux region in its interior (technically, we should say that the closed circuit loop does not cut any net flux - but in 2D it's easier to say what I just wrote). If you can do that, then all voltages along any path you could imagine in the area enclosed by your circuit path, will be path independent (they will only depend on endpoints).
How can you find such a circuit path? Easy: instead of having the circuit path following the coil's filament, we consider the circuit path jumping in the space between the coil terminals. As explained by Feynman, shown by Hayt (posted an excerpt just a few pages above in this thread), detailed by Ramo Whinnery and VanDuzer, exemplified by Purcell, and Haus and Melcher, and Faria, and in the published papers by Romer, Roche, Nicholson, and on and on and on... now you can apply KVL to your freshly lumped circuit and be happy. It's fake, because voltage will still in general depend on path, but in our little bubble we can pretend it doesn't. In that sense, in that little safe space we just cut out from the rest of the real world, KVL holds.
Let me rephrase it: if you can hide the changing magnetic flux inside a lumped component, and you do not look inside it (meaning: your circuit path does not go inside those forbidden zone components and thus it is impossible to go around the dB/dt region) then the "amended" KVL holds.

Yet, whenever you consider circuit paths that go around the magnetic region, -pouff- the dream shatters. For example, if your circuit path consists of only one inductor and the jump at its terminal, you will see KVL die in the definition itself of voltage across the terminals of the lumped inductor. If you accept the definition of voltage as (minus) the path integral of the total electric field (such as that given by the IEC), the following paragraph says just that


https://i.postimg.cc/5y3vxj7f/screenshot-6.png

i.e. you have a voltage -Ldi/dt across the terminals of the (self-)inductor, but zero voltage along the filament of its coil. Voltage referred to the same points A and B is different depending on the particular path you refer it to. Exactly what Lewin says in his video "Kirchhoff law is for the birds=https://youtu.be/LzT_YZ0xCFY", at minute 33:

"And now I'm going to cause you some sleepless nights. And I'm going to attach here a voltmeter... And now I'm going to ask you what would this voltmeter show. And you'll probably say: 'well didn't you say that the integral of E dot dl through this wire is zero?' So you will think that V here is zero. But that's not true. You know what V is going to be? It's going to be + L di/dt."

Oh, look! Belcher and Lewin are saying the very same thing.
Anyway, let's go back to Belcher's note and the infamous sentence KVL keep waving like a victory flag. To show that Belcher was talking about the lumped RLC circuit, here is the rest of page 15


https://i.postimg.cc/dV77fWYs/screenshot-9.png

Do you recognize the equation +V - IR - Q/C - Ldi/dt = 0 ? It's the equation for the series lumped RLC circuit.
This part of Belcher's note is about the series lumped RLC circuit where L is the self inductance. NOT the unlumpable LEWIN's RING (where, incidentally but not importantly, the self inductance is negligible). It is about the different approach IN LUMPED CIRCUIT THEORY between properly applying Faraday (using a circuit path the goes through the filament and accounting for the magnetic flux intercepted by the path: 5 + 3 + 0 = 8 ) and using the 'amended version of KVL' (using a circuit path that jumps at the inductor terminals and pretending -L di/dt is a potential difference to save KVL: 5 + 3 - 8 = 0).

One can still save KVL for lumped circuits by bringing the rhs (the surface integral of B.dS) to the left side (and pretending it is a path integral of E.dl).
The trick works ONLY IF you can devise a circuit path that DOES NOT contain the variable magnetic flux region.

You can do it for the lumpable RLC circuit.
And this is the "amended", or "modified", or "extended" or "new" KVL that is so very often badly explained in high school and in first, second year introductory uni books (they use the 5 + 3 - 8 = 0 formalism that erroneously lead students to think there is a voltage buildup in the wires of a coil - Lewin says that "the physics stinks").

You CANNOT DO IT for Lewin's ring.
Why? Because it is required that the two resistor be on the opposite sides of the variable magnetic region. So, your circuit path is BY DEFINITION required to contain the magnetic flux region. The circuit is unlumpable.


source: https://electronics.stackexchange.com/questions/551244/what-would-a-voltmeter-measure-if-you-had-an-electromotive-force-generated-by-a/551428#551428

And as such, it cannot be properly modeled by lumped transformer models, without changing the true nature of the system (i.e. without introducing jumps in voltage whenever you encounter one of these lumped coils).


source: https://i.postimg.cc/YCKNjzg2/Spot-the-differences.png

In order to model it with two or four lumped coils, the magnetic field region must be splitted to accomodate a circuit path that does not include any of it. I used the same 'stellated' path style used by Feynman in figure 22-9 at page 22-7 of his second volume of lectures.

Some ask: "don't you see the transformer?" Well, when you are inside the coil, when your circuit path go around the dB/dt coil you no longer have the luxury of using a lumped component model (the secondary of a transformer to which you can apply KVL) for the coil. You have an unlumpable circuit and you need to deal with it accordingly: ditch KVL and use Faraday.

I have a crystal ball that almost never fails me. It is now telling me that, despite being shown here that Belcher was not talking about Lewin's ring when he wrote that sentence, you will nevertheless keep use that very sentence in the future to show that Belcher agrees with Mehdi on Lewin being wrong on the Lewin ring. Just like Mehdi pretendend both Belcher and Feynman agrees with him on all the line, including Lewin's ring. By using your terminology: he is either "clueless", or "ignorant" or "not being honest". In any case: disappointing.

And I have not even mentioned the other note written by Belcher many years ago with Lewin, where they discuss the RL circuit and the "Kirchhoff second law modified for inductors", saying (regarding the 5 + 3 - 8 = 0 formalism)


source: Lewin and Belcher note for 802.11, updated by Lewin to add pointer to Giancoli and to his lecture.
snippet url: https://i.postimg.cc/zGMhDsjH/screenshot-7.png

which also contains the treatment of the ring made of uniform resistive material and of two resistive halves in a variable magnetic field. Even there, you will see that Belcher's and Lewin's view are the same.

Next stop: a bit more detail on McDonald's note.
(but first, a few fun posts )

[Jesse Gordon]

Instead of using my little red wires, I used a single length of 14AWG  in a loop, and soldered the ends together with 3/4" overlap so I wouldn't have any contact resistance issues to worry about, like this: https://postimg.cc/nXD7ynQf

I cannot run it for very long because the wire starts getting hot.

The wire getting hot means there's a significant contribution by Mr. Ohm and so we can no longer neglect him.

EDIT (sorry, I pushed the POST button to early)

haha yeah, I saw your initial post and was tempted to reply "I love the way you drive home your point... But what is it? hahaha" but I figured you weren't done so I'd let you finish 

However:
Measuring across where the red wires used to be gives about +50mv.
Measuring across where the resistors used to be gives about -50mv.

(NOTE: Signs are to indicate the phase! I was using an AC volt meter, but I also determined the phase.)

Measuring from two points exactly opposite on the copper ring gives about 0mv.

You get 50mV from the voltage drop due to the wire resistance, -100mV from the EMF in the volt meter loop, resulting in -50mV total.

You get 0mV across two opposite points on the loop, but only in one case, if your volt meter loop encloses a part of the core (linking the flux and having an induced EMF) and also the ohmic voltage drop exactly counters the EMF in the volt meter loop. But it will be path dependent, in any other case you will get a non-zero voltage reading.

But your prediction was unambiguously wrong. Remember, you predicted that there would be 0v across the wires replacing the resistors, and about 100mv measured 'around the ends' where the red wires used to be.

What gives? Your odds aren't very good here. First you suggested that maybe vastly different sizes of toroids in my EI-Core configuration might not sum to zero in the "KVL in an iron core" setup. You were wrong, sure, everyone makes a mistake.

(Ha! I guess technically, my EI core is actually two rectangular toroids butted up, so it's more of an OO core configuration hahahahahaha. Irrelevant though.)

Now you've made yet another prediction, you said I'd get around 0,100,0,100 mv on my shorted winding. I got around 50,50,50,50 which is not even arguably close to what you predicted.

It'd be one thing if I got like, oh, say 10mv on the outside-the-core sections and around 90mv on the through-the-core section. You could have argued you were right. But you weren't even close.

You also asked if it "feels odd" to me that the unloaded volts/turn might be vastly different for two series toroids with same number of primary turns but vastly different permeabilities.
I answered, but I also ask if it feels odd to you.

So, does it feel odd to you? Or did it?

If it didn't feel odd to you, then why'd you ask? Just hoping I wouldn't know the answer?

If it did feel odd to you, then that's a third prediction you "made," or rather suggested, which was also wrong.

Also, above you say that "But it will be path dependent." What will be path dependent? What path? The path of my volt meter leads? Or the path of the shorted winding?

By the way, have you read Dr. Belchers writup on the subject yet?

He goes over the idea of an unloaded transformer having voltage.

He basically cites Faraday's law and says that if you want to reassure yourself that the electric field actually exists, just increase the output voltage of the transformer to where it jumps an arc. He says you will see a spark and that PROVES (his word, my emphasis) that there is an electric field there, whether you put a volt meter onto the circuit or not.

Others here have likewise used similar electroscope/statically deflected oscilloscopes as thought experiments to show that the EMF is still there even if no current is flowing as a result of it.

In fact, I think maybe this is what's getting everyone in knots:

Dr. Belcher writes:

At 4:31 into the video, Mehdi draws the open circuit to the left above.  There is no current flowing
because the curcuit is open.  Let’s discuss this situation before we put the voltmeter into the circuit. 
There will be zero electric field in the wires, because in the wires the induced electric field exactly
cancels the coulomb electric field, as we saw before.

And everybody stops reading there and declares that a transformer does not have a voltage output.

But Dr. Belcher continues immediately following the above quote:

But we will still see a charge accumulation on the ends of the wire, as shown in the schematic to the right above.
The upper end of the wire will be charged negatively and the lower end of the wire will be charged positively.
Moreover we can calculate the potential difference across the gap by using Faraday’s Law (which applies for
any open surface and its bounding contour, where or not there are any wires around.  Going around the circle
counterclockwise gives us (l  is the height of the gap)



If you want to reassure yourself that this electric field actually exists, make larger than the
breakdown voltage in air, about a million volts per meter, and you will see a spark across the gap that
proves that there is an electric field there, whether you put a voltmeter into the circuit or not.

So there. A transformer secondary puts out a voltage. KVL depends on guess what, VOLTAGE. (Word Kirchhoff's, emphasis mine.)

So why the tarzan can't Kirchhoff's VOLTAGE Law be applied to a transformer secondary as a lumped element?

So what is this whole debacle about? Is it about whether a transformer output has a voltage because "There will be zero electric field in the wires, because in the wires the induced electric field exactly cancels the coulomb electric field?"

Look at what Dr. Belcher says:

Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds)
+V - IR - Q/C - L(dI/dt) = 0, but the first three terms here are the -∫E.dl through the various circuit
elements, and the last term has nothing to do with the -∫E.dl through the inductor, which is zero.

Do you see that last term, which Belcher says has NOTHING (his word, my emphasis) to do with the first 3 terms?

Do you see that last term? That's Faraday's law.

I think you're ignoring Faraday's law, which is, according to Belcher, part of the deal here.

Of course if you ignore Faraday's law, then you're going to say that there's no voltage on the output winding of a transformer, because Faradays law is the term which describes the induced voltage difference across the ends of the winding!

Am I all wrong? What gives? What do you take Belcher to be saying here?

Thank you.

[Jesse Gordon]

1. That sentence of Belcher is about the RLC lumped circuit of section 10. Read pages 15 and 16. It's not about the unlumpable Lewin ring.

That's where I was quoting from. Wouldn't you say that he clearly describes that there are two different attributes, both of which use the unit volt, but one of which is always zero across an inductor and one which is what a volt meter reads, which is how KVL holds as argued by Mehdi?
He says "Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds) "

Ok, let me join the dots for you.

About that sentence by Belcher
You already posted the two relevant pages of Belcher's note. Let me show you that the partial sentence you keep repeating ("In this sense, KVL holds as argued by Mehdi Sagadhdar, but..." - oh, no! You stop right before the 'but') is not about the unlumpable Lewin's ring, but another, lumpable, circuit. You need to read carefully, lest you mistake similar words, like "many" with "any", or something like that.
The famous sentence appears in section 11 on page 16, but it is related to a discussion that began in section 10, on page 15.

Source: Belcher's note available on Mehdi's YT channel. Let's see what section 10 is about, first.

10. Another circuit

link to image: [url]https://i.postimg.cc/DZwxkkyJ/screenshot-3.png[/url]

The experiment above was not considered in the video, but I offer it up as an exercise for the reader. I have a “one-loop” inductor, with a capacitor and resistor, as shown, where I assume the self-magnetic field is only non-zero inside the loop. The battery is shown with the positive terminal down, which will result in a current flow counterclockwise around the circuit, giving a self-magnetic field out of the paper.

At the top of p. 15, he writes

[url]https://i.postimg.cc/vTphV47f/screenshot-4.png[/url]

Take note of the equation, You will see it repeated shortly. For the time being, let's look at the other picture:


[url]https://i.postimg.cc/ZqCLVPfp/screenshot-5.png[/url]

Oh, look: same circuit, same test points to which attach the probes and different voltages depending on whether the voltmeter is on the left or on the right of the loop. I wonder where I have ever seen that before.
Oh yes, Lewin's ring. There is a difference though: Lewin's ring is not lumpable, while this RLC circuit with lumped R, L and C component is lumpable.

How so? What you need to do to consider it lumped is to devise a circuit path that DOES NOT CONTAIN the changing magnetic flux region in its interior (technically, we should say that the closed circuit loop does not cut any net flux - but in 2D it's easier to say what I just wrote). If you can do that, then all voltages along any path you could imagine in the area enclosed by your circuit path, will be path independent (they will only depend on endpoints).
How can you find such a circuit path? Easy: instead of having the circuit path following the coil's filament, we consider the circuit path jumping in the space between the coil terminals. As explained by Feynman, shown by Hayt (posted an excerpt just a few pages above in this thread), detailed by Ramo Whinnery and VanDuzer, exemplified by Purcell, and Haus and Melcher, and Faria, and in the published papers by Romer, Roche, Nicholson, and on and on and on... now you can apply KVL to your freshly lumped circuit and be happy. It's fake, because voltage will still in general depend on path, but in our little bubble we can pretend it doesn't. In that sense, in that little safe space we just cut out from the rest of the real world, KVL holds.
Let me rephrase it: if you can hide the changing magnetic flux inside a lumped component, and you do not look inside it (meaning: your circuit path does not go inside those forbidden zone components and thus it is impossible to go around the dB/dt region) then the "amended" KVL holds.

Yet, whenever you consider circuit paths that go around the magnetic region, -pouff- the dream shatters. For example, if your circuit path consists of only one inductor and the jump at its terminal, you will see KVL die in the definition itself of voltage across the terminals of the lumped inductor. If you accept the definition of voltage as (minus) the path integral of the total electric field (such as that given by the IEC), the following paragraph says just that


[url]https://i.postimg.cc/5y3vxj7f/screenshot-6.png[/url]

i.e. you have a voltage -Ldi/dt across the terminals of the (self-)inductor, but zero voltage along the filament of its coil. Voltage referred to the same points A and B is different depending on the particular path you refer it to. Exactly what Lewin says in his video "Kirchhoff law is for the birds=https://youtu.be/LzT_YZ0xCFY", at minute 33:

"And now I'm going to cause you some sleepless nights. And I'm going to attach here a voltmeter... And now I'm going to ask you what would this voltmeter show. And you'll probably say: 'well didn't you say that the integral of E dot dl through this wire is zero?' So you will think that V here is zero. But that's not true. You know what V is going to be? It's going to be + L di/dt."

Oh, look! Belcher and Lewin are saying the very same thing.
Anyway, let's go back to Belcher's note and the infamous sentence KVL keep waving like a victory flag. To show that Belcher was talking about the lumped RLC circuit, here is the rest of page 15


[url]https://i.postimg.cc/dV77fWYs/screenshot-9.png[/url]

Do you recognize the equation +V - IR - Q/C - Ldi/dt = 0 ? It's the equation for the series lumped RLC circuit.
This part of Belcher's note is about the series lumped RLC circuit where L is the self inductance. NOT the unlumpable LEWIN's RING (where, incidentally but not importantly, the self inductance is negligible). It is about the different approach IN LUMPED CIRCUIT THEORY between properly applying Faraday (using a circuit path the goes through the filament and accounting for the magnetic flux intercepted by the path: 5 + 3 + 0 = 8 ) and using the 'amended version of KVL' (using a circuit path that jumps at the inductor terminals and pretending -L di/dt is a potential difference to save KVL: 5 + 3 - 8 = 0).

One can still save KVL for lumped circuits by bringing the rhs (the surface integral of B.dS) to the left side (and pretending it is a path integral of E.dl).
The trick works ONLY IF you can devise a circuit path that DOES NOT contain the variable magnetic flux region.

You can do it for the lumpable RLC circuit.
And this is the "amended", or "modified", or "extended" or "new" KVL that is so very often badly explained in high school and in first, second year introductory uni books (they use the 5 + 3 - 8 = 0 formalism that erroneously lead students to think there is a voltage buildup in the wires of a coil - Lewin says that "the physics stinks").

You CANNOT DO IT for Lewin's ring.
Why? Because it is required that the two resistor be on the opposite sides of the variable magnetic region. So, your circuit path is BY DEFINITION required to contain the magnetic flux region. The circuit is unlumpable.


source: [url]https://electronics.stackexchange.com/questions/551244/what-would-a-voltmeter-measure-if-you-had-an-electromotive-force-generated-by-a/551428#551428[/url]

And as such, it cannot be properly modeled by lumped transformer models, without changing the true nature of the system (i.e. without introducing jumps in voltage whenever you encounter one of these lumped coils).


source: [url]https://i.postimg.cc/YCKNjzg2/Spot-the-differences.png[/url]

In order to model it with two or four lumped coils, the magnetic field region must be splitted to accomodate a circuit path that does not include any of it. I used the same 'stellated' path style used by Feynman in figure 22-9 at page 22-7 of his second volume of lectures.

Some ask: "don't you see the transformer?" Well, when you are inside the coil, when your circuit path go around the dB/dt coil you no longer have the luxury of using a lumped component model (the secondary of a transformer to which you can apply KVL) for the coil. You have an unlumpable circuit and you need to deal with it accordingly: ditch KVL and use Faraday.

I have a crystal ball that almost never fails me. It is now telling me that, despite being shown here that Belcher was not talking about Lewin's ring when he wrote that sentence, you will nevertheless keep use that very sentence in the future to show that Belcher agrees with Mehdi on Lewin being wrong on the Lewin ring. Just like Mehdi pretendend both Belcher and Feynman agrees with him on all the line, including Lewin's ring. By using your terminology: he is either "clueless", or "ignorant" or "not being honest". In any case: disappointing.

And I have not even mentioned the other note written by Belcher many years ago with Lewin, where they discuss the RL circuit and the "Kirchhoff second law modified for inductors", saying (regarding the 5 + 3 - 8 = 0 formalism)


source: Lewin and Belcher note for 802.11, updated by Lewin to add pointer to Giancoli and to his lecture.
snippet url: [url]https://i.postimg.cc/zGMhDsjH/screenshot-7.png[/url]

which also contains the treatment of the ring made of uniform resistive material and of two resistive halves in a variable magnetic field. Even there, you will see that Belcher's and Lewin's view are the same.

Next stop: a bit more detail on McDonald's note.
(but first, a few fun posts )

Thank you! I have to run to work, I'll re-read this later.

But to clarify two things, are we in agreement then that in cases where an inductor or transformer output has it's dB/dt contained entirely within itself, it can be perfectly lumped as an element for the sake of KVL?

So I don't need to keep arguing with people about whether my KVL in an iron core transformer is valid? It's a transformer, the magnetic circuit of the core contains the dB/dt and the leads that come out of it can be considered output wires from a black box and can be considered a voltage source just like any other for the sake of KVL?

(Assuming, of course, the frequencies involved in the test are of a significantly larger wavelength than the apparatus itself.)

So many people have been arguing so many angles, it would help me a lot to just get that cleared up.

Also, if I understand correctly, you're saying that my Lewin Clock would be lumpable only at the resistors because that's the only place I can measure a voltage difference without running my leads around an area of dB/dt, and that the ∮E.dl or more specifically the Faraday Law Induced Voltage -L(dI/dt) across the windings is there and is a voltage but cannot be unambiguously measured due to the practical issues of dB/dt being enclosed in my volt meter lead path and inducing an error? Do we agree on that too?

Thanks!

[Sredni]

But to clarify two things, are we in agreement then that in cases where an inductor or transformer output has it's dB/dt contained entirely within itself, it can be perfectly lumped as an element for the sake of KVL?

So I don't need to keep arguing with people about whether my KVL in an iron core transformer is valid?

Oh, for Stokes' sakes!
No, you can't use KVL on the circuit running around a core. You are putting your circuit INSIDE the transformer. How can you possibly think you can still consider the contribute of the cut flux as lumpable? The circuit with the two resistors that is your circuit, and identifies your circuit path is going around a nonzero net flux.

You have a fundamental misconception about Faraday's law. It's not your probe wires that need not to 'cut' throught the flux, it's the surface delimited by the closed curve formed by your probe wires (which are arcs, segments, do not have an area) AND the branch of circuit you are probing that does not have to cut any flux line.
EDIT: and of course, in the case of the circuit it's the circuit path itself that must not go around the flux region. Picture it this way: consider the circuit path as rigid iron wire, and then apply an elastic membrane. No net flux should go through that membrane.

Look at what you did with your EI transformer: if you had that membrane on your circuit path, it would be rammed by the central leg like there's no tomorrow.

Also, if I understand correctly, you're saying that my Lewin Clock would be lumpable only at the resistors because that's the only place I can measure a voltage difference without running my leads around an area of dB/dt,

The Lewin clock AS  A CIRCUIT is not lumpable.
You can apply KVL at the measurement loops that do not cut the field lines (I would not even say you "lumped the loop", I don't think it even has a meaning). In particular you can apply KVL to the measurement loops formed by: voltmeter on the left, its probes and the resistor on the left. And analogously to the right.
Buy you cannot apply it to the loop formed by left voltmeter, its probes and the right branch with the right resistor.
And you cannot apply it to the Lewin ring itself.

[Sredni]

Dr. Belcher writes:

At 4:31 into the video, Mehdi draws the open circuit to the left above.  There is no current flowing
because the curcuit is open.  Let’s discuss this situation before we put the voltmeter into the circuit. 
There will be zero electric field in the wires, because in the wires the induced electric field exactly
cancels the coulomb electric field, as we saw before.

And everybody stops reading there and declares that a transformer does not have a voltage output.

I am sure that in the universe where Spock has a goatee everybody will say that.
In this universe, though, I have heard it say from one person only, and it's also on video. At 28:10 of "Kirchhoff's Voltage Law Fails, or does it - Who is Right" the one published on September 16, 2021



(I need to specify because some three or four videos have been removed from its listing - and I wouldn't be surprised if he pulled the remaining ones...), this gentleman, immediately after having shown a clip of Lewin saying "what is the E field in the wire of the self-inductor? What do I hear? What do you say it is? It's zero! Exactly because there is no resistance",  shows a surprised face and says "regardless of the fact that I can put an oscilloscope there and measure - here is a picture of my own oscilloscope - that the voltage DOES NOT EXISTS because Ohm's law says it can't."

EDIT: to be clear, here Bob is asserting the Lewin says that the voltage across a coil is zero, because Ohm's law says it has to be zero. While anyone with an oscilloscope knows better that a MIT professor, because when they put their probes across the terminals they can see a wiggly line on a little screen. And all of this despite the fact that just a few minutes later in Lewin's video, Lewin explains that the voltage across the inductor is + L di/dt - while the integral of E.dl in the wire is zero (because if the resistance of the wire is zero, Ohm's law says the field has to be zero)

Well, guess what - neglecting the difference between saying "there is no voltage"/"there is no voltage output" and "voltage is zero", what you and Bob do not understand is that, since voltage can be multivalued, you can have both:

Voltage on the path that goes through the coil ('voltage along the coil') IS ZERO.
Voltage on the path that jumps between terminals ('voltage across the coil') is + L di/dt, a nonzero value whose waveform you can observe on the oscilloscope screen.

It is amazing how certain people cannot manage this thing.

"Can you believe it? I made this experiment to measure the energy per unit mass necessary to take this 1kg pellet from ground to the first floor. And I found that when I pushed the pellet along a waxed slide the energy per unit mass required was different from that for the slide with one inch of honey on its surface!!!"
"Wait, what??? You get different values for the energy per unit mass between the same starting and ending point??? That's impossible. You must have done something wrong!"
"I know, right? This is not logical. There must be something wrong with the measurement procedure..."
"Certainly a probing error. Let's see on YouTube if someone in a garage has an explanation."

Oh, dear...

[Jesse Gordon]

But to clarify two things, are we in agreement then that in cases where an inductor or transformer output has it's dB/dt contained entirely within itself, it can be perfectly lumped as an element for the sake of KVL?

So I don't need to keep arguing with people about whether my KVL in an iron core transformer is valid?

Oh, for Stokes' sakes!
No, you can't use KVL on the circuit running around a core.

My apologies, I may not have explained my question clearly.

Please allow me try again.

Let's say I have a toroid transformer, or an EI transformer. It's got a primary and two secondaries.

The two secondaries are individual separate isolated output windings.

Each secondary produces 100mV AC RMS 60hz.

Nothing fancy, no components laced through the core, no half turns, nothing fancy.

An ordinary step down mains powered 60hz transformer.

That's all, just an ordinary power transformer, two secondaries each producing 100mV AC RMS 60hz.

Can I consider these two 100mV AC RMS 60hz signals to be lumped element voltage sources coming from a self contained black box, and may I use them as lumped elements to form a loop with the two secondaries and two resistors all in series, and will KVL hold for this setup?

Thank you!

[Sredni]

Let's say I have a toroid transformer, or an EI transformer. It's got a primary and two secondaries.
The two secondaries are individual separate isolated output windings.
Each secondary produces 100mV AC RMS 60hz.

That's all, just an ordinary power transformer, two secondaries each producing 100mV AC RMS 60hz.

Can I consider these two 100mV AC RMS 60hz signals to be lumped element voltage sources coming from a self contained black box, and may I use them as lumped elements to form a loop with the two secondaries and two resistors all in series, and will KVL hold for this setup?

You mean two secondaries in series? Sure, it's the first figure in the bottom row. The one that says "two secondaries in series".
And if you want to use four secondaries, second picture in the bottom row. The one that says "four secondaries in series".


https://i.postimg.cc/YCKNjzg2/Spot-the-differences.png

Maybe the image is too small and you didn't see it, in my previous post?

[Jesse Gordon]

Let's say I have a toroid transformer, or an EI transformer. It's got a primary and two secondaries.
The two secondaries are individual separate isolated output windings.
Each secondary produces 100mV AC RMS 60hz.

That's all, just an ordinary power transformer, two secondaries each producing 100mV AC RMS 60hz.

Can I consider these two 100mV AC RMS 60hz signals to be lumped element voltage sources coming from a self contained black box, and may I use them as lumped elements to form a loop with the two secondaries and two resistors all in series, and will KVL hold for this setup?

You mean two secondaries in series? Sure, it's the first figure in the bottom row. The one that says "two secondaries in series".
And if you want to use four secondaries, second picture in the bottom row. The one that says "four secondaries in series".


https://i.postimg.cc/JnvnsgYG/Spot-the-differences.png

Maybe the image is too small and you didn't see it, in my previous post?

Thank you!

[Jesse Gordon]

...  But Lewin isn't any less of a showman.  ...

Professor Dr. Walter Lewin a showman? Naaaaah. Just no way. No.

But he will show you something so amazing that you will be telling your grandchildren about it!
In fact, it is probably the only time in your life that you will see a transformer! 

[Jesse Gordon]

Yes, it's like "Ow My Balls!"* with some wires thrown in.  But Lewin isn't any less of a showman. 

That's where the similarities between the two end. Every reputable author says the same thing about trying to apply KVL to a circuit subjected to a non-conservative field: caveat emptor, if you try to find the inductive EMF in the circuit as a voltage you'll come a gutser. But, people shrug and don't pay attention. Lewin does the same the other authors do, only that he goes one step further and asks his students to explain WHY exactly you can't find the "missing" "voltage". Wouldn't expect less from an MIT-quality lecture.

Mehdi does differently. He says that this "voltage" is really somewhere in the circuit (sometimes in the wire, sometimes in the resistors) and through some kind of clever technique you will be able to find it. Those who believe his false claims set out to devise all kinds of pseudo-scientific and contradictory explanations and "experiments" to try to confirm the word of their idol.

But Mehdi does worse. He divides the community and incites people against each other, all in the name of a polemic with the only intent of increasing his viewership.

Fortunately, there are courageous people who are turning this into an opportunity to debunk this bunk and introduce people to the tried and tested concepts behind the electromagnetic phenomenon.

Thank you for being one of those courageous people!

So to clarify, I'm trying to get some coherence on this one point:

If I have a regular EI or toroid transformer and it's got two secondary windings, I can use those two winding outputs as "two wire black box components" in a loop with resistors and stuff and they qualify as lumpable elements because the magnetic flux is (almost completely) entirely within the iron core, and thus, I can consider them lumped elements in a loop and apply KVL and KVL will hold, right?

Thank you!

[thinkfat]

Instead of using my little red wires, I used a single length of 14AWG  in a loop, and soldered the ends together with 3/4" overlap so I wouldn't have any contact resistance issues to worry about, like this: https://postimg.cc/nXD7ynQf

I cannot run it for very long because the wire starts getting hot.

The wire getting hot means there's a significant contribution by Mr. Ohm and so we can no longer neglect him.

EDIT (sorry, I pushed the POST button to early)

haha yeah, I saw your initial post and was tempted to reply "I love the way you drive home your point... But what is it? hahaha" but I figured you weren't done so I'd let you finish 

However:
Measuring across where the red wires used to be gives about +50mv.
Measuring across where the resistors used to be gives about -50mv.

(NOTE: Signs are to indicate the phase! I was using an AC volt meter, but I also determined the phase.)

Measuring from two points exactly opposite on the copper ring gives about 0mv.

You get 50mV from the voltage drop due to the wire resistance, -100mV from the EMF in the volt meter loop, resulting in -50mV total.

You get 0mV across two opposite points on the loop, but only in one case, if your volt meter loop encloses a part of the core (linking the flux and having an induced EMF) and also the ohmic voltage drop exactly counters the EMF in the volt meter loop. But it will be path dependent, in any other case you will get a non-zero voltage reading.

But your prediction was unambiguously wrong. Remember, you predicted that there would be 0v across the wires replacing the resistors, and about 100mv measured 'around the ends' where the red wires used to be.

My prediction was under the assumption that Mr. Ohm can be ignored. Obviously he wasn't agreeing with that. But that doesn't invalidate my point.

What gives? Your odds aren't very good here. First you suggested that maybe vastly different sizes of toroids in my EI-Core configuration might not sum to zero in the "KVL in an iron core" setup. You were wrong, sure, everyone makes a mistake.

The odds are entirely in my favor, though you are yet unable to see it.

Now you've made yet another prediction, you said I'd get around 0,100,0,100 mv on my shorted winding. I got around 50,50,50,50 which is not even arguably close to what you predicted.

And I explained why. Besides you got 50, -50, 50, -50 around the loop, mind the phase, and I also explained why. Anyway, you should have gotten a total of 200mV around the inner loop, according to Mr. Faraday, and you didn't, this should make you think. But apparently it doesn't. The reason you're getting 0V is because you're neglecting to account for parts of the EMF in your setup. Had you probed correctly, the total around the inner wire loop would have been the expected 200mV,

Also, above you say that "But it will be path dependent." What will be path dependent? What path? The path of my volt meter leads? Or the path of the shorted winding?

For the sake of your measurements, only the path of your voltmeter loops are relevant.

By the way, have you read Dr. Belchers writup on the subject yet?

He goes over the idea of an unloaded transformer having voltage.

He basically cites Faraday's law and says that if you want to reassure yourself that the electric field actually exists, just increase the output voltage of the transformer to where it jumps an arc. He says you will see a spark and that PROVES (his word, my emphasis) that there is an electric field there, whether you put a volt meter onto the circuit or not.

But the question was never if there's an electric field at the terminals of a transformer or not. You will always have an electric field at discontinuities around a loop.
I'll ignore some part of your quoting Dr. Belcher because what he writes there is undisputed.

So why the tarzan can't Kirchhoff's VOLTAGE Law be applied to a transformer secondary as a lumped element?

You can, but only as long the transformer can be completely regarded as a black box which is fully described by its datasheet values. However, in your experiment, you chose measurement paths that are inside the transformer and exposed to magnetic flux and thus this simplification is not valid.

So what is this whole debacle about? Is it about whether a transformer output has a voltage because "There will be zero electric field in the wires, because in the wires the induced electric field exactly cancels the coulomb electric field?"

Look at what Dr. Belcher says:

Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds)
+V - IR - Q/C - L(dI/dt) = 0, but the first three terms here are the -∫E.dl through the various circuit
elements, and the last term has nothing to do with the -∫E.dl through the inductor, which is zero.

Do you see that last term, which Belcher says has NOTHING (his word, my emphasis) to do with the first 3 terms?

Do you see that last term? That's Faraday's law.

I think you're ignoring Faraday's law, which is, according to Belcher, part of the deal here.

Of course if you ignore Faraday's law, then you're going to say that there's no voltage on the output winding of a transformer, because Faradays law is the term which describes the induced voltage difference across the ends of the winding!

Am I all wrong? What gives? What do you take Belcher to be saying here?

Thank you.

Dr. Belcher says that if you want KVL to hold, you need to subtract the EMF in the loop. That's what I pointed out above: The EMF induced in your inner wire loop is 200mV, so if you sum up all the electric fields in the loop they should add up to the EMF. But in your case they added up to 0V, which is obviously wrong according to Dr. Belcher.

PS: I object to Dr. Belchers statement that the EMF is a voltage difference.

[Jesse Gordon]

1. That sentence of Belcher is about the RLC lumped circuit of section 10. Read pages 15 and 16. It's not about the unlumpable Lewin ring.

That's where I was quoting from. Wouldn't you say that he clearly describes that there are two different attributes, both of which use the unit volt, but one of which is always zero across an inductor and one which is what a volt meter reads, which is how KVL holds as argued by Mehdi?
He says "Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds) "

Ok, let me join the dots for you.

About that sentence by Belcher
You already posted the two relevant pages of Belcher's note. Let me show you that the partial sentence you keep repeating ("In this sense, KVL holds as argued by Mehdi Sagadhdar, but..." - oh, no! You stop right before the 'but') is not about the unlumpable Lewin's ring, but another, lumpable, circuit.

The "but" doesn't have anything to do with it not being lumpable.

And I just re-read  Belcher's writeup, and I think you're wrong in saying that "In this sense, KVL holds as argued by Mehdi" was said about the RLC circuit that Belchar shows.

Specifically, Belcher goes over Lewin's loop specifically ( two resistors in a loop on opposite sides) then also goes over several specific loop configurations that Mehdi showed.

Then Belcher gives an RLC loop diagram that Mehdi did NOT use.

Belcher then goes onto a new Section,  "11 KVL" which makes one reference to the Non-Mehdi RLC loop above just to say that a common misconception holds that the -L(dI/dt) voltage read in the above RLC diagram represents -∫E.dl

In no other way does section "11 KVL" tie it'self to (or exclude itself from) any specific loop topology. In fact, it specifically says "As argued by Mehdi" which means section "11 KVL" CANNOT be about the RLC loop, because Mehdi didn't argue anything about that loop.


I stopped at the "but" because it just says that "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."

It's still a voltage difference though.


I really don't see Belcher addressing the issue of probing or lumping at all.

It looks like he's just saying that even though a superconducting wire has no voltage drop due to -∫E.dl, it does have voltage drop due to ∮E.dl or Faradays law, and thus, KVL holds, that is to say, once the ∮E.dl is taken into account, then yes, the sum  of the voltage differences around the circuit is zero, and that KVL holds.

He says nothing about whether it is testable in the real world, but he says it holds.

How did you get from "but" to believing that Becher is saying that it Lewin's loop is unlumpable? Or that his section "11 KVL" does not apply to Lewin's loop?

After all, the entire basis for his conclusion in "11 KVL" is that ∮E.dl does give the voltage across the wires in order for all the voltage differences around the loop to sum to zero: Just because Lewin's loop may be difficult or impossible to measure in the real world doesn't mean that ∮E.dl  suddenly vanishes.

The famous sentence appears in section 11 on page 16, but it is related to a discussion that began in section 10, on page 15.

Source: Belcher's note available on Mehdi's YT channel. Let's see what section 10 is about, first.

10. Another circuit

link to image: https://i.postimg.cc/DZwxkkyJ/screenshot-3.png

The experiment above was not considered in the video, but I offer it up as an exercise for the reader. I have a “one-loop” inductor, with a capacitor and resistor, as shown, where I assume the self-magnetic field is only non-zero inside the loop. The battery is shown with the positive terminal down, which will result in a current flow counterclockwise around the circuit, giving a self-magnetic field out of the paper.

At the top of p. 15, he writes

https://i.postimg.cc/vTphV47f/screenshot-4.png

Take note of the equation, You will see it repeated shortly. For the time being, let's look at the other picture:


https://i.postimg.cc/ZqCLVPfp/screenshot-5.png

Oh, look: same circuit, same test points to which attach the probes and different voltages depending on whether the voltmeter is on the left or on the right of the loop. I wonder where I have ever seen that before.
Oh yes, Lewin's ring. There is a difference though: Lewin's ring is not lumpable, while this RLC circuit with lumped R, L and C component is lumpable.

How so? What you need to do to consider it lumped is to devise a circuit path that DOES NOT CONTAIN the changing magnetic flux region in its interior (technically, we should say that the closed circuit loop does not cut any net flux - but in 2D it's easier to say what I just wrote). If you can do that, then all voltages along any path you could imagine in the area enclosed by your circuit path, will be path independent (they will only depend on endpoints).
How can you find such a circuit path? Easy: instead of having the circuit path following the coil's filament, we consider the circuit path jumping in the space between the coil terminals. As explained by Feynman, shown by Hayt (posted an excerpt just a few pages above in this thread), detailed by Ramo Whinnery and VanDuzer, exemplified by Purcell, and Haus and Melcher, and Faria, and in the published papers by Romer, Roche, Nicholson, and on and on and on... now you can apply KVL to your freshly lumped circuit and be happy. It's fake, because voltage will still in general depend on path, but in our little bubble we can pretend it doesn't. In that sense, in that little safe space we just cut out from the rest of the real world, KVL holds.
Let me rephrase it: if you can hide the changing magnetic flux inside a lumped component, and you do not look inside it (meaning: your circuit path does not go inside those forbidden zone components and thus it is impossible to go around the dB/dt region) then the "amended" KVL holds.

Yet, whenever you consider circuit paths that go around the magnetic region, -pouff- the dream shatters. For example, if your circuit path consists of only one inductor and the jump at its terminal, you will see KVL die in the definition itself of voltage across the terminals of the lumped inductor. If you accept the definition of voltage as (minus) the path integral of the total electric field (such as that given by the IEC),

Are you saying that the IEC defines volts in such a way that transformers do not have an output voltage?

That's silly.

Why do you bring up the IEC? They know better than Belcher?

Poor old Faraday, eh.

All the abuse he gets, good thing he made himself a shield.

the following paragraph says just that


https://i.postimg.cc/5y3vxj7f/screenshot-6.png

i.e. you have a voltage -Ldi/dt across the terminals of the (self-)inductor, but zero voltage along the filament of its coil. Voltage referred to the same points A and B is different depending on the particular path you refer it to. Exactly what Lewin says in his video "Kirchhoff law is for the birds=https://youtu.be/LzT_YZ0xCFY", at minute 33:

"And now I'm going to cause you some sleepless nights. And I'm going to attach here a voltmeter... And now I'm going to ask you what would this voltmeter show. And you'll probably say: 'well didn't you say that the integral of E dot dl through this wire is zero?' So you will think that V here is zero. But that's not true. You know what V is going to be? It's going to be + L di/dt."

Oh, look! Belcher and Lewin are saying the very same thing.
Anyway, let's go back to Belcher's note and the infamous sentence KVL keep waving like a victory flag. To show that Belcher was talking about the lumped RLC circuit, here is the rest of page 15


https://i.postimg.cc/dV77fWYs/screenshot-9.png

Do you recognize the equation +V - IR - Q/C - Ldi/dt = 0 ? It's the equation for the series lumped RLC circuit.
This part of Belcher's note is about the series lumped RLC circuit where L is the self inductance. NOT the unlumpable LEWIN's RING (where, incidentally but not importantly, the self inductance is negligible). It is about the different approach IN LUMPED CIRCUIT THEORY between properly applying Faraday (using a circuit path the goes through the filament and accounting for the magnetic flux intercepted by the path: 5 + 3 + 0 = 8 ) and using the 'amended version of KVL' (using a circuit path that jumps at the inductor terminals and pretending -L di/dt is a potential difference to save KVL: 5 + 3 - 8 = 0).

Belcher is explaining the common misconception, and showing that L(dI/dt) is COMPLETELY SEPARATE from -∫E.dl and that when Faraday's law is a term, then in fact the voltage difference across the inductor portions summed with the voltage difference across the non-inductor portions will be zero.

One can still save KVL for lumped circuits by bringing the rhs (the surface integral of B.dS) to the left side (and pretending it is a path integral of E.dl).
The trick works ONLY IF you can devise a circuit path that DOES NOT contain the variable magnetic flux region.

You can do it for the lumpable RLC circuit.
And this is the "amended", or "modified", or "extended" or "new" KVL that is so very often badly explained in high school and in first, second year introductory uni books (they use the 5 + 3 - 8 = 0 formalism that erroneously lead students to think there is a voltage buildup in the wires of a coil - Lewin says that "the physics stinks").

You CANNOT DO IT for Lewin's ring.
Why? Because it is required that the two resistor be on the opposite sides of the variable magnetic region. So, your circuit path is BY DEFINITION required to contain the magnetic flux region. The circuit is unlumpable.


source: https://electronics.stackexchange.com/questions/551244/what-would-a-voltmeter-measure-if-you-had-an-electromotive-force-generated-by-a/551428#551428

And as such, it cannot be properly modeled by lumped transformer models, without changing the true nature of the system (i.e. without introducing jumps in voltage whenever you encounter one of these lumped coils).


source: https://i.postimg.cc/YCKNjzg2/Spot-the-differences.png

In order to model it with two or four lumped coils, the magnetic field region must be splitted to accomodate a circuit path that does not include any of it. I used the same 'stellated' path style used by Feynman in figure 22-9 at page 22-7 of his second volume of lectures.

Some ask: "don't you see the transformer?" Well, when you are inside the coil, when your circuit path go around the dB/dt coil you no longer have the luxury of using a lumped component model (the secondary of a transformer to which you can apply KVL) for the coil. You have an unlumpable circuit and you need to deal with it accordingly: ditch KVL and use Faraday.

I have a crystal ball that almost never fails me. It is now telling me that, despite being shown here that Belcher was not talking about Lewin's ring when he wrote that sentence, you will nevertheless keep use that very sentence in the future to show that Belcher agrees with Mehdi on Lewin being wrong on the Lewin ring. Just like Mehdi pretendend both Belcher and Feynman agrees with him on all the line, including Lewin's ring. By using your terminology: he is either "clueless", or "ignorant" or "not being honest". In any case: disappointing.

Yeah yeah yeah, you always say that.

I could just as easily say that my crystalball tells me that despite you being shown what Belcher said, you will continue to go on misrepresenting it blah blah blah.

Anyway, uhhh, it looks to me like Belcher is quoting Feynman, and in fact is representing Feynman's definition as +V - IR - Q/C - L (dI/dt) = 0.

If Belcher is talking about a loop topology that Mehdi didn't argue about, how then can Belcher say "As argued by Mehdi?"

What did Belcher mean? "As Mehdi would have argued had he argued with a loop with a capacitor?" Bleh.

If you back up and look at section 10, it looks to me like Belcher probably introduced the LRC loop topology specifically to match Feyman's definition.

The important take away though is that the fourth term, which is -L(dI/dt) (Faraday's Law) and IS included in all of Lewin's and Mehdi's loops.

I really don't see a strong argument to be made there. Just because Mehdi's and Lewin's loops may not contain a term for a capacitor, that doesn't mean that they don't contain the term for Faraday's Law.

The whole point of "11 KVL" is that due to -L(dI/dt), there is an induced voltage in the opposite polarity of the restively dropped voltage, and the sum of the two categories of voltage will be zero.

That will be true for any loop which has -L(dI/dt) and which has resistance.

Which all of the loops have.

And the rest of the point of "11 KVL" is that even though -∫E.dl must be zero for a superconductor, - L (dI/dt) is COMPLETELY separate from -∫E.dl, and - L (dI/dt) is NOT zero for a superconductor enclosing dB/dt.

And since Lewin's and Mehdi's loops all are (for the sake of discussion) superconductors enclosing dB/dt, the volts across the ends of the wires is non-zero due to the term for Faraday's law.

Belcher isn't even talking about lumbability.

And I have not even mentioned the other note written by Belcher many years ago with Lewin, where they discuss the RL circuit and the "Kirchhoff second law modified for inductors", saying (regarding the 5 + 3 - 8 = 0 formalism)


source: Lewin and Belcher note for 802.11, updated by Lewin to add pointer to Giancoli and to his lecture.
snippet url: https://i.postimg.cc/zGMhDsjH/screenshot-7.png

LOL That reads like Lewin's writing, not like Dr. Belcher's.

which also contains the treatment of the ring made of uniform resistive material and of two resistive halves in a variable magnetic field. Even there, you will see that Belcher's and Lewin's view are the same.

Next stop: a bit more detail on McDonald's note.
(but first, a few fun posts )

In summary, in as few but succinct words as you can muster, what exactly are you trying to say about Belcher and Mehdi?

Mehdi DID NOT argue for KVL on any loop with capacitor in it. So how can that be the one that "Mehdi argued" for?

And what is your point with Feynman's definition of voltage? Did not Belcher point out that Faraday's law is what we're interested in, and that it is separate from -∫E.dl?
And did not Belcher show Faraday's Law in Lewin's and Mehdi's loops as well?

Does Belcher talk about lumpability anywhere?

Do you consider your arguments on Belcher's meaning to be weak, medium, or strong? (I guess "strong" would be if Belcher specifically stated what  argument of Mehdi's he was supporting.)

What argument of Mehdi's is Belcher supporting?

Oh yeah, and you were going to gaze deeply into that  crystalball of yours and tell me what McDonald "really meant" when he said that Lewin's loop was within the range of applicability to Kirchhoff's Voltage Equations.

My crystalball tells me that yours is going to mess up McDonalds words too :DD


Well, at least we agree that transformer windings have voltage, unless you're the IEC, and that as long as there is a way to measure the voltage across the wire without our measurement being tainted by stray magnetic fields, then KVL will be observably true.

And we agree that there are situations where probing can be difficult in areas of stray magneticfields.

We disagree about what Dr. Belcher and Dr. McDonald meant.
We may also disagree about our ability to eliminate said influences of stray magnetic fields.


Can we agree at this point that whether or not it can be measured in the real world, the L(dI/dt) voltage differential across the ends of the wire segments in Lewin's loop summed with the resistive losses in the same loop do add up to zero?

As a separate question, if yes to above:

Can we agree that in Lewin's loop, even if it's not possible to measure it, according to Feynman, the  sum of the voltage differences around the loop  is zero?

[Jesse Gordon]

Instead of using my little red wires, I used a single length of 14AWG  in a loop, and soldered the ends together with 3/4" overlap so I wouldn't have any contact resistance issues to worry about, like this: https://postimg.cc/nXD7ynQf

I cannot run it for very long because the wire starts getting hot.

The wire getting hot means there's a significant contribution by Mr. Ohm and so we can no longer neglect him.

EDIT (sorry, I pushed the POST button to early)

haha yeah, I saw your initial post and was tempted to reply "I love the way you drive home your point... But what is it? hahaha" but I figured you weren't done so I'd let you finish 

However:
Measuring across where the red wires used to be gives about +50mv.
Measuring across where the resistors used to be gives about -50mv.

(NOTE: Signs are to indicate the phase! I was using an AC volt meter, but I also determined the phase.)

Measuring from two points exactly opposite on the copper ring gives about 0mv.

You get 50mV from the voltage drop due to the wire resistance, -100mV from the EMF in the volt meter loop, resulting in -50mV total.

You get 0mV across two opposite points on the loop, but only in one case, if your volt meter loop encloses a part of the core (linking the flux and having an induced EMF) and also the ohmic voltage drop exactly counters the EMF in the volt meter loop. But it will be path dependent, in any other case you will get a non-zero voltage reading.

But your prediction was unambiguously wrong. Remember, you predicted that there would be 0v across the wires replacing the resistors, and about 100mv measured 'around the ends' where the red wires used to be.

My prediction was under the assumption that Mr. Ohm can be ignored. Obviously he wasn't agreeing with that. But that doesn't invalidate my point.

You made no point, except that I did not understand reality. You made a prediction of what reality was gonna be. But your prediction was wrong, and since your prediction being right was the force of your point, you have no point.

You simply did not understand reality, which is why your prediction was wrong.

What gives? Your odds aren't very good here. First you suggested that maybe vastly different sizes of toroids in my EI-Core configuration might not sum to zero in the "KVL in an iron core" setup. You were wrong, sure, everyone makes a mistake.

The odds are entirely in my favor, though you are yet unable to see it.

By "odds" I really meant that your batting average is pretty poor at this point.
So far it's 3 for 3 incorrectly predicting reality.

Now you've made yet another prediction, you said I'd get around 0,100,0,100 mv on my shorted winding. I got around 50,50,50,50 which is not even arguably close to what you predicted.

And I explained why. Besides you got 50, -50, 50, -50 around the loop, mind the phase, and I also explained why. Anyway, you should have gotten a total of 200mV around the inner loop, according to Mr. Faraday, and you didn't, this should make you think. But apparently it doesn't. The reason you're getting 0V is because you're neglecting to account for parts of the EMF in your setup. Had you probed correctly, the total around the inner wire loop would have been the expected 200mV,

I did get 200mv, I just didn't measure all of it.

Look at it this way:

200mv is induced due to Faraday's law, right?

And 200mv is lost due to resistance.  Right?

Let's say The 100mv and 100mv is induced where the wire passes through the transformer core.

But the resistive loss is evenly distributed around the copper ring, right?

And due to the geometry of the copper ring, my four measuring points were basically at quarters.

In other words, the purely resistive part outside the transformer was about 1/4 of the length and 1/4 of the length.

And the portion passing through the core was also about 1/4 and 1/4 of the length.

Thus, each quarter of the copper ring had about 50mv dropped. Ya?

Outside the core, I would just be measuring the ohmic drop.

But the quarter of the loop which passes through the core would be 100mv Faraday Law voltage minus 50mv ohmic drop, which gives 50.

So there IS 200mv generated, and 200mv lost, it's just not generated evenly around the loop, but it's lost evenly around the loop.

Right or wrong, you gotta admit it does add up, and it does seem to make sense.

Like I said before, resistors, capacitors, and inductors ALL have ALL THREE of inductance, capacitance, and resistance. (excepting of course superconductors which have no resistance.)
Normally the named attribute is the only major attribute (i.e. a resistor has very little capacitance or inductance) but in cases like we did with the copper wire loop, we have to model in the inductive and resistive components to our inductors. Model it as an inductor with a built in series resistor. That's exactly what it is.

Also, above you say that "But it will be path dependent." What will be path dependent? What path? The path of my volt meter leads? Or the path of the shorted winding?

For the sake of your measurements, only the path of your voltmeter loops are relevant.

By the way, have you read Dr. Belchers writup on the subject yet?

He goes over the idea of an unloaded transformer having voltage.

He basically cites Faraday's law and says that if you want to reassure yourself that the electric field actually exists, just increase the output voltage of the transformer to where it jumps an arc. He says you will see a spark and that PROVES (his word, my emphasis) that there is an electric field there, whether you put a volt meter onto the circuit or not.

But the question was never if there's an electric field at the terminals of a transformer or not. You will always have an electric field at discontinuities around a loop.
I'll ignore some part of your quoting Dr. Belcher because what he writes there is undisputed.

So why the tarzan can't Kirchhoff's VOLTAGE Law be applied to a transformer secondary as a lumped element?

You can, but only as long the transformer can be completely regarded as a black box which is fully described by its datasheet values. However, in your experiment, you chose measurement paths that are inside the transformer and exposed to magnetic flux and thus this simplification is not valid.

Are you talking about my EI-Core transformer with the two red secondary windings?

Because Sredni has said that an EI-Core transformer's secondary winding outputs qualify as black box because the dB/dt is contained (for all practical purposes) entirely inside the iron core.

You need to take that up with him if you think he's wrong.

But think about it. If you have a toroidal transformer, and you pass a wire once through the center to form a secondary, it will have EXACTLY a 1 turn secondary. It doesn't matter what else you do, that wire will still "enclose" the EXACT same one turn of dB/dt. You can take a magnetic field meter and prove that there is no dB/dt outside the toroid's surface.

Because there is no dB/dt outside the toroid, changing the path of the leads can neither add to nor subtract from the dB/dt being experienced by that one turn.

Like I said, please take up with Sredni.

btw, what about a transformer like this? https://postimg.cc/VdKPNnSB

It's a bobbin design, but the ends of the bobbin mushroom out and fold back to enclose the entire transformer, and the wires come out holes.

Would that make a good lumped element for a KVL loop?

So what is this whole debacle about? Is it about whether a transformer output has a voltage because "There will be zero electric field in the wires, because in the wires the induced electric field exactly cancels the coulomb electric field?"

Look at what Dr. Belcher says:

Thus with Feynman et al.’s definition, the sum of all the voltage differences around the circuit is zero (that is, KVL holds)
+V - IR - Q/C - L(dI/dt) = 0, but the first three terms here are the -∫E.dl through the various circuit
elements, and the last term has nothing to do with the -∫E.dl through the inductor, which is zero.

Do you see that last term, which Belcher says has NOTHING (his word, my emphasis) to do with the first 3 terms?

Do you see that last term? That's Faraday's law.

I think you're ignoring Faraday's law, which is, according to Belcher, part of the deal here.

Of course if you ignore Faraday's law, then you're going to say that there's no voltage on the output winding of a transformer, because Faradays law is the term which describes the induced voltage difference across the ends of the winding!

Am I all wrong? What gives? What do you take Belcher to be saying here?

Thank you.

Dr. Belcher says that if you want KVL to hold, you need to subtract the EMF in the loop. That's what I pointed out above: The EMF induced in your inner wire loop is 200mV, so if you sum up all the electric fields in the loop they should add up to the EMF. But in your case they added up to 0V, which is obviously wrong according to Dr. Belcher.

No, because again, like I keep saying MODEL REALITY!

Reality:

I have a loop consisting of 2 resistors and 2 inductors.
But the inductors have the same resistance as the 2 resistors.

Let's say for the sake of argument, that my loop resistance is 16 mohms.

The resistors have zero volts induced on them, and are 4mohm.
The inductors have 100mv induced in them, but are also 4mohm.

The total loop resistance is 16mohm, and the current is 12.5 amps.

So as you can see, the two inductors each have 100mv induced across them, but 50mv of that is lost due to resistive heating.

So again, if you model each inductor as a resistor+inductor lumped element, (WHICH, by the way, is what you always have to do in the real world when you need good accuracy because components always have some parasitic attributes) then it all adds up and KVL holds just fine.

[thinkfat]

Are you talking about my EI-Core transformer with the two red secondary windings?

Because Sredni has said that an EI-Core transformer's secondary winding outputs qualify as black box because the dB/dt is contained (for all practical purposes) entirely inside the iron core.

You're still completely disregarding that you have multiple loops in your EI-Core transformer experiment.

@Sredni isn't wrong, you just have troubles understanding what he said because you only hear what seems to suit your understanding. That's called "confirmation bias". That transfomer is a black box only at its terminals. But your measurements are not at its terminals.

Let's say The 100mv and 100mv is induced where the wire passes through the transformer core.

And there's your error, right there. This is complete BS.

[Sredni]

About that sentence by Belcher
Let me show you that the partial sentence you keep repeating ("In this sense, KVL holds as argued by Mehdi Sagadhdar, but..." - oh, no! You stop right before the 'but') is not about the unlumpable Lewin's ring, but another, lumpable, circuit.

The "but" doesn't have anything to do with it not being lumpable.
And I just re-read  Belcher's writeup, and I think you're wrong in saying that "In this sense, KVL holds as argued by Mehdi" was said about the RLC circuit that Belchar shows.

See, I told you my crystal ball almost never fails me.
You really don't see it! Do you?
You read the sentence

"In this sense, KVL holds as argued by Mehdi Sagadhdar, 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."

and just before the but, you go on a celebratory trip and shut down. And yet, the circuit it is referred to is the lumpable RLC circuit whose equation is just above. Let's see what the but says:

"...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."

And what could possibly be the other three elements? Well, the generator, the resistor and the capacitor, of course. He is talking about a lumpable circuit that, once lumped, allows for KVL to be applied. That sentence, it is one sentence, is not about Lewin's ring. (Also because in Lewin's ring the inductance L is neglible and one could also perform the experiment using a falling magnet, thus eliminating the secondary coil and the related mutual inductance as well - but let's forget about this).

If Belcher is talking about a loop topology that Mehdi didn't argue about, how then can Belcher say "As argued by Mehdi?" What did Belcher mean? "As Mehdi would have argued had he argued with a loop with a capacitor?" 
[...]
Mehdi DID NOT argue for KVL on any loop with capacitor in it. So how can that be the one that "Mehdi argued" for? 
[...]
What argument of Mehdi's is Belcher supporting? 

Dang, you really nailed me, here.
If only if could find a part in Mehdi's first video where he considers a lumped circuit and applies the 'modified KVL' to it, and hopefully says something along the lines of "KVL holds"...
Oh, let see...
At 8:21 in his first video on the topic, Mehdi draws his conclusions about a LUMPABLE circuit. This one:


https://i.postimg.cc/zBSSpd8x/screenshot.png

and he says:

"So you see that the voltage across both R1 and R2 is equal to the voltage across R1 plus the voltage across R2 which is the same voltage ACROSS the loop. "

Like you and Bob, he cannot understand that voltage, being path dependent in the presence of variable magnetic fields, can have different values depending (doh!) on the path and he is stuck with the terminology used in lumped circuit theory (where we consider the voltage across the terminals). In this case, since we are in the presence of a variable magnetic field, voltage depends on path and in particular: the voltage ACROSS the loop is Vr1+Vr2, while the voltage ALONG the loop is zero.
But the way he put resistors on one side makes this a lumpable circuit. In fact, it can be lumped by considering a circuit path that jumps at the terminals so that there is no variable magnetic field enclosed by said path. If we look at the circuit this way, the only voltage we need to consider in our limited safe space of lumped circuit theory is the voltage ACROSS the loop, which is not zero.

But Mehdi is clearly oblivious of all this, and keeps thinking that there can be only one value for the voltage between two points

"This shows that the voltage ACROSS the loop is not zero, unlike what we've thought, but is equal to Vr1 plus Vr2. The loop is the secondary of a transformer, with the primary being my coil."

Well, no shit, Sherlock! That is a lumpable circuit and as such it can be modeled with lumped components. And sure enough, he produces a LUMPED circuit model:


https://i.postimg.cc/285FFFJx/screenshot-2.png

A model that exhibit a massive jump in voltage when you encounter the lumped symbol of the inductor. Lumped circuit theory can only model the jump in voltage at the terminals because you are not allowed to look inside the transformer, BUT the voltage ALONG the loop is still zero (or, to be precise, the negligible ohmic loss in copper).

Let's hear it straight from the horse's mouth. I mean, from Mehdi, at 8:41:

"Dr. Lewin's model misses a transformer in the loop, with the voltage across the winding equal to Vr1 plus Vr2. KVL HOLDS"

Well, we have now established that Mehdi talked about a LUMPED circuit in his first video (even though he does not realize that it IS NOT Lewin's ring, which is unlumpable exactly because the resistors are required to be on the opposite sides of the magnetic flux region). And that he applied KVL to said lumped circuit (which we can do, in the 'modified' form. Too bad it is not Lewin's ring). And he also says "KVL holds"!

In lumped circuits, such as this one (which is NOT Lewin's ring, let me repeat it) and the series RLC circuit considered by Belcher at page 15, we can make Faraday's law look like it's KVL. We just need to take the surface integral on the right, change its sign and put it in the lhs.
What have we done, by doing so? We started with a formula that says the circulation of E is NOT zero (when the circuit path follows the filament of the coil and thus INCLUDES the variable dB/dt region) and by cutting away the part of path the follows the coil and replacing it with the jump at its terminals we ended up with a formula that says that the circulation of E is ZERO (because the modified circuit path now skips - DOES NOT INCLUDE - the variable dB/dt) region.
In this modified circuit - THAT DOES NOT INCLUDE THE dB/dt REGION - KVL holds in the sense intended by Mehdi, but the voltage ACROSS the inductor is the result of the application of Faraday's law and the exclusion of its filament from the circuit's path.

And this is the key: in order to pull this trick (which I call the 'amended KVL') you need to be able to find a circuit path that DOES NOT INCLUDE THE VARIABLE MAGNETIC REGION AT ITS INTERIOR. You can do it when you put both resistors on the same side of the ring. You CANNOT do it for Lewin's ring (because Lewin's ring is Lewin's ring ONLY IF THE RESISTORS ARE ON THE OPPOSITE SIDES OF THE VARIABLE MAGNETIC FIELD REGION AND THE CIRCUIT PATH INCLUDES THAT REGION).
Now try to focus:

You cannot exclude the variable magnetic flux region from the circuit path of a circuit that requires its circuit path to contain the variable magnetic flux region. No matter how hard you try.

Geometry matters, exactly because in the case of Lewin's ring we are talking about a non lumpable circuit whose circuit path is required to circle a variable magnetic region.

P.S
Incidentally, the last sentence in Belcher's note is the following:

"An excellent discussion of “electromotive force” (a terrible and misleading name) is given in the text by Griffiths, Introduction to Electrodynamics 4th Edition."

and guess what? Griffiths has the Romer-Lewin ring in one of his problems. Problem 7.50 uses the same diagram as Romer's paper. And in the solution he states... "Notice that V1 != V2, even though they are connected to the same points!"
Well, it really looks like the reference Belcher suggests has been written by another of Lewin's minions.

[Jesse Gordon]

About that sentence by Belcher
Let me show you that the partial sentence you keep repeating ("In this sense, KVL holds as argued by Mehdi Sagadhdar, but..." - oh, no! You stop right before the 'but') is not about the unlumpable Lewin's ring, but another, lumpable, circuit.

The "but" doesn't have anything to do with it not being lumpable.
And I just re-read  Belcher's writeup, and I think you're wrong in saying that "In this sense, KVL holds as argued by Mehdi" was said about the RLC circuit that Belchar shows.

See, I told you my crystal ball almost never fails me.
You really don't see it! Do you?
You read the sentence

"In this sense, KVL holds as argued by Mehdi Sagadhdar, 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."

and just before the but, you go on a celebratory trip and shut down. And yet, the circuit it is referred to is the lumpable RLC circuit whose equation is just above. Let's see what the but says:

"...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."

And what could possibly be the other three elements? Well, the generator, the resistor and the capacitor, of course. He is talking about a lumpable circuit that, once lumped, allows for KVL to be applied. That sentence, it is one sentence, is not about Lewin's ring. (Also because in Lewin's ring the inductance L is neglible and one could also perform the experiment using a falling magnet, thus eliminating the secondary coil and the related mutual inductance as well - but let's forget about this).

If Belcher is talking about a loop topology that Mehdi didn't argue about, how then can Belcher say "As argued by Mehdi?" What did Belcher mean? "As Mehdi would have argued had he argued with a loop with a capacitor?" 
[...]
Mehdi DID NOT argue for KVL on any loop with capacitor in it. So how can that be the one that "Mehdi argued" for? 
[...]
What argument of Mehdi's is Belcher supporting? 

Dang, you really nailed me, here.
If only if could find a part in Mehdi's first video where he considers a lumped circuit and applies the 'modified KVL' to it, and hopefully says something along the lines of "KVL holds"...
Oh, let see...
At 8:21 in his first video on the topic, Mehdi draws his conclusions about a LUMPABLE circuit. This one:


[url]https://i.postimg.cc/zBSSpd8x/screenshot.png[/url]

and he says:

"So you see that the voltage across both R1 and R2 is equal to the voltage across R1 plus the voltage across R2 which is the same voltage ACROSS the loop. "

Like you and Bob, he cannot understand that voltage, being path dependent in the presence of variable magnetic fields, can have different values depending (doh!) on the path and he is stuck with the terminology used in lumped circuit theory (where we consider the voltage across the terminals). In this case, since we are in the presence of a variable magnetic field, voltage depends on path and in particular: the voltage ACROSS the loop is Vr1+Vr2, while the voltage ALONG the loop is zero.
But the way he put resistors on one side makes this a lumpable circuit. In fact, it can be lumped by considering a circuit path that jumps at the terminals so that there is no variable magnetic field enclosed by said path. If we look at the circuit this way, the only voltage we need to consider in our limited safe space of lumped circuit theory is the voltage ACROSS the loop, which is not zero.

But Mehdi is clearly oblivious of all this, and keeps thinking that there can be only one value for the voltage between two points

"This shows that the voltage ACROSS the loop is not zero, unlike what we've thought, but is equal to Vr1 plus Vr2. The loop is the secondary of a transformer, with the primary being my coil."

Well, no shit, Sherlock! That is a lumpable circuit and as such it can be modeled with lumped components. And sure enough, he produces a LUMPED circuit model:


[url]https://i.postimg.cc/285FFFJx/screenshot-2.png[/url]

A model that exhibit a massive jump in voltage when you encounter the lumped symbol of the inductor. Lumped circuit theory can only model the jump in voltage at the terminals because you are not allowed to look inside the transformer, BUT the voltage ALONG the loop is still zero (or, to be precise, the negligible ohmic loss in copper).

Let's hear it straight from the horse's mouth. I mean, from Mehdi, at 8:41:

"Dr. Lewin's model misses a transformer in the loop, with the voltage across the winding equal to Vr1 plus Vr2. KVL HOLDS"

Well, we have now established that Mehdi talked about a LUMPED circuit in his first video (even though he does not realize that it IS NOT Lewin's ring, which is unlumpable exactly because the resistors are required to be on the opposite sides of the magnetic flux region). And that he applied KVL to said lumped circuit (which we can do, in the 'modified' form. Too bad it is not Lewin's ring). And he also says "KVL holds"!

In lumped circuits, such as this one (which is NOT Lewin's ring, let me repeat it) and the series RLC circuit considered by Belcher at page 15, we can make Faraday's law look like it's KVL. We just need to take the surface integral on the right, change its sign and put it in the lhs.
What have we done, by doing so? We started with a formula that says the circulation of E is NOT zero (when the circuit path follows the filament of the coil and thus INCLUDES the variable dB/dt region) and by cutting away the part of path the follows the coil and replacing it with the jump at its terminals we ended up with a formula that says that the circulation of E is ZERO (because the modified circuit path now skips - DOES NOT INCLUDE - the variable dB/dt) region.
In this modified circuit - THAT DOES NOT INCLUDE THE dB/dt REGION - KVL holds in the sense intended by Mehdi, but the voltage ACROSS the inductor is the result of the application of Faraday's law and the exclusion of its filament from the circuit's path.

And this is the key: in order to pull this trick (which I call the 'amended KVL') you need to be able to find a circuit path that DOES NOT INCLUDE THE VARIABLE MAGNETIC REGION AT ITS INTERIOR. You can do it when you put both resistors on the same side of the ring. You CANNOT do it for Lewin's ring (because Lewin's ring is Lewin's ring ONLY IF THE RESISTORS ARE ON THE OPPOSITE SIDES OF THE VARIABLE MAGNETIC FIELD REGION AND THE CIRCUIT PATH INCLUDES THAT REGION).
Now try to focus:

You cannot exclude the variable magnetic flux region from the circuit path of a circuit that requires its circuit path to contain the variable magnetic flux region. No matter how hard you try.

Geometry matters, exactly because in the case of Lewin's ring we are talking about a non lumpable circuit whose circuit path is required to circle a variable magnetic region.

P.S
Incidentally, the last sentence in Belcher's note is the following:

"An excellent discussion of “electromotive force” (a terrible and misleading name) is given in the text by Griffiths, Introduction to Electrodynamics 4th Edition."

and guess what? Griffiths has the Romer-Lewin ring in one of his problems. Problem 7.50 uses the same diagram as Romer's paper. And in the solution he states... "Notice that V1 != V2, even though they are connected to the same points!"
Well, it really looks like the reference Belcher suggests has been written by another of Lewin's minions.

Wow, all that and you didn't really answer my question. You never answer a question head-on, do you 

Exactly what argument did Mehdi make that Belcher agreed with?

Are you saying that the ONLY Mehdi-argument that Belcher agreed with was a fully lumpable circuit?

[Jesse Gordon]

Are you talking about my EI-Core transformer with the two red secondary windings?

Because Sredni has said that an EI-Core transformer's secondary winding outputs qualify as black box because the dB/dt is contained (for all practical purposes) entirely inside the iron core.

You're still completely disregarding that you have multiple loops in your EI-Core transformer experiment.

@Sredni isn't wrong, you just have troubles understanding what he said because you only hear what seems to suit your understanding. That's called "confirmation bias". That transfomer is a black box only at its terminals. But your measurements are not at its terminals.

Let's say The 100mv and 100mv is induced where the wire passes through the transformer core.

And there's your error, right there. This is complete BS.

To clarify regarding my EI-Core transformer, with the two red wires that pass through the core, are you saying that if I connected my volt meter leads across the ends of one of those red wires, are you saying that I could change my reading by changing the path of the volt meter leads as I moved them around the outside of the transformer?

Make another prediction. I got an EI-Core. I got a volt meter. I can pass a wire through one side, the other side, or both sides if you like.

Tell me where I should run the secondary turn wire, where I should connect my volt meter leads, and what I should do to witness this alleged path-dependence.

I think you're wrong. Because the dB/dt is contained "entirely" within the iron core, changing the path of the leads external to the core can make no difference in measured voltaged because it can make no difference in the quantity of area of enclosing dB/dt, because in order to change the enclosed area of dB/dt, the volt meter lead would have to physically pass through part of the iron core.

But if you think you're right, make another prediction here. If you can get 4 correct predictions in a row, then you can bring your average above 50% 

Exactly how would I witness this alleged path-dependence you assert?

[thinkfat]

Are you talking about my EI-Core transformer with the two red secondary windings?

Because Sredni has said that an EI-Core transformer's secondary winding outputs qualify as black box because the dB/dt is contained (for all practical purposes) entirely inside the iron core.

You're still completely disregarding that you have multiple loops in your EI-Core transformer experiment.

@Sredni isn't wrong, you just have troubles understanding what he said because you only hear what seems to suit your understanding. That's called "confirmation bias". That transfomer is a black box only at its terminals. But your measurements are not at its terminals.

Let's say The 100mv and 100mv is induced where the wire passes through the transformer core.

And there's your error, right there. This is complete BS.

To clarify regarding my EI-Core transformer, with the two red wires that pass through the core, are you saying that if I connected my volt meter leads across the ends of one of those red wires, are you saying that I could change my reading by changing the path of the volt meter leads as I moved them around the outside of the transformer?

Make another prediction. I got an EI-Core. I got a volt meter. I can pass a wire through one side, the other side, or both sides if you like.

Tell me where I should run the secondary turn wire, where I should connect my volt meter leads, and what I should do to witness this alleged path-dependence.

I think you're wrong. Because the dB/dt is contained "entirely" within the iron core, changing the path of the leads external to the core can make no difference in measured voltaged because it can make no difference in the quantity of area of enclosing dB/dt, because in order to change the enclosed area of dB/dt, the volt meter lead would have to physically pass through part of the iron core.

Exactly how would I witness this alleged path-dependence you assert?

I apologize in advance for the quality of the drawing I whipped up in "Libreoffice Draw". I'm not really an artistic person and this stupid program isn't helping me be, either.

The attached drawing is a cross section through your EI-Core transformer with your Lewin-Loop.

"V1" is connected like you're probing right now. The volt meter reads 100mV or thereabouts.

"V2" is connected through a different path. I predict that the volt meter will read 0mV (or close to it).

There you go, knock yourself out.

[Jesse Gordon]

PS: I object to Dr. Belchers statement that the EMF is a voltage difference.

Wow, Dr. thinkphat, your objections are duly noted.

Actually, Dr. Belcher was quoting Dr. Feynman.

Dr. Belcher writes:

One textbook that makes perfectly clear what the “voltage across the inductor” is is the textbook by
Feynman, Leighton, and Sands, The Feynman Lectures on Physics (Addison‐Wesley, Reading, MA 1964),
Vol II, p22‐2).  In that textbook, the authors state explicitly that the -∫E.dl through the inductor must
be zero, and they define the voltage difference across the inductor (which the correctly identify as an
“electromotive force”, as ∮E.dl, which by Faraday’s Law is -L(dI/dt).

So there you have it. Feynman, Leighton, and Sands also identify the voltage difference across the inductor as an EMF.

I suppose you object to that too?

Besides, so far, 3 out of 3 of your predictions failed the reality check. Dr. Belchers on the other hand seem to pass the reality check. I think I'll go with what he says on that matter.
(And one out of one logic attempted failed as well.)

[Jesse Gordon]

Are you talking about my EI-Core transformer with the two red secondary windings?

Because Sredni has said that an EI-Core transformer's secondary winding outputs qualify as black box because the dB/dt is contained (for all practical purposes) entirely inside the iron core.

You're still completely disregarding that you have multiple loops in your EI-Core transformer experiment.

@Sredni isn't wrong, you just have troubles understanding what he said because you only hear what seems to suit your understanding. That's called "confirmation bias". That transfomer is a black box only at its terminals. But your measurements are not at its terminals.

Let's say The 100mv and 100mv is induced where the wire passes through the transformer core.

And there's your error, right there. This is complete BS.

To clarify regarding my EI-Core transformer, with the two red wires that pass through the core, are you saying that if I connected my volt meter leads across the ends of one of those red wires, are you saying that I could change my reading by changing the path of the volt meter leads as I moved them around the outside of the transformer?

Make another prediction. I got an EI-Core. I got a volt meter. I can pass a wire through one side, the other side, or both sides if you like.

Tell me where I should run the secondary turn wire, where I should connect my volt meter leads, and what I should do to witness this alleged path-dependence.

I think you're wrong. Because the dB/dt is contained "entirely" within the iron core, changing the path of the leads external to the core can make no difference in measured voltaged because it can make no difference in the quantity of area of enclosing dB/dt, because in order to change the enclosed area of dB/dt, the volt meter lead would have to physically pass through part of the iron core.

Exactly how would I witness this alleged path-dependence you assert?

I apologize in advance for the quality of the drawing I whipped up in "Libreoffice Draw". I'm not really an artistic person and this stupid program isn't helping me be, either.

The attached drawing is a cross section through your EI-Core transformer with your Lewin-Loop.

"V1" is connected like you're probing right now. The volt meter reads 100mV or thereabouts.

"V2" is connected through a different path. I predict that the volt meter will read 0mV (or close to it).

There you go, knock yourself out.

What are you talking about? I don't have a third secondary winding. You have drawn a third secondary winding.
Obviously if you put in a third secondary winding and wire it in series with another secondary winding, you can cause the voltages to either add or subtract.
You've basically formed a fake secondary winding with zero dB/dt enclosed.


That is NOT MY SETUP.

I AM NOT running my volt meter leads through the core of the transformer. If I did, I'd be adding more secondary windings.

What sort of diversion is this? Can't you see that according to Faraday's law the one wire is a clockwise turn and the other is a counter clockwise turn, and that the voltage across one will be the negative of the other, and when summed they will be zero?

You saw the video, I simply have two single-pass secondary windings. That is all.

Where the tarzan did you get the idea that I had a third volt meter lead run through the transformer, thus forming a third secondary winding?

But FOR A GIVEN SECONDARY WINDING, without changing the number of turns between tests, why on earth isn't my transformer secondary windings considered a black box for the sake of KVL?

You're grabbing at straws my friend, or in this case, you're grabbing at secondary windings.

Dude, look. The ability to change the number of turns on the secondary doesn't mean that for a given number of turns the output of the secondary is not a lumpable voltage source which can be considered a black box.