Does Kirchhoff's Law Hold? Disagreeing with a Master

[jesuscf]

Tho to be honest i never seen physicists use circuit schematics to describe anything other than electrical things. It seams to me its more of an electrical engineering thing where engineers have no clue about some random physical system, so they do "when you have hammer every problem looks like a nail" and mold the problem to look like a circuit since that's the one thing they do know how to deal with easily.

At least i never saw this "circuit meshes are not just for electrons" concept even mentioned any of my physics classes, while i have used the trick extensively in a lot of engineering classes to make sense of magnetic circuits, water flow, heat flow etc.. and to actually calculate stuff with it.

I believe it is even worst than that.  In my experience any linear electric circuit with more than 3 undefined nodes is enough to mess up most physicists.  And if you really want to have fun watching them trying to solve a circuit, add a non-linear element, say for example, a diode.

[bsfeechannel]

Ad hominem... that will prove you right.

You're right. I should have proved that his claims are bullshit before I accused him of brainwashing millions with the promise that they don't need to study Maxwell provided they sustain a false belief that Kirchhoff always holds.

Sorry about that.

KVL is a pseudo-theory?

Well, there is this rumor that for circuits under varying magnetic fields KVL sucks.

Do you know KVL can be derived from Maxwell Equations?

Some people say that KVL has nothing to do with Maxwell, but I never gave much credit to that.

So electrical engineers don't study linear circuits now!  Wow, that must be a new curriculum!

I don't know about electrical engineers, but those who don't study Maxwell don't understand electromagnetism.

By applying the same logic an inductor is unlumpable...  therefore we can not use KVL in circuit that includes an inductor!?

And you're the proof of that. Since you haven't read the Feynman's lectures recommended by Mehdi himself, you simply don't understand why an inductor is a lumped component and why Lewin's circuit is not solvable by KVL.

[jesuscf]

I don't know about electrical engineers, but those who don't study Maxwell don't understand electromagnetism.

So, you are not an electrical engineer.  Are you familiar with the Dunning–Kruger effect?

And you're the proof of that. Since you haven't read the Feynman's lectures recommended by Mehdi himself, you simply don't understand why an inductor is a lumped component and why Lewin's circuit is not solvable by KVL.

Here, once again in case you missed  from "Engineering Electromagnetics" by Hyat and Buck, Seventh Edition:

"Equation (21) (Curl integral of E.dl=0) is therefore just a more general form of Kirchhoff's circuital law for voltages, more general in that we can apply it to any region where an electric field exists and we are not restricted to a conventional circuit composed of wires, resistances, and batteries.  Equation (21) must be amended before we can apply it to time-varying fields.  We shall take care of this in Chapter 10 [Maxwell's Equations], and in Chapter 13 [Plane Wave Reflection and Dispersion] we will them be able to establish the general form of Kirchhoff's voltage law for circuits in which currents and voltages vary with time."

That paragraph says it all, better than anybody yet... So, are you aware of the common practice of lumping about every kind of coupled electric circuit?  Probably not, because you are not an electrical engineer, but Mehdi is an electrical engineer and that is what he did to demonstrate that Lewin's conclusion is incorrect.  Maybe you should really understand what the Dunning–Kruger effect is.

Finally, you don't read Feynman lectures on Physics, you listen to them.

[Berni]

Can you explain why a the section of wire in Dr. Lewins experiment can't be inductor lump modeled as a 1/4 fractional turn around a transformer? In what way does it act differently than a transformer?

[bsfeechannel]

Read carefully Feyman's lecture Vol. 2,  Chapter 22 (the same you've already linked before), sections 22-1, 22-2 and 22-3 at least. If you do not manage to see the answer there, we'll be happy to help.

[Sredni]

The problem is that if you do that you are lumping the unlumpable.

By applying the same logic an inductor is unlumpable...  therefore we can not use KVL in circuit that includes an inductor!?

See? I was right! You did not read previous posts. But it also appear you did not read the books you mention.
And when you read them, it seems to me, you read something that is not there. For example, in the passage you twice quoted from Hayt:

"Equation (21) (Curl integral of E.dl=0) is therefore just a more general form of Kirchhoff's circuital law for voltages, more general in that we can apply it to any region where an electric field exists and we are not restricted to a conventional circuit composed of wires, resistances, and batteries.  Equation (21) must be amended before we can apply it to time-varying fields.  We shall take care of this in Chapter 10 [Maxwell's Equations], and in Chapter 13 [Plane Wave Reflection and Dispersion] we will them be able to establish the general form of Kirchhoff's voltage law for circuits in which currents and voltages vary with time."

It appears you believe that "amended before we can apply to time-varying fields" means "it will work even when the circuit path encloses a time-varying magnetic field". Well, it does not. The amended KVL works when the time-varying magnetic field is neatly tucked inside a lumped component and can not be tampered with, either by crossing it, or by running "net" circles around it (I lost count of how many times I've explained this in more detail in my previous post, so if you need clarification start reading back posts).
This impossibility to tamper with the magnetic field region can be summarized with seeing the offending component as zero-dimensional, or point-like. Lumped is a word that comes to mind.

When you consider the inductor as a lumped component, you use Faraday to deduce the voltage at its terminals, and then pretend that voltage is like a 'potential difference' in the circuit it is part of. Now, the circuit should not enclose any varying magnetic field inside its contour, if I want 'amended KVL' to work there.



But even though 'amended KVL' works in the circuit, KVL still does not work inside the inductor's path.

In the same way it does not work inside Romer-Lewin's ring.


EDIT: added "even though"

[Berni]

Read carefully Feyman's lecture Vol. 2,  Chapter 22 (the same you've already linked before), sections 22-1, 22-2 and 22-3 at least. If you do not manage to see the answer there, we'll be happy to help.

But did you also read the beginning of section 22-8 too?

[bsfeechannel]

Read carefully Feyman's lecture Vol. 2,  Chapter 22 (the same you've already linked before), sections 22-1, 22-2 and 22-3 at least. If you do not manage to see the answer there, we'll be happy to help.

But did you also read the beginning of section 22-8 too?

Cool. Since I said at least 22-1, 22-2, 22-3, I'm pleased that you read the whole chapter and I hope that you've finally found why a section of wire in Dr. Lewins experiment can't be inductor lump modeled as a 1/4 fractional turn around a transformer and in what way it acts differently than a transformer.

[Berni]

Cool. Since I said at least 22-1, 22-2, 22-3, I'm pleased that you read the whole chapter and I hope that you've finally found why a section of wire in Dr. Lewins experiment can't be inductor lump modeled as a 1/4 fractional turn around a transformer and in what way it acts differently than a transformer.

I have quickly went trough it last year already because it is a very good explanation.

But what point in the lecture exactly does it say that this can't be done? Yes it does explain that when considering a lumped inductor all magnetic fields have to be contained inside it. This is another way of saying that the inductors field should not affect anything else around it. Note that the inductor still has wires coming out that are in two different physical locations in order to give you two terminals, this means it can't be a fully closed loop inside the shielded "lumping" box. We still need extra wire outside the box to close it and connect it to for example a voltmeter. The diference between the wires inside the box and outside the box is just that the ones outside have no magnetic field around then and so no EMF. This is the exact same thing as getting rid of the shielding box but placing the wires to the voltmeter in such a path that they generate no EMF. So any piece of wire taking any path inside the shielded box can be considered an inductor (Doesn't have to be coiled up around a former or a core). And if we are careful not to interact the rest of the circuit then the shielding box can be removed and it behaves the same. So putting all of this together any length of superconducting wire can be considered a lumped inductor (tho care must be taken if its not shielded). Are any of my claims here false?

But Dr. Lewins experimental circuit is not laid out in such a way that other parts of the circuit would avoid the field. All sections of wire are enveloping the magnetic field and are so affected by it in the form of EMF. But if you look at a transformer it also has this feature common. There are multiple sections of wire enveloping a common magnetic field in the core. It would be really annoying if we couldn't apply circuit analysis to any circuit containing a transformer, so the inductor model was 'upgraded' to allow it to be friends with other inductors in the same field, this is explained in the section i mentioned:
http://www.feynmanlectures.caltech.edu/II_22.html#Ch22-S8

This concept of mutual inductance allows transformers to be modeled with multiple inductors almost as easily as a single inductor. Notice that the mutual inductance value is separate from self inductance, this allows the proportion of the two to be adjusted to obtain any intensity of coupling you want. This is effectively saying how much of the flux the two coupled inductors are sharing (Its also what determines leakage inductance in transformers). Fractional turns in transformers are also possible because a length of wire might not necessarily enclose 100% of the flux in the core.

Putting it all together now. So since any length of wire can be considered an inductor and because these inductors around a common 'core'  can be considered a transformer then this circuit could be considered a transformer with 4 secondary coils connected into a configuration with 2 resistors. If not, can you explain why?

[Sredni]

Cool. Since I said at least 22-1, 22-2, 22-3, I'm pleased that you read the whole chapter and I hope that you've finally found why a section of wire in Dr. Lewins experiment can't be inductor lump modeled as a 1/4 fractional turn around a transformer and in what way it acts differently than a transformer.

I have quickly went trough it last year already because it is a very good explanation.

But what point in the lecture exactly does it say that this can't be done? Yes it does explain that when considering a lumped inductor all magnetic fields have to be contained inside it.

Right there, buddy, right there.
That's pretty much it.

EDIT: This post has been shortened and cleansed to avoid upsetting other children.
Whatever was written here can be found in any good EM book.

[jesuscf]

Cool. Since I said at least 22-1, 22-2, 22-3, I'm pleased that you read the whole chapter and I hope that you've finally found why a section of wire in Dr. Lewins experiment can't be inductor lump modeled as a 1/4 fractional turn around a transformer and in what way it acts differently than a transformer.

I have quickly went trough it last year already because it is a very good explanation.

But what point in the lecture exactly does it say that this can't be done? Yes it does explain that when considering a lumped inductor all magnetic fields have to be contained inside it. This is another way of saying that the inductors field should not affect anything else around it. Note that the inductor still has wires coming out that are in two different physical locations in order to give you two terminals, this means it can't be a fully closed loop inside the shielded "lumping" box. We still need extra wire outside the box to close it and connect it to for example a voltmeter. The diference between the wires inside the box and outside the box is just that the ones outside have no magnetic field around then and so no EMF. This is the exact same thing as getting rid of the shielding box but placing the wires to the voltmeter in such a path that they generate no EMF. So any piece of wire taking any path inside the shielded box can be considered an inductor (Doesn't have to be coiled up around a former or a core). And if we are careful not to interact the rest of the circuit then the shielding box can be removed and it behaves the same. So putting all of this together any length of superconducting wire can be considered a lumped inductor (tho care must be taken if its not shielded). Are any of my claims here false?

But Dr. Lewins experimental circuit is not laid out in such a way that other parts of the circuit would avoid the field. All sections of wire are enveloping the magnetic field and are so affected by it in the form of EMF. But if you look at a transformer it also has this feature common. There are multiple sections of wire enveloping a common magnetic field in the core. It would be really annoying if we couldn't apply circuit analysis to any circuit containing a transformer, so the inductor model was 'upgraded' to allow it to be friends with other inductors in the same field, this is explained in the section i mentioned:
http://www.feynmanlectures.caltech.edu/II_22.html#Ch22-S8

This concept of mutual inductance allows transformers to be modeled with multiple inductors almost as easily as a single inductor. Notice that the mutual inductance value is separate from self inductance, this allows the proportion of the two to be adjusted to obtain any intensity of coupling you want. This is effectively saying how much of the flux the two coupled inductors are sharing (Its also what determines leakage inductance in transformers). Fractional turns in transformers are also possible because a length of wire might not necessarily enclose 100% of the flux in the core.

Putting it all together now. So since any length of wire can be considered an inductor and because these inductors around a common 'core'  can be considered a transformer then this circuit could be considered a transformer with 4 secondary coils connected into a configuration with 2 resistors. If not, can you explain why?

Berni you are 100% right and you summarize it nicely.  Any electrical/electronics engineer will agree with you.  That is exactly what Mehdi demonstrated in his video as well as what your nice LTSpice simulation shows in the first page of this thread.  Dr. Lewin and others only see a "simple" circuit with two "ideal" resistors and two "ideal" wires which results in an analytical "solution" of one equation with one unknown where KVL apparently doesn't hold; but the circuit turns out to be more complex than they expected. A more realistic representation of the circuit has at least 9 coupled inductors, four resistors, and a voltage source.. with an analytical solution that consists of around 10 linear differential equations and 10 unknowns!  Too much for anybody that has not been trained on the solution of these problems.

[bsfeechannel]

Any electrical/electronics engineer will agree with you.

Any electrical/electronics engineer without a clue about electromagnetism will agree with you.

TIFIFY.

[bsfeechannel]

I have quickly went trough it last year already because it is a very good explanation.

I told you to read it carefully, not quickly.

But what point in the lecture exactly does it say that this can't be done?

Glad you asked.

This is the exact same thing as getting rid of the shielding box but placing the wires to the voltmeter in such a path that they generate no EMF.

[snip]

Are any of my claims here false?

Yes. There are. What generates the EMF is the varying magnetic field. Not the wires.

What the wires do is to nullify any electric field along their path. Just that.

Putting it all together now. So since any length of wire can be considered an inductor and because these inductors around a common 'core'  can be considered a transformer then this circuit could be considered a transformer with 4 secondary coils connected into a configuration with 2 resistors. If not, can you explain why?

With pleasure. Feynman explains mutual induction after he explains that an inductor is a lumped component.

An inductor can only be considered a lumped component if, and I quote, we assume that there is a negligible magnetic field in the external region near the terminals a and b.  

There are no negligible magnetic fields near the "terminals" of your "inductors" in Lewin's circuit.

So, sorry, you can't lump model Lewin's circuit. It is impossible.

Any more questions?

[jesuscf]

Any electrical/electronics engineer will agree with you.

Any electrical/electronics engineer without a clue about electromagnetism will agree with you.

TIFIFY.

Whatever you say man, if it makes you feel better about yourself.  Have a happy life.

[Berni]

I told you to read it carefully, not quickly.

I have read the relevant parts of it in more detail, was just saying why i noticed the section at the end about mutual inductance, as i remember it being there from back then.

A good part of the lecture also goes into circuit analysis and capacitors so i just quickly glossed over those parts rather that going into the details.

Yes. There are. What generates the EMF is the varying magnetic field. Not the wires.

What the wires do is to nullify any electric field along their path. Just that.

Yep that's how you get induction happen in wires. But what does this effect have to do with containing the field inside the component?

With pleasure. Feynman explains mutual induction after he explains that an inductor is a lumped component.

An inductor can only be considered a lumped component if, and I quote, we assume that there is a negligible magnetic field in the external region near the terminals a and b.  

There are no negligible magnetic fields near the "terminals" of your "inductors" in Lewin's circuit.

So, sorry, you can't lump model Lewin's circuit. It is impossible.

Any more questions?

So now what if you replace each section of wire with 1000 turns around the loop then putting it into a shielded box including the solenoid coil while leaving the resistors and voltmeters outside. This is now a transformer lump model because all fields happen inside (the shielding box is ideal so no field makes it outside) and everything inside the box is nothing else but coupled inductors. Don't you agree that such a circuit would behave identically to Dr. Lewins experiment? (Apart from all the voltages being 4000 times higher)

[Vtile]

 

[Berni]

That's how the wires react to the induced field.

Exactly, your point is?

The induced E field depends on the magnetic B field (rate of change) inside the component.

Yes and it also depends on the area cross section trough the field. If the conductor is aligned with the field lines or the fields motion you also get zero EMF even tho the delta B is non zero.

Oh, for the love of...
Try to draw your new 'equivalent' circuit. Then you should see how equivalent it is to the Romer-Lewin ring.

The equivalent circuit is already here:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg1945312/#msg1945312

We just have to fix the inductor values to match the new turns ratios.
L = La*N^2

La = L / N^2 = 1µ / (1/4)^2 = 16 µH

L_new= La * N^2 = 16µ * 1000^2 = 16H

So just replace L2 to L7 with 16H and you have the new equivalent circuit. The inductances seam rather high because i chose fairly high inductance in the original equivalent circuit. This just means that the ring would be fairly large in diameter to give it a large loop area.

Or did you mean make an equivalent circuit for Romers setup? Where a single multichannel oscilloscope can be used due to ground being common.

[Sredni]

EDIT:

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

"Books" are static paper based documents that can be found in libraries. They are like smartphones, but (usually) bigger, with lots and lots of extremely thin flexible e-ink screens and a very long battery life. Libraries are...
Oh, never mind. Keep on pushing that square peg into that round hole. With a big enough hammer, it will fit.

[bsfeechannel]

Try to draw the circuit, WITH THE VARYING B FIELD REGION, and see if you can manage to do what you proposed: "replace each section of wire with 1000 turns around the loop then putting it into a shielded box including the solenoid coil while leaving the resistors and voltmeters outside".
My bet is that you will end up with circuit (a).

You beat me to it. As always your explanations are precise and rigorous. What Berni tried to do is that, since he believes that the wires are generating voltage, he instructed spice to consider an inductor in their stead. Of course, if you do that, you'll not measure what Lewin did. So he had to "compensate" for that discrepancy on the lead wires and replaced them by coupled inductors.



However, this is bullshit. The loop wires are not inductors, because you have a ginormous magnetic field at their terminals and the lead wires are not coupled with the solenoid because they form another loop where there is no varying magnetic field inside.



This comes from the fact that he can't understand when Feynman says The whole contribution to the line integral of E comes from the path outside the inductance from terminal b to terminal a. The line integral in the wires is simply zero.
 
He invented a voltage that doesn't exist and had to come up with a compensation that's not necessary.

The conclusion of this thread is that we lamentably have a whole bunch of half assed engineers that do not study, much less understand Maxwell,  and are so mentally crippled that they cannot even do a simple circuit analysis without using Spice as a crutch. They don't even know what they're doing with that tool.

I weep for the future.

PS
BTW, how do I embed images properly in this forum?

1) Upload your picture as an attachment.
2) Post you message.
3) View the message and copy the link to the picture.
4) Press Modify
5) Place your cursor to the point of your message where you want your picture.
6) Paste the link enclosed by [ img ][ /img ] (without the spaces).
7) Press save
8 ) See the world burn

[Berni]

Ah alright that's what is bothering you, alright fine il do some drawing too.

By the way bsfeechannel two of your batteries are drawn backwards (Botton inner two)



So since we are so bothered with how the magnetic field affects things other than wires in the circuit lets fix that by putting the major wires into a shielded box. This box has infinitesimally small holes to conveniently get out wires out of it and is made out of a superconducting material or a material with an infinite permeability. This makes it impossible for the field inside to escape, but because magnetic monopolies are not possible in our universe means that the upwards flux must close itself somewhere. A superconducting box would get eddy currents induced on the inside that produces this opposite downwards flux in the walls, or in the case of an infinite permeability box the field lines would just follow the path of least resistance along the inner surface of the box to flow back down.



For convenience i also added some voltmeters around the scene. I think all of you will agree with the readings they are showing. Notice that the rightmost voltmeter is showing zero because the sum magnetic field outside the box is zero (If it was showing anything else than we don't have an ideal shielding box).

So since the field is contained and the box contains nothing else but coupled inductors we can turn it into a ideal transformer and all the voltmeters still show the same readings (Follow each path and add it up if you don't believe me)



This shows that an ideal transformer can behave like the above circuit when it is in a box, something that shouldn't be surprising.

So now lets make it actually look a bit like a transformer by giving each wire actual wingdings that go all the way around. For clarity i only went around once (Any grayed out all but two coils to make it easier to see) but you could go around any number of times. Given that the magnetic field stays the same this produces 5 times the voltage, but the circuit otherwise behaves identically.



Okay but we don't actually have this magical ideal shielding box. So lets look at what would happen if the box was removed?
Well unsurprisingly the most inner voltmeters that used to show 0.1V and 0.9V would show the same value. The path trough them does not enclose any extra flux so there is no reason for them to show something different. This now completes the chain, the circuit behaves like a transformer even if we don't contain the fields.

Where things do get messed up is all other voltmeters. The magnetic field is now affecting all there probe wires and as a result affecting the voltmeter readings. If we wish to continue doing circuit analysis then the model has to be updated to give those wires correct coupled inductance too, after that the voltmeter readings from circuit analysis will once again match the real thing.

Any objections to this explanation?

And i still don't see what part of Maxwell i supposedly don't understand. All of this makes perfect sense to me from the point of view of Maxwell or from the point of view of mesh  circuit analysis. Where do the explanations above violate Maxwell?

Sorry if it sounds rude but i get the feeling that you two understand Maxwell perfectly well but have some issues understanding circuit analysis and circuit modeling.

EDIT: Oh and where did i put in a magical voltage out of nowhere?

[Sredni]

So since we are so bothered with how the magnetic field affects things other than wires ---

<sigh>

You do realize that in the Romer-Lewin ring, the whole ring, resistors included, sits in a region of space where there is NO MAGNETIC FIELD (ideal infinitely long primary coil)?
Why bother putting in a 'magnetic shield'?

Do you want to reconsider your post?

i get the feeling that you two understand Maxwell perfectly well but have some issues understanding circuit analysis and circuit modeling.

Before starting circuit analysis you need to correctly model your circuit.
And you are not modeling correctly.

[bsfeechannel]

Ah alright that's what is bothering you, alright fine il do some drawing too.

What's bothering me is that people don't understand electromagnetism and don't want to learn it. And keep coming up with all kinds of pseudo scientific excuses just to try to make their pseudo scientific theory work. This is an insult to serious engineering and is below the level of dignity of this forum.

We're not here to propagate pseudo-science.

By the way bsfeechannel two of your batteries are drawn backwards (Botton inner two)

I've corrected the picture, thank you, but it won't make any difference. That doesn't in any way model Lewin's circuit because those voltages are not there. It's just an invention to try to cheat Maxwell and make it look as if Kirchhoff always holds.

So since we are so bothered with how the magnetic field affects things other than wires in the circuit lets fix that by putting the major wires into a shielded box.

Varying magnetic fields do not affect wires. This is something you don't understand. The electrical field inside a wire is ZERO. So wires don't care about varying magnetic fields.

It is the path outside the wire that produces a voltage.

I'll repeat: IT IS THE PATH  O U T S I D E  THE WIRE THAT PRODUCES A VOLTAGE under a varying magnetic field.

And if there is not a varying magnetic field in an area defined by a wire and some path outside that wire, the voltage is ZERO.

This box has infinitesimally small holes to conveniently get out wires out of it and is made out of a superconducting material or a material with an infinite permeability. This makes it impossible for the field inside to escape, but because magnetic monopolies are not possible in our universe means that the upwards flux must close itself somewhere. A superconducting box would get eddy currents induced on the inside that produces this opposite downwards flux in the walls, or in the case of an infinite permeability box the field lines would just follow the path of least resistance along the inner surface of the box to flow back down.



For convenience i also added some voltmeters around the scene. I think all of you will agree with the readings they are showing. Notice that the rightmost voltmeter is showing zero because the sum magnetic field outside the box is zero (If it was showing anything else than we don't have an ideal shielding box).

So since the field is contained and the box contains nothing else but coupled inductors we can turn it into a ideal transformer and all the voltmeters still show the same readings (Follow each path and add it up if you don't believe me)



This shows that an ideal transformer can behave like the above circuit when it is in a box, something that shouldn't be surprising.

In this case your modelling is absolutely correct because THIS is a lumped circuit. All the magnetic field is confined outside the area of the circuit. Provided that your voltmeters do not invade the area of the "box", you can place them anywhere.

Okay but we don't actually have this magical ideal shielding box. So lets look at what would happen if the box was removed?

Well unsurprisingly the most inner voltmeters that used to show 0.1V and 0.9V would show the same value. The path trough them does not enclose any extra flux so there is no reason for them to show something different. This now completes the chain, the circuit behaves like a transformer even if we don't contain the fields.

Where things do get messed up is all other voltmeters. The magnetic field is now affecting all there probe wires and as a result affecting the voltmeter readings. If we wish to continue doing circuit analysis then the model has to be updated to give those wires correct coupled inductance too, after that the voltmeter readings from circuit analysis will once again match the real thing.

Any objections to this explanation?

A lot. This is where you, Mehdi and co., fail miserably. When you remove the box you destroy your transformer. The lines of the magnetic field will return elsewhere. You do not have a lumped component anymore, much less a coupled inductor. But you insist that there must be some kind of error, because the transformer must still exist somehow. After all, what is a transformer? Is it not made of a piece of wire? Well the wire is there, so there must be a transformer too.

Wrong. The wires couldn't care less about the varying magnetic field.

And i still don't see what part of Maxwell i supposedly don't understand. All of this makes perfect sense to me from the point of view of Maxwell or from the point of view of mesh  circuit analysis.

It makes perfect sense to you because your Maxwell is not the real Maxwell. With your Maxwell, the voltages of a circuit must always add up to zero.

With the real Maxwell, voltages may or may not add up to zero, depending on a series of conditions.

Where do the explanations above violate Maxwell?

Here and I quote:

This now completes the chain, the circuit behaves like a transformer even if we don't contain the fields.

Where things do get messed up is all other voltmeters. The magnetic field is now affecting all there probe wires and as a result affecting the voltmeter readings. If we wish to continue doing circuit analysis then the model has to be updated to give those wires correct coupled inductance too, after that the voltmeter readings from circuit analysis will once again match the real thing.

This is bullshit. The magnetic field does not affect the probes nor the voltmeter readings. No coupling occurs. No correction is needed.

This is not Maxwell.

The real thing is what the voltmeters are reading.

You're trying to find facts to support your a-priori conclusions. This how religion works, not science.

Sorry if it sounds rude but i get the feeling that you two understand Maxwell perfectly well but have some issues understanding circuit analysis and circuit modeling.

Circuit analysis is just a special case of Maxwell. If you say that we understand Maxwell, you're saying that we understand circuit analysis perfectly well.

And you have a serious problem with circuit modeling, because you see voltages where they aren't.

[ogden]

Ah alright that's what is bothering you, alright fine il do some drawing too.

I wonder when you realize that those guys do not have word "agree" in their vocabulary They are ready to disprove their own words - if it is you who is speaking

[bsfeechannel]

Ah alright that's what is bothering you, alright fine il do some drawing too.

I wonder when you realize that those guys do not have word "agree" in their vocabulary They are ready to disprove their own words - if it is you who is speaking

I can't see where we are disproving ourselves. We are not claiming anything. We're consistently showing that the claim that Kirchhoff always hold is nothing but quackery.

[bsfeechannel]

By the way. Here is the real thing without the lumping box, in case someone still has some doubts.