Does Kirchhoff's Law Hold? Disagreeing with a Master

[Berni]

This is exactly why the other "less scientific" definition of voltage (The one about how many electrons there are in one spot) is used in circuit analysis and pretty much everywhere else where you need to actually calculate something.

You keep talking of that as if it were a different physical quantity, measured in different units. It's not. The 'scalar potential' that is part of the (V, A) pair is just the path integral of the conservative part of the total electric field.
It's as if you decomposed a mathematical function into its odd and even parts and than claimed that the odd part is a different, 'less mathematic' definition of function.

You can easily see where that decomposition comes from by writing Faraday's law (use dS for the differential element of area to avoid confusion with the vector potential A, and use E_total instead of E to highlight that it is the resulting field, superposition of coulombian and induced fields). Then express B in terms of the vector potential A,  turn the surface integral on the right into a path integral along the surface contour using Stokes (or "the rotor's") theorem. Now take the integral on the right to the left, changing sign. Bring everything inside the same path integral. You are left with a field whose circulation along a closed path is always zero.
Hey, that's a conservative field! Well of course, you have stripped the induced - non conservative - part from the total field.

Congratulations, it can be very useful, but it's only half of the story.

I will come back to this post with formulas and drawings when I will be able to scan.

You can have different results in the same quantity if that quantity is defined differently.

For example if we take something we all know well, Speed aka Velocity.
So you are running 10 m/s along a road. So your speed is 10m/s we can all agree
What if you are running 10 m/s along the back of a truck that's going 50m/s ? Okay now we need to actually use vectors to know how to add them together to get the speed along the ground. So suppose its in the same direction as the truck so we are doing 60m/s
But we are all on a planet that's going along the sun at 30500 m/s. Well okay now we have to define speed as being the difference in speed between the ground and you.
So we already have lots of different speeds we could be considered moving depending on how you look at the quantity of speed.
But then we start going faster, we send the truck along a tunnel of vacuum at 299792453 m/s (5m/s slower than the speed of light) and you run in the forward direction at 10m/s along the back of the truck and you suddenly are moving faster than the speed of light?! And yet again we have to redefine what speed is and take into account Einsteins special relativity, throwing out all the kinematics equations from highschool physics to get the right result. And the result depends on where you are standing and watching the guy running along the truck.
...
It gets messy even for something this simple (And this same velocity mess is partially responsible for making magnetic fields work trough the very same special relativity effect).


And yes exactly as you said i turned it into a conservative field by defining the path with a length of wire (More detail in 2nd response in previous post) and looking at what field would end up along the path given the magnetic field around it. Note that this doesn't need an area, just a path, but the whole thing can be simplified down to an area with Faradays law as long as the path is closed.

[ogden]

You say that resistor with voltage drop have zero E field inside. That means that integral E.dl over it is zero meaning that it does not have voltage drop on it! It's paradox, don't you see?

Indeed. But I never said that the resistor has zero E-field inside. I said that the circulation of the conservative part of the E field is zero.

You just pick one or another type of E field according to your agenda 

I think I have all the parts of the puzzle, all made by you. Now you can buckle-up for Part2.

The conservative part of the E field is stronger in the copper as well. It has to be in order to cancel the induced part.

Did you just say that Dr.Lewin is mistaken? - Because he claims that nonconservative field is zero inside copper coil (or secondary of transformer). Remember - resistance is so small that we ignore it, but there can't be conservative field in the conductor of zero resistance.

So, copper part have *only* nonconservative field, resulting voltage (integral E.dl) equals 1V. You agreed because you did not argue when I said that it is possible to measure 1V AC voltage on transformer secondary  w/o resistor connected. (It would be dumb to argue anyway).

In our "box + resistor" case resistor is outside magnetic field of the transformer, so Faraday's law cannot do anything about it, so there cannot be nonconservative fields in form of EMF inside it. What remains is conservative field which we already agreed exists in resistor, it's integral E.dl is 1V when connected to coil generating 1V.

According to logic above, sum of fields in copper and resistor, integral E_conservative.dl and integral E_nonconservative.dl is zero. [edit] At given time of observation obviously.

  I will try again.
1) Does KVL hold when inside box is DC battery? 2) Does KVL hold when inside box is battery-powered AC generator? 3) Does KVL hold when inside box is piezo-based 1V AC voltage generator? 4) Does KVL hold when inside box is transformer?

1) yes, outside and inside
2) it depends. Does the generator have a time-varying B field inside ? Is so and if the flux is neatly tucked inside the box, then 'extended KVL' (which is Faraday under disguise) will appear to work outside, but won't work inside when you cross the flux-varying region.
3) I am not familiar with piezoelectric generators, but if there is no dphi/dt involved we probably can treat them as batteries.
4) 'new KVL' which is Faraday under disguise will appear to work outside and fail miserably inside if you attempt to cross the flux-varying region.

Fact that you even try to answer those questions is hilarious by it's own We agreed that for voltmeter it does not matter what's inside the box, it cannot sort out electrons - they were moved by class-AB amplifier, little monkeys or Mr.Faraday.

[edit]  Typo correction using strikethrough

[Sredni]

Did you just say that Dr.Lewin is mistaken? - Because he claims that nonconservative field is zero inside copper coil (or secondary of transformer).

He must have meant the total field.
Keep in mind that the left side of Faraday's equation, circulation of E.dl refers to the total field.

Of course it might happen that the conservative field be zero as well: if all fields are conservative, the conservative field is all you've got and in that case the conservative field will be zero inside a perfect conductor. It happens for example in electrostatics: point charge generates a conservative E-field, you place a piece of copper nearby, free charges on the copper surface redistribute to create a contribution that will erase the field inside the copper. So sum of conservative E field due to point charge plus conservative field due to free surface charge equals total conservative E field inside the conductor is zero. And I think it will work with batteries and a copper wire.
It's all about context.

Can you show where Lewin said that?

So, copper part have *only* nonconservative field, resulting voltage (integral E.dl) equals 1V. You agreed because you did not argue when I said that it is possible to measure 1V AC voltage on transformer secondary  w/o resistor connected. (It would be dumb to argue anyway).

No I do not agree and I have already explained how that can happen in one of my previous post (many pages back).
The fact that you can have a voltage at the open secondary does not imply that there is a net resultant E field in the conductor. Charge density varies wherever there are gradients of permeability and conductivity. This can be put into formulas but it require a bit of vector calculus you would refuse to read (IIRC I also said there was a bit of vector calculus involved). I will try nonetheless to scan a few formulas when I get off my bed.

In our "box + resistor" case resistor is outside magnetic field of the transformer, so Faraday's law cannot do anything about it, so there cannot be nonconservative fields in form of EMF inside it.

I have to stop you there: as long as you stay outside you can pretend that the contribute of -dphi/dt are either 'battery-like' emf of 'resistor-like' voltage drops. But when you get inside the box - and you have to get inside the box to compute the path integral of the total E-field along the circuit's path, you have to surrender this delusion and come to terms with Faraday.

According to logic above, sum of fields in copper and resistor, integral E_conservative.dl and integral E_nonconservative.dl is zero. [edit] At given time of observation obviously.

The above logic is flawed because it does not keep into account the right hand side of Faraday's equations.

circulation of E_conservative + circulation of E_nonconservative = -dphi/dt
circulation of E_conservative == 0 by definition!
circulation of E_nonconservative = -dphi/dt

Fact that you even try to answer those questions is hilarious by it's own We agreed that for voltmeter it does not matter what's inside the box, it cannot sort out electrons - they were moved by class-AB amplifier, little monkeys or Mr.Faraday.

We agree that voltmeters are not affected by the path of their probes when you are not allowed to cut through or run circles around the flux varying region. From the outside of a toroidal transformer it does not matter how I place my probes, I can even run circles around the transformer but since the flux is all inside, I will not be able to encircle any net flux: as much goes inside the surface delimited by my probes, will come out.

[ogden]

Did you just say that Dr.Lewin is mistaken? - Because he claims that nonconservative field is zero inside copper coil (or secondary of transformer).

He must have meant the total field.
Keep in mind that the left side of Faraday's equation, circulation of E.dl refers to the total field.

Of course it might happen that the conservative field be zero as well: if all fields are conservative, the conservative field is all you've got and in that case the conservative field will be zero inside a perfect conductor. It happens for example in electrostatics: point charge generates a conservative E-field, you place a piece of copper nearby, free charges on the copper surface redistribute to create a contribution that will erase the field inside the copper. So sum of conservative E field due to point charge plus conservative field due to free surface charge equals total conservative E field inside the conductor is zero. And I think it will work with batteries and a copper wire.
It's all about context.

Can you show where Lewin said that?

You don't seem to understand what EMF actually is. Do you? Note that Dr.Lewin uses E-field to describe conservative field and EMF when he talks about nonconservative field. If you start "Is Kirchhoff's Loop Rule for the Birds?" video at around 15:10, you will hear it.

So, copper part have *only* nonconservative field, resulting voltage (integral E.dl) equals 1V. You agreed because you did not argue when I said that it is possible to measure 1V AC voltage on transformer secondary  w/o resistor connected. (It would be dumb to argue anyway).

No I do not agree and I have already explained how that can happen in one of my previous post (many pages back).

LOL. From which alternate universe your physics come from? When I measure 1V on the transformer terminals, you claim that it is not 1V actually?

In our "box + resistor" case resistor is outside magnetic field of the transformer, so Faraday's law cannot do anything about it, so there cannot be nonconservative fields in form of EMF inside it.

I have to stop you there: as long as you stay outside you can pretend that the contribute of -dphi/dt are either 'battery-like' emf of 'resistor-like' voltage drops. But when you get inside the box - and you have to get inside the box to compute the path integral of the total E-field along the circuit's path, you have to surrender this delusion and come to terms with Faraday.

Don't even say "Faraday" in area where there's no magnetic field! Also please leave resistor where it is - outside the box. I repeat: box is shielded and you don't know what's actually inside - monkey with piezo igniter, signal generator or transformer.

According to logic above, sum of fields in copper and resistor, integral E_conservative.dl and integral E_nonconservative.dl is zero. [edit] At given time of observation obviously.

The above logic is flawed because it does not keep into account the right hand side of Faraday's equations.

Leave Faraday's equations alone because their job is done when we know EMF voltage which is 1V. We are talking about fields now or integral E.dl of the various types of fields to be precise.

From the outside of a toroidal transformer it does not matter how I place my probes

Fine. No need to remind so often that voltmeter have probe wires.

[Sredni]

Did you just say that Dr.Lewin is mistaken? - Because he claims that nonconservative field is zero inside copper coil (or secondary of transformer).

He must have meant the total field.
Keep in mind that the left side of Faraday's equation, circulation of E.dl refers to the total field.
--snip--
Can you show where Lewin said that?

If you start "Is Kirchhoff's Loop Rule for the Birds?" video at around 15:10, you will hear it.

What I hear is "electric field" and I agree: the total, resulting electric field in copper is negligible. Zero in a perfect conductor. As I have always said.
Where do you hear him saying that (in this particular circuit) the conservative electric field in copper is zero?

So, copper part have *only* nonconservative field, resulting voltage (integral E.dl) equals 1V. You agreed because you did not argue when I said that it is possible to measure 1V AC voltage on transformer secondary  w/o resistor connected. (It would be dumb to argue anyway).

No I do not agree and I have already explained how that can happen in one of my previous post (many pages back).

LOL. From which alternate universe your physics come from? When I measure 1V on the transformer terminals, you claim that it is not 1V actually?

No, I do not agree with the "copper part have *only* nonconservative field, resulting voltage (integral E.dl) equals 1V."
This is where you are mistaken.

Oh, the alternate universe I am in is the same universe Ramo, Whinnery and Van Duzer wrote that book that I keep suggesting to you. But it probably does not exist in your universe.

Don't even say "Faraday" in area where there's no magnetic field!

Why not?
There is no magnetic field outside the coils, and yet the voltmeters read different values when they are attached to the same points. That's Faraday in action. You can explain it with the curling electric field, the one that goes as 1/r. I really need to post a lot of pictures.

[ogden]

If you start "Is Kirchhoff's Loop Rule for the Birds?" video at around 15:10, you will hear it.

What I hear is "electric field" and I agree: the total, resulting electric field in copper is negligible. Zero in a perfect conductor. As I have always said.
Where do you hear him saying that (in this particular circuit) the conservative electric field in copper is zero?

Where do you hear him saying in his videos *any* of two terms: "conservative" or "non-conservative"? He does not use such at all. You deleted/ignored my comment about EMF to suit your agenda and I am glad you did it.

In case anybody wonders why I do not continue discussion - because my job is done. Answer yourself simple question: what is expected result of "integral E.dl" between terminals of transformer or voltmeter? - Voltage. It was defined from the very beginning of "box + resistor" debate, 1V AC peak-peak. I just trapped Dr.Lewin's cultists and they took the bait.

[bsfeechannel]

Other post[/url] of yours is unfortunately off-topic because it is not specified that there is Dr.Lewin's experiment in the box.

Oh! I didn't notice that the topic had suddenly become off-topic. My bad.

[Berni]

To give things some better perspective i have put together a few images that graphically show the fields.

1) Circuit under test


R1 = 1 KOhm
R2 = 1 KOhm
Rwire = 0 Ohm

Yes this circuit is changed a bit but it makes the graphics easier since my colors don't quite have the dynamic range in available colors to make voltages visible that are an order of magnitude apart.

2) Charge Density


For a EMF of 1V the the scale shown has to be multiplied by 0.25V
The color shows charge density at every point in the circuit. This could also be considered a topographical map of the coulomb E field. The voltmeters are reading the difference in the E field across the terminals, so we can see that V1= -0.5V  and V2= +0.5V. So we do get the paradox behavior of two meters showing different numbers across the same two points.

These colors also directly correspond to the "non textbook" definition of voltage used in circuit analysis.

As you can also see the "ground reference" of the circuit is placed at node A. All voltages are measured in reference to A


3) Magnetic EMF


For 1V EMF the scaling factor here is 0.5V

So now lets also visualize the EMF in every point. This is a bit tricky because as we know its a non conservative field. To be able to show it the scale shown here actually wraps around (Similar as phase in phase diagrams). To get the voltage between two points you simply travel along the wire and check the difference between the starting and ending value. Due to the scale wraparound you can go around the circle multiple times and just keep adding more voltage each time you go around in that direction. If you go around it once you find you get 1V, go around twice you get 2V. These same voltages are induced in the outer probe loop.

Notice that the EMF voltage across the resistors and voltmeters is essentially zero due to them being physically small compared to the loop. This is an important fact and is the reason why voltmeters can't see EMF voltage. There is simply no significant noncosenrvative magnetically induced E field across them. Its the electrons on the wire that see most of it and get shoved into the terminals of the resistors and voltmeters, hence why only the end effect of this magnetic EMF is seen by components.

This is also where the gradients in the wires on Figure 2 have come from. They are simply the opposite of the EMF as the charge separation E field balances out with the EMF E field.


4) True voltage


So now lets combine the two and get the real voltage as formally defined.

Well... we have problems. Here is where the paradox comes up. Suddenly any piece of wire that is enclosing the magnetic flux is undefined (RED) or has multiple solutions. It depends how we traveled along the EMF Figure 3. To correctly color this in the pixels would need to have multiple colors at the same time (Sorry im not making an animation out of this)

The resistor and voltmeter have defined voltage across them because there is no EMF across them, so no matter what path we take the result is identical. As such i could color them in.

5) True-er? voltage


We can help ourselves a bit and use the claim that wires always have 0V across them, so if we have one part of a wire defined, then we can color in the rest of the wire with the same voltage and this is what we get. We still can't color in the small parts in the middle because suddenly multiple voltages meet there. And here is how we get to the multiple voltages at the same point result that Dr. Lewin demonstrated. It's a perfectly valid result and there are indeed two voltages present.

6) EMF in the bigger picture


Here i have shown the EMF outside the wires too.(This is part of how Fig 3 was created in the first place)

You can chose any two points (Here 1 and 2 for example) and read off the EMF voltage between them by just looking at the difference between them.

This can be also seen as a graphical demonstration of Faradays law:


To calculate the same voltage with Faradays law you have to construct a surface area that you can put down there into the limits of that initgeral. This is done by first connect the two points to the magnetic fields origin (These are wires that have 0V EMF) and then draw any non intersecting shape of a line between those two points to close the loop. The size of the resulting E field according to Faradays law is this voltage shown by color in the picture.

Notice that the resistors never needed to be involved. This is because Faradays law only deals with the relationship between a changing magnetic and electric field. It has nothing to do with electric fields caused by charges, but since the integral of those fields around a closed loop is always zero it means it doesn't matter if you include them into Faradays law anyway. It still works fine. The reason it affects the coulomb electric field is that the electrons can't tell the two fields apart and will happily move themselves into equilibrium where they generate that opposite coulomb E field and this is what then drives electrons trough our voltmeters.


If anyone does not agree with the given diagrams you are welcome to modify them and color them in the way you think they should look.

EDIT: Embeded images properly

[ogden]

Other post[/url] of yours is unfortunately off-topic because it is not specified that there is Dr.Lewin's experiment in the box.

Oh! I didn't notice that the topic had suddenly become off-topic. My bad.

Well, you cannot reply to discussion about shielded transformer with message that requires magnetically unshielded transformer! 

Again you demonstrated your tactic by removing part of my message that explains why your other post became off-topic:

Other pos of yours is unfortunately off-topic because it is not specified that there is Dr.Lewin's experiment in the box. It was defined that box is magnetically shielded and there is no EMF induced in the wires coming out of the box.

[rfeecs]

To give things some better perspective i have put together a few images that graphically show the fields.

This is very nice.  I think we pretty much all agree that you can decompose the E field into conservative and non conservative parts.  Or fields due to charge separation and fields due to changing magnetic field.

You are actually not showing fields, you are trying to show potentials in different colors.  As you say, the potential is not defined in the case of a non conservative field.  Perhaps just showing E-fields would be easier, since they are defined everywhere and give all the information needed to describe what's happening.

[Berni]

Yes its showing potentials hence why i was referring to it as sort of a topographical map of a E field.

All of these charts show E fields with the potentials in Volts. But the E field that is induced by a changing magnetic field is still non conservative hence why it was a bit tricky to show. Its E fields generated by charges that are conservative and always defined.

It also shows how you don't need a closed loop to have EMF in a wire. Hence why modeling each wire as a section around the loop is perfectly sensible. You only need a closed loop when you want to use Faradays law to directly calculate the EMF voltage. It doesn't mean that you can't have EMF without a closed loop just because Faradays law uses a loop area, it just means you have to use other laws to calculate your EMF in those cases.

All of this is why this circuit can be lump modeled just fine and used in circuit analysis(Where to the dismay of some in this thread KVL works)

[Sredni]

WTF is the keyboard combination that can make you lose the whole post??
This site does not have a draft saving function? I was copying a ***** line and all went poof!
The ****! What the ****** *****!!!

Short version, then.

EDIT: No, not even that.

This post has been shortened and cleansed to avoid upsetting other children.
Whatever was written here can be found in one or more of the following books (in no particular order, and without mentioning the usual suspects Feynman, Purcell, Griffiths, Ohanian, Jackson):

Panofsky, Phillips
Classical Electricity and Magnetism 2nd ed

John Kraus
Electromagnetism 2nd to 4th ed

Ramo, Whinnery, VanDuzer
Fields and Waves in Communication Electronics 2nd or 3rd ed

Bleaney
Electricity and Magnetism 3rd ed

Nayfeh, Brussel
Electricity and Magnetism

Kip
Fundamentals of Electricity and Magnetism 2nd ed

Lorrain, Courson
Electromagnetic Fields and Waves 2nd ed

[Berni]

WTF is the keyboard combination that can make you lose the whole post??
This site does not have a draft saving function? I was copying a ***** line and all went poof!
The ****! What the ****** *****!!!

Yeah forum web software has not advanced much at all in the last 20 years.

In the case of the field produced by a primary cylindrical coil here is the induced e field magnitude:



here is plotted with direction in a plane perpendicular to the axis of the infinitely long primary coil (here represented by the orange ring):



Seems perfectly defined (of course it is time-varying but we can express exactly how - this is snapshot frozen in time). The voltage, on the other hand...

Sorry i did indeed word that a bit wrong.

I meant that the potential is undefined yes, it happens when fields form a loop like this.

I visualized the potential inside the field because its the easiest to see with color grading. If you want field vectors then just compare the color of a pixel to its neighbors to get your vector arrow. Drawing a sea of arrows wouldn't be as easy to see (and i don't have any quick way of doing that in CorelDraw while color grading is just a simple filter layer)

I'll skip the part regarding that paper you mentioned back when we had this discussion and that kept using AREA in computing the emf for a single line.
We're going 'full field' now, so forget areas - welcome boundary conditions!
You are able to plot the induced field only when you specify the boundary condition set by the coil generating the field.
After all Maxwell's equations in their differential form are... partial differential equations and if you do not specify boundary and initial conditions, how can you choose the solutions that suits your problem among the infinitely many? In their integral form, since the are essentially integral relations between areas and boundaries you have to specify... well, you know what. Maybe there is some equivalence hidden in there?

You only need a closed loop when you want to use Faradays law to directly calculate the EMF voltage. It doesn't mean that you can't have EMF without a closed loop just because Faradays law uses a loop area, it just means you have to use other laws to calculate your EMF in those cases.

Except the EMF is only half of the story.
When you put the secondary coil in, the charges in the conductors will rearrange to produce the coloumbian field and the resulting field depends on how you close (or do not close) the loop. After all E_total has the same direction of j. You can end up with a total E that is opposed to E_induced (it helps using a finite albeit big value for sigma). I had written something else in the lost post but **** it! Anyway I still need to scan my drawings so...

Alright then lets hear how you think one should calculate the charge density on the ends of a open wire in a changing magnetic field.

And so, what is the true voltage?
Because it seems to me that in your coloring analysis you skipped the Mabilde-McDonald voltage right away and went on calling "true voltage" other voltages.
If I understand correctly, what you call "Charge density" is the voltage definable as potential difference that is associated with the coloumbian aka conservative part of the total field. Why is not that the true voltage?

True voltage is voltage as per textbook definition of an integral of all forces acting on a electron along the path. This is definition you have to use to get the two voltages at one point paradox as Dr. Lewin demonstrates it.

I can't call the charge density approach true voltage because that is not how voltage is formally defined. But this is the voltage that all voltmeters detect and show as a result and it is never undefined so i tend to use this so called "effective voltage" or "conservative voltage" or "columbian voltage" or whatever you want to call it, just because its more useful to work with, while not breaking any of Faradays or Maxwells math.

[bsfeechannel]

I can't call the charge density approach true voltage because that is not how voltage is formally defined. But this is the voltage that all voltmeters detect and show as a result and it is never undefined so i tend to use this so called "effective voltage" or "conservative voltage" or "columbian voltage" or whatever you want to call it, just because its more useful to work with, while not breaking any of Faradays or Maxwells math.

This post is wonderful. Because it is the declaration of what we suspected right from the beginning. The "effective/conservative/coulumbian" voltage is a matter of conviction. Of all infinite possibilities of detecting voltage between two points under a varying magnetic field, one is chosen as the "right" one because it's the one that coincides with what would be measured if you could replace the effect of the EMF by lumped generators (batteries, whatever).

Do you remember when I proposed the following "challenge"?



I asked one of the forum members to tell me what voltmeter was measuring the right voltage. He said V3. Because that coincided with what all voltmeters were measuring in this circuit I had proposed before.



Then I showed how difficult that would be. Because a nanometric variation in the position of the meter would cause a detectable error on reasonably precise voltmeters. The voltage he thought to be correct could only be detected at an arbitrarily precise position.



Let's now change a little bit that picture, but not significantly in terms of its theoretical meaning.



V₅ is how we measure the voltage on the secondary of any transformer under load since the beginning of its invention soon after Faraday discovered the phenomenon of induction in the early 19th century. I maintained V₁ just because it is also physically possible, but that measurement has no meaning for the application in question. In this case we proposed that the resistors had the same value, so V₁ = -V₅.

Does it mean that we've been measuring the wrong voltage all this time? Because the voltage measured by V₃ not only doesn't have any practical usefulness, but also would be impossible to be measured directly because we have an obstruction which is the solid core in the middle.

So that's what the "Kirchhoff always holds" and "the right way to measure a voltage" [under varying fields] leads to: absurd conclusions.

By the time people are trying to convince nature of the contrary (just this thread has been now running for 2 months), if this people had deigned to sit down, forgotten what they think they know about the subject, and studied electromagnetism for real, they'd be making sense of it without all that struggle.

People forget that the most important piece of equipment in any lab is the brain. And it needs constant upgrades.

[ogden]

In fact, when you bring a voltmeter inside the ring, you can measure any voltage you want between -0.1V and +0.9V

You can read +1V and -1V as well - if you short probe leads that go around solenoid. Some academic scientists and their worshippers may say "Look! I discovered that voltage is path-dependent" while actual "discovery" is just electromagnetic induction. Engineer will say: your probing sux

You can bend it as you want, truth is that voltmeter reading (but not actual voltage in the connection point) depends on the path of test leads, especially if they are placed in the varying magnetic flux. All this is very complicated way of teaching how to NOT measure voltage.

p.s. When you realize who your debate opponent is, you may see your discussion in a whole new light.

[Berni]

Yeah forum web software has not advanced much at all in the last 20 years.

Well, some web software has advanced. Stack Exchange for example, saves the drafts, upload images directly, has a nice TeX editor... Too bad they pissed me off with their censorship attitude. But, never mind.

Yeah true, but the strict moderation is what makes stack exchange so useful when you just want a quick, concise and correct answer to a technical question. The best answers float up to the top and some answers actually have a significant amount of effort behind them.

I am a bit at a loss, here. I thought you were looking for the true one and only voltage, the one that has is so uniquely defined that it can be expressed as a potential difference, independent of path. And yet you say that potential is undefined?
Are you referring only to the possibility to run more than one time around the core (in which case, we could overlook it, limiting ourselves to a full circle at most) or is this a more fundamental lack of uniqueness?
Because the way you used colors makes me believe you are selecting a particular class of paths to represent your color coded voltages, namely paths along the circle. You fix 0 at one node (A, IIRC) and then compute the path integral along the circle from A to another point P on the circle. Do we agree that this does not exclude the possibility that the voltage from A to P depends on the path?
Which one of the many voltages you have shown is the path-independent one?
(My guess is that it has to be the first one, the conservative one you called "charge density". And yet you say

What is considered true voltage is dependent on what side of a argument about KVL you are on.

I fully support both definitions of voltage. I was never trying to say that multiple voltages at the same points are impossible (I fully agree with Dr. Lewins two voltages when used with the appropriate definition of voltage). I was just trying to explain why that happens and why you can't use this kind of voltage in KVL.

It just so happens that the textbook definition of voltage is less useful since as you can see all my diagrams that use it there have some red(undefined) in it, while the dreadful "coulomb voltage" is always defined at every point while giving the exact same result on the voltmeters and resistors. It simply untangles the same math out of these undefined values by looking at potential in a different way.

Figure 3 has an explanation in text that you have to TRAVEL along the diagram and that the scale wraps around at +1 and -1. This is why you can go around multiple times and it matters in what direction you go. Going counter clockwise of course gives the opposite sign than going counterclockwise so path and direction DOES matter. This is why i could not simply overlay this on to Figure 4 to get true voltage. It matters what way around you went in Figure 3.

The textbook definition of voltage is indeed PATH DEPENDANT. No need to tell me that as i never claimed the opposite in this thread. Im claiming that columbian voltage is path independent. Its this difference between the two voltage definitions that causes the undefined potential problem.

Which seems to me an admission that... the true voltage is path dependent, as Lewin has always said. But let's forget about this for the moment. The part I am more interested in is the following

I can't call the charge density approach true voltage because that is not how voltage is formally defined. But this is the voltage that all voltmeters detect and show as a result and it is never undefined so i tend to use this so called "effective voltage" or "conservative voltage" or "columbian voltage" or whatever you want to call it, just because its more useful to work with, while not breaking any of Faradays or Maxwells math.

So to be clear, is this the voltage Mabilde is measuring? The one that Kirchhoffian call the 'true and one voltage'? You just decided to call it with another name (not a problem, we just need to be clear) but can you clarify that this is the case and that what you called "Charge Density" in the picture and call now "effective, conservative, coloumbian voltage" is the Mabilde-McDonald voltage?

Before addressing the meaning of said voltage, let me say that there is one problem with you statement above. You wrote that "that is the voltage that all voltmeters detect and show as a result". I am afraid you are mistaken.
To show the Mabilde-McDonald voltage you need a special measurement setup, consisting in a careful choice of your probes' path. The voltage all voltmeters detect is the one with the operational definition of path integral of E. The one that depends on the path of your probes when there is a changing magnetic field. In fact, when you bring a voltmeter inside the ring, you can measure any voltage you want between -0.1V and +0.9V and that is what the voltmeter show. Even outside you have two different values depending on how you place the probes around the core.
So, no. The 'effective, conservative, coloumbian voltage' is not the voltage that all voltmeters detect and show as a result. You did the experiment yourself!

But I think I know where you got that idea.
I will address that in a separate post, along with my answer to this

Yes Mabilde is measuring the "coulomb voltage" but also Dr. Lewin is measuring the "coulomb voltage" since that's the voltage that all oscilloscopes measure (Or did Tektronix make two special scopes for his experiment that measure both components of voltage together?).

Probes are part of the circuit and "coulomb voltage" is generated inside the probes wires as they are also exposed to the magnetic field, so no need to run your probes in a special way or put your voltmeter in a special spot. But you have to realize that voltage is there and needs to be considered in your results. If you are looking to get the potential at the ends of those wires rather than at the voltmeter terminals then you have to subtract out any voltage introduced by the probes. So the charge density at the end of those probe wires does indeed change as you have the probe wires take different paths, hence why the voltmeter shows a different voltage.

So if say voltmeters don't measure "coulomb voltage" what do they measure then? Maybe show it on an example circuit to give it some context (Like the simple single coil and single resistor we had before).

Alright then lets hear how you think one should calculate the charge density on the ends of a open wire in a changing magnetic field.

EDIT: fixed sentence I had left without conclusion.

Well? How do we calculate it then? Or is there no need to calculate it because it's zero perhaps?

[Sredni]

Stack Exchange for example, saves the drafts, upload images directly, has a nice TeX editor... Too bad they pissed me off with their censorship attitude. But, never mind.

Yeah true, but the strict moderation is what makes stack exchange so useful when you just want a quick, concise and correct answer to a technical question. The best answers float up to the top and some answers actually have a significant amount of effort behind them.

Nah, the problem is twofold: first, science is not and should not be democratic - so the 'most voted answer is the best' is not necessarily true and the mechanism is flawed from the start. While it might work fine for some 90% of the content, when it comes to specialized stuff, it breaks miserably. This flaw is exacerbated by the editing power that one can exert even if he/she has no clue of what is being discussed (meaning the so called 'expert' in one branch might only have an approximate and sometimes erroneous knowledge of other branches). Imagine if you and ogden had the power to close this discussion because it's crystal clear that this is just a probing error (and you have more yellow square than me and MHz). Or to look if from the other side, if Mhz and I had the power to shut up Kirchhoffians by editing and removing their posts (and once they are removed, if the site has enough traffic there won't be enough people to notice or even care to reopen them).
Nobody Many readers in this blog would not have discovered the surprising role of surface charge in keeping the current within a conductor (I will get to that when I will have completed my drawings and scans).

I was happy with the way Physics SE is run: there is highly competent people making the selection there. Not so much in EE. Waste my time once, shame on you. Waste my time twice...
Scientific populism will be a problem a few years ahead.
But enough digressing.

Well? How do we calculate it then? Or is there no need to calculate it because it's zero perhaps?

We use Maxwell's equations. What else?
Zero? With an abrupt discontinuity at the ends and an induced field of known geometry? What makes you think that?
It is zero in a closed isotropic circular conducting torus perfectly aligned with the circular induced field. But even then, my guts say you just have to move it off axis to see charge pile up on the 'lateral' surface (well, is there any other surface on a torus?). And if you place portion of different resistance, you will certainly see charge pile up at the surface of separation.
I've found plenty of literature supporting my point of view. I need a little bit of time to sift through the best works and select a few images. Keep your popcorns in a warm place, I'm almost done with my flu.

edit: nobody was a truly bold statement. In my defense, it's all Jackson's fault. I'll explain later

[ogden]

Suppose I put my electron in, with particular initial conditions (like velocity in a particular direction starting from A) and that I have recorded its trajectory from A to B. Would you agree in calling the voltage computed along that path the most meaningful voltage for this particular experiment?

No. I don't give a chit how fast that electron moves inside voltmeter. If it is faster than in the probe tip, then measurement is trash. I want to measure voltage between probe tips. If probe tips are shorted meaning voltage is 0V but I get 1V indication, I cannot call it meaningful by any stretch of imagination.

If voltage indication changes depending on how you manipulate with probe wires - you cannot trust your measurements not to mention make big scientific thing out of it. 

You can read +1V and -1V as well - if you short probe leads that go around solenoid. Some academic scientists and their worshippers may say "Look! I discovered that voltage is path-dependent" while actual "discovery" is just electromagnetic induction.

Oh, come on. I thought we were past that.
Voltage in non-conservative E-field IS path-dependent. This is not even up for discussion.

Yes. This is where I agree to you. I already said that and can repeat: "voltmeter reading (but not actual voltage in the connection point) depends on the path of test leads, especially if they are placed in the varying magnetic flux."

[Berni]

Nah, the problem is twofold: first, science is not and should not be democratic - so the 'most voted answer is the best' is not necessarily true and the mechanism is flawed from the start. While it might work fine for some 90% of the content, when it comes to specialized stuff, it breaks miserably. This flaw is exacerbated by the editing power that one can exert even if he/she has no clue of what is being discussed (meaning the so called 'expert' in one branch might only have an approximate and sometimes erroneous knowledge of other branches). Imagine if you and ogden had the power to close this discussion because it's crystal clear that this is just a probing error (and you have more yellow square than me and MHz). Or to look if from the other side, if Mhz and I had the power to shut up Kirchhoffians by editing and removing their posts (and once they are removed, if the site has enough traffic there won't be enough people to notice or even care to reopen them).
Nobody Many readers in this blog would not have discovered the surprising role of surface charge in keeping the current within a conductor (I will get to that when I will have completed my drawings and scans).

I was happy with the way Physics SE is run: there is highly competent people making the selection there. Not so much in EE. Waste my time once, shame on you. Waste my time twice...
Scientific populism will be a problem a few years ahead.
But enough digressing.

Ah i never actually posted on there so i had no idea how that works, i just often take useful answers from there and i had good experience with that part.

Well? How do we calculate it then? Or is there no need to calculate it because it's zero perhaps?

We use Maxwell's equations. What else?
Zero? With an abrupt discontinuity at the ends and an induced field of known geometry? What makes you think that?
It is zero in a closed isotropic circular conducting torus perfectly aligned with the circular induced field. But even then, my guts say you just have to move it off axis to see charge pile up on the 'lateral' surface (well, is there any other surface on a torus?). And if you place portion of different resistance, you will certainly see charge pile up at the surface of separation.
I've found plenty of literature supporting my point of view. I need a little bit of time to sift through the best works and select a few images. Keep your popcorns in a warm place, I'm almost done with my flu.

edit: nobody was a truly bold statement. In my defense, it's all Jackson's fault. I'll explain later

Well i shown how to calculate the charge density on the end of a open wire with Faradays law, but apparently according to you that's wrong, so i would like to see what is the correct way of using Maxwells equations to find the result.

I was not claiming its zero, just guessing your answer because you keep saying wires always have no voltage across them (apart from restive drop). So you are now saying that wires can have voltage across them?

[bsfeechannel]

Nah, the problem is twofold: first, science is not and should not be democratic - so the 'most voted answer is the best' is not necessarily true and the mechanism is flawed from the start. While it might work fine for some 90% of the content, when it comes to specialized stuff, it breaks miserably. This flaw is exacerbated by the editing power that one can exert even if he/she has no clue of what is being discussed (meaning the so called 'expert' in one branch might only have an approximate and sometimes erroneous knowledge of other branches). Imagine if you and ogden had the power to close this discussion because it's crystal clear that this is just a probing error (and you have more yellow square than me and MHz). Or to look if from the other side, if Mhz and I had the power to shut up Kirchhoffians by editing and removing their posts (and once they are removed, if the site has enough traffic there won't be enough people to notice or even care to reopen them).
Nobody Many readers in this blog would not have discovered the surprising role of surface charge in keeping the current within a conductor (I will get to that when I will have completed my drawings and scans).

Now I understand what you mean. This tendency is really dangerous and detrimental to any kind of knowledge.

But enough digressing.

No way. This is highly pertinent to the present discussion.

Keep your popcorns in a warm place, I'm almost done with my flu.

The things we do to help poor souls to walk on the path of salvation.

[bsfeechannel]

If probe tips are shorted meaning voltage is 0V but I get 1V indication, I cannot call it meaningful by any stretch of imagination.

Maybe nature wants to tell you something you are ignoring.

If voltage indication changes depending on how you manipulate with probe wires - you cannot trust your measurements not to mention make big scientific thing out of it. 

Well, Michael Faraday, a scientist, had the same problem that you do way back in 1831. Then he banged his head, like you did, until he realized he was in front of a new phenomenon that no one had noticed before.

When he published his findings, people started to test his claims and found they were true. They soon realized the potential of that new discovery and started to take advantage of it, instead of trying to deny it.

And this changed the lifestyle of most of us since then.

I already said that and can repeat: "voltmeter reading (but not actual voltage in the connection point) depends on the path of test leads, especially if they are placed in the varying magnetic flux."

But if you don't like what your voltmeter is telling you because of the arrangement of its probes, you can replace it by a radio receiver or a lamp.




If Kirchhoff always held, you couldn't have the modern world and we wouldn't be able to have this very conversation. Learn to live with that.

[ogden]

If probe tips are shorted meaning voltage is 0V but I get 1V indication, I cannot call it meaningful by any stretch of imagination.

Maybe nature wants to tell you something you are ignoring.

It's *you* who are ignoring, not me. I said: "You can read +1V and -1V as well - if you short probe leads that go around solenoid. Some academic scientists and their worshippers may say "Look! I discovered that voltage is path-dependent" while actual "discovery" is just electromagnetic induction."

Well, Michael Faraday, a scientist, had the same problem that you do way back in 1831.

I say "it's electromagnetic induction", you say: "no! - it's electromagnetic induction!". You apparently have problem, not me.

If Kirchhoff always held, you couldn't have the modern world and we would be able to have this very conversation. Learn to live with that.

LOL. Have to repeat that you are "arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct", like broken record.

[Berni]

LOL. Have to repeat that you are "arguing against the nonexistent strawman who is apparently suggesting that Farady's law is incorrect, and Kirchoffs is always correct", like broken record.

I have to agree with Ogden. Who are you actually arguing with?

To make things easier i will summarize most of my claims in a list:
1) There are indeed two voltages present at the measured points in Dr. Lewins experiment when using the formal textbook definition of voltage.
2) The formal definition of voltage is path dependant
3) Faradays law is correct, however the E field in that equation refers only to the non conservative E field generated by the magnetic field on the other side of the equation. No other E fields are included on the left side (Tho you can include the conservative E field too since it integrates to zero anyway).
4) Voltmeters can only measure charge density across the terminals and can't detect the non conservative component of voltage around the whole loop, only observe the effects of this non conservative field in the form of charge separation.
5) If voltmeters ware capable of measuring voltage as formally defined then measuring the voltage across a transformer secondary would always result in 0V with the secondary terminals open, or when the transformer is powering a load the voltage would be the restive drop in the wingdings.
6) In Dr. Lewins circuit charge density is always defined as a single number for all points at any given moment, giving every point of the circuit a defined "effective voltage"
7) Closed loops of wire with a defined area are not a requirement for having induction happen. Open loops of wire can experience induction and even act like LC tank circuits.
8 ) Open lengths of wire in a changing magnetic field indeed have zero textbook voltage along them, but in most cases do have a different charge density at the ends giving them "effective voltage" that is capable of being detected with voltmeters or in extreme cases make electrons arc across gaps.
9) Lengths of wire connecting the voltmeter to the probing points are part of the circuit and need to be analyzed along with the rest of the circuit. These wires transfer the voltage from the probing points to the voltmeter terminals where it is actually measured. If it is found that these wires generate a voltage that affects the voltmeters reading then this voltage must be subtracted out to get the voltage at the probe points. Failure to realize this, correct it, or compensate for it is considered as "bad probing".
10) Changing the path of the probe wires in Dr. Lewins circuit does change the voltmeter reading due to changing the charge density present on the voltmeter terminals. However when doing correct probing as mentioned above the result of the voltage at the probing points it always the same, regardless of wire path or voltmeter location (The effect is always substracted out).
11) Kirchhoffs circuit laws always work in circuit mesh models where all voltages use the "effective voltage" definition
12) Kirchhoffs cirucit laws can not be directly applied to just any real life circuit with the assumption of ideal wires, especially when high frequency AC signals are involved or significant magnetic effects are present
13) Kirchoffs voltage law does not contain an intergal of E as Dr. Lewin shows. Its actually a algebraic sum of all voltages on components and as such can only be used on a lumped model.
14) Kirchoffs cirucit laws do not go against Faradays law or Maxwells equations. All three can exist without conflict. Faradays law and KVL describe two different things and as such are not mutually exclusive.
15) Kirchoffs citucit laws have nothing to do with Maxwells equations, but they are used together whenever circuit analysis is used on reactive components such as inductors or capacitors.
16) The circuit from Dr. Lewins experiment can easily be lump modeled using multiple coupled inductors to represent wires. As such all common methods of circuit analysis can be applied to it including KVL to get results matching the real physical experiment
17) The inductor lump models can be split any number of times and distributed around the loop to expose any point of interest in the circuit.
18) Circuit mesh models assume there is no flux outside of individual components, however coupled inductors models can be used to get this flux sharing behavior when desired.
19) The "effective voltage" is just as real as the formal textbook voltage, yet more useful due to being always defined and shown by real life voltmeters.


I might have missed a few but these are the ones i remember right now. Any disagreement on these?

[ogden]

I might have missed a few but these are the ones i remember right now. Any disagreement on these?

I would add definition of voltage to 2 ). Version "True voltage is integral of all forces acting on a electrons along the path" is kinda tricky because some may think that electron(s) shall be carried all the way along the path for voltage to appear, which is untrue. IMHO worth to mention more straightforward "the work needed per unit of charge to move a test charge between the two points". It also "connects" better to volt = joule/coulomb equation.

I disagree with 8 ) because both "all forces on electrons along the path" and "work per unit of charge" voltage definition variants allows voltage to be present on terminals of zero resistance "open lengths of wire" or inductor. After all there's well-known equation: V = L(di/dt)

Kinda offtopic or maybe not. -How special relativity is related to this discussion:


https://youtu.be/1TKSfAkWWN0

p.s. How to (easily) avoid this gigantic thumbnail appearing when I include URL to YT video?

[Sredni]

Making the pictures is taking more time than I had thought and I have work to do.
EDIT: But then...

This post has been shortened and cleansed to avoid upsetting other children.
Whatever was written here can be found in one or more of the following books (in no particular order, and without mentioning the usual suspects Feynman, Purcell, Griffiths, Ohanian, Jackson):

Panofsky, Phillips
Classical Electricity and Magnetism 2nd ed

John Kraus
Electromagnetism 2nd to 4th ed

Ramo, Whinnery, VanDuzer
Fields and Waves in Communication Electronics 2nd or 3rd ed

Bleaney
Electricity and Magnetism 3rd ed

Nayfeh, Brussel
Electricity and Magnetism

Kip
Fundamentals of Electricity and Magnetism 2nd ed

Lorrain, Courson
Electromagnetic Fields and Waves 2nd ed