### Author Topic: Does Kirchhoff's Law Hold? Disagreeing with a Master  (Read 89446 times)

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#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #700 on: January 27, 2019, 09:02:13 am »
Attachments didn't all fit in one post

#### Sredni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #701 on: January 27, 2019, 01:48:41 pm »
Here there was a picture showing why I wanted an asymmetric coil to generate the uniformly distributed magnetic field.

But the principles behind that can be found in any good book about electromagnetism.
« Last Edit: February 13, 2019, 07:32:29 am by Sredni »
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#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #702 on: January 27, 2019, 07:01:46 pm »
I have added path integrals to my code and have tried to compute the fields origin point from the B field by using a weighted average but that doesn't seam to work so far.

Il try instead to automate the calculation of such a partitioned rectangle and see what that gives. But i will admit your last drawing does look a bit worrying for my method.

Oh and thanks i have updated my previous post with the typo.

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #703 on: January 28, 2019, 04:26:47 pm »
The circuit is simple enough that very little circuit analysis is actually needed on it.

We know the voltage around it is 1V, We know the total loop resistance is 1 KOhm so trough I=U/R=1V / 1KOhm = 1mA.
At this point the voltages and currents across components are known so the circuit is solved.

Thank you for your replies, they are really helping in spotting the problem and will be useful to answer your question about what part of Feynman's lectures is being misunderstood.

Quote
Since you are looking for the textbook definition the voltage between points AB is both 0V and 1V.

Well, clearly Kirchhoff doesn't hold for the most elementary of the circuits when varying magnetic fields are present.

What you might have tried to do (at least I have) was to replace the wire and the field by a battery or some other lumped generator like in the picture below.

However, when you do that, obviously you will have to account for the electric field that this component will introduce along path #2. But path#2, we've already seen, has no electric field. So this is not a circuit of exclusively lumped components and no circuit analysis from the point of view of Kirchhoff can be employed.

But all is not lost. The answer to the next question may seem kind of obvious, but I am trying to prevent any hasty conclusions. I had to spend some time meditating about it myself.

I elongated path #2 so that we have a larger area without any varying magnetic field to the right like in the picture below. My question is, please, what is the voltage between points A' and B' via path #3?

« Last Edit: January 28, 2019, 04:31:25 pm by bsfeechannel »

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #704 on: January 28, 2019, 07:29:19 pm »
Did get around to implementing the thing now and played with it some and indeed that is the case.

It appears for this method to work reliably it does require the B field to one of the flowing:
-Infinite uniform field everywhere
-Confined to a radially symmetric shape
-Confined to a much smaller shape than the path (So that you observe the smoother far field)

I don't quickly see a way to make it work reliably in other cases. I get the feeling that EM simulation is actually required in these more complex cases. But if nothing else this integral feature did help me verify more of Maxwells behavior in my thrown together simulation, moving and resizing the yellow loop around does act exactly as Faradays law says it should. So i am reasonably confident that the E field it spits out is correct.

So yeah my sectioning method does appear to require special case conditions to work. In extreme cases of very long and skinny rectangles (Like 20:1 aspect ratio) it can get the short side wrong by 50%, but the total sum around is always correct (Since the origin gets canceled out). So i do have to admit i was a little bit wrong here, but hey now i can just stick those special cases into my shitty "EM Simulator" (If it even deserves to be called that) and have it calculate the lumpy distribution of EMF for me.
« Last Edit: January 28, 2019, 07:30:57 pm by Berni »

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #705 on: January 28, 2019, 07:56:31 pm »

Well, clearly Kirchhoff doesn't hold for the most elementary of the circuits when varying magnetic fields are present.

What you might have tried to do (at least I have) was to replace the wire and the field by a battery or some other lumped generator like in the picture below.

However, when you do that, obviously you will have to account for the electric field that this component will introduce along path #2. But path#2, we've already seen, has no electric field. So this is not a circuit of exclusively lumped components and no circuit analysis from the point of view of Kirchhoff can be employed.

Yes the battery is how the "Upgraded KVL" as you call it would deal with the EMF. You get a circuit that acts pretty much the same in the textbook voltage definition. Same current flows trough the circuit. Going from A to B down the bar gets you 1V and going from A to B around the loop you get 1V too (Remember voltage sources appear negative due to the opposite E field inside). Since we turned the field into a lumped battery means the circuit is no longer exposed to a field and so the sum around the loop should be 0V and if you go around you indeed get 0V.

If you do it in the form of inductors or magical batteries it doesn't matter. As long as the circuit mesh is somehow informed about the effects of the B field.

But all is not lost. The answer to the next question may seem kind of obvious, but I am trying to prevent any hasty conclusions. I had to spend some time meditating about it myself.

I elongated path #2 so that we have a larger area without any varying magnetic field to the right like in the picture below. My question is, please, what is the voltage between points A' and B' via path #3?

The voltage along that path is also 1V because i assume there is no wire there.

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #706 on: January 28, 2019, 10:45:54 pm »
The voltage along that path is also 1V because i assume there is no wire there.

That's what I thought. For your convenience I decided to tabulate below all the voltages in this circuit.

 Node Node Path Voltage (V) Reason A' A #2 0 Ideal wire A B #1 1 EMF across resistor B B' #2 0 Ideal wire B' A' #3 -1 EMF across the air A' B' #3 1 EMF across the air B' A' #2 0 Ideal wire

Now let's add a 1V battery between nodes A' and B' like in the picture below. Will the voltages in the table above remain the same or will they change?

« Last Edit: January 28, 2019, 10:47:35 pm by bsfeechannel »

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #707 on: January 29, 2019, 06:05:55 am »
Still the same voltages.

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #708 on: January 29, 2019, 11:12:41 pm »
Precisely.

If you look at the table again, now considering the battery in the circuit, you are going to notice that nodes A', A, B, and B' form a mesh through path #1, two stretches of path#2 and path #3, where all the voltages add up to zero. A' and B' form a mesh through path #3 and the portion of path #2 that encloses the varying magnetic field, where the voltages do not add up to zero.

 Node Node Path Voltage (V) Reason A' A #2 0 Ideal wire A B #1 1 EMF across resistor B B' #2 0 Ideal wire B' A' #3 -1 EMF across the air || battery Total 0 No varying magnetic field in the mesh A' B' #3 1 EMF across the air || battery B' A' #2 0 Ideal wire Total 1 Presence of varying magnetic field in the mesh

This would be enough to hint that Kirchhoff only holds when varying magnetic fields are not present in a mesh. But let's not be diverted by that "coincidence", because our interest is elsewhere.

Let's turn our attention to the fact that our first attempt at employing circuit analysis failed because, when we introduced a battery in path #2, (although nothing changed for the resistor) we changed the electric field along that path. Now that we have introduced the battery in a path with a voltage that is exactly equal to the EMF of that path, nothing has changed. If we now disconnect the mesh on the left -- the one with the varying magnetic field -- the mesh on the right would see no difference in terms of voltage.

 Node Node Path Voltage (V) Reason A' A #2 0 Ideal wire A B #1 1 EMF across resistor B B' #2 0 Ideal wire B' A' #3 -1 Battery Total 0 No varying magnetic field in the mesh

And if we analyze the resulting closed path formed  by the portion of path#2 to the left and a straight line from A'' and B'' (not pictured), the voltages still remain as before.

 Node Node Path Voltage (V) Reason A'' B'' #4 1 EMF across the air B'' A'' #2 0 Ideal wire Total 1 Presence of varying magnetic field in the closed path

So it seems that this last resulting circuit better models the original circuit, because, although it doesn't represent what is actually going on along path #2 -- in fact it hides it -- at least it doesn't lie about that. It doesn't introduce a field where a field should not be.

« Last Edit: January 29, 2019, 11:16:17 pm by bsfeechannel »

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #709 on: January 30, 2019, 06:09:58 am »
Now comes hopefully our last question. Given the circuit below, with our familiar ideal wire, varying magnetic field and ideal resistor, supposing that the field occupies the closed loop entirely, without any area that be free from it, and supposing we would like to replace the 1V EMF with a battery that will be located exactly where it occurs in the circuit, where would you place this battery? In other words, what path would you choose to connect this battery?

« Last Edit: January 30, 2019, 02:17:40 pm by bsfeechannel »

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #710 on: January 30, 2019, 05:10:59 pm »
Here it is then.

Since the field ends at the resistive bar that's where i put the battery.

But given that the behavior of the circuit doesn't change if its placed anywhere else its not that critical. The placement locations of components in circuit mesh schematics has no effect, its just that usually we try to match the real life placement for easier understanding of what components are what in the diagram.

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #711 on: January 30, 2019, 08:22:33 pm »
Thank you for all your replies.

We can see pretty much that this is theoretically and physically impossible, because a battery and a resistor can't occupy the same space at the same time.

So, not only this circuit more than violates--it rapes--Kirchhoff big time, as we have seen, but also cannot have an equivalent version with lumped components.

Now I owe you an answer to your question, what part of Feynman's lectures, namely Chapter 22 is being misunderstood? The short answer is all of it. It is so because people are disregarding basic assumptions that Feynman adamantly stresses in his text.

An answer a little less short is given by Prof. Belcher in his "MIT-quality report" where he elegantly showed where exactly Mehdi, and for that matter all those who still believe that KVL can have the slightest chance to hold under a varying magnetic field, goofed it up. However, after the report, Mehdi continued to espouse his previous ideas, which means that he didn't in fact learn anything. Perhaps, noticing this, even before Mehdi made his second video, Prof. Belcher said in his report:
Quote
I am grateful to Mr. Sadaghdar for a number of discussions about Faraday’s Law and KVL, which have improved my understanding of both.
I.e., my understanding improved.

Belcher concludes:
Quote
Many introductory texts on electromagnetism are not precise about what exactly they mean by the voltage drop across the inductor, and many students come to incorrect conclusions about what this actually means. The most common misconception is that the  - LdI/dt voltage read by the voltmeter just above represents a −∫abE⋅dl through the inductor. But if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires.

So, replacing perfectly conducting wires with batteries, or generators, is a noob mistake. It's a trap for young players. This means that the circuit below is not modelling Lewin's circuit.

In fact, Lewin's circuit is not lumpable, because we do not have anywhere inside the loop where we don't have varying magnetic fields, where we could replace the EMF with a battery and get away with it. The voltages that you can measure at the terminals of the resistors of the internal loop are the result of electric fields that are being generated along the very same path where the resistors are.

The failure to understand this basic principle of electromagnetism leads to all kinds of wrong conclusions.

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #712 on: January 30, 2019, 09:03:46 pm »
Thank you for all your replies.

We can see pretty much that this is theoretically and physically impossible, because a battery and a resistor can't occupy the same space at the same time.

So, not only this circuit more than violates--it rapes--Kirchhoff big time, as we have seen, but also cannot have an equivalent version with lumped components.

Now I owe you an answer to your question, what part of Feynman's lectures, namely Chapter 22 is being misunderstood? The short answer is all of it. It is so because people are disregarding basic assumptions that Feynman adamantly stresses in his text.

An answer a little less short is given by Prof. Belcher in his "MIT-quality report" where he elegantly showed where exactly Mehdi, and for that matter all those who still believe that KVL can have the slightest chance to hold under a varying magnetic field, goofed it up. However, after the report, Mehdi continued to espouse his previous ideas, which means that he didn't in fact learn anything. Perhaps, noticing this, even before Mehdi made his second video, Prof. Belcher said in his report:
Quote
I am grateful to Mr. Sadaghdar for a number of discussions about Faraday’s Law and KVL, which have improved my understanding of both.
I.e., my understanding improved.

I agree.

Again i never said in this whole thread that KVL always holds in real circuits. What made you think i did?

Well theoretically you can have two components occupy one space just fine, just like you can have ideal wires with zero inductance, or resistors with negative resistance values. In fact a real coil is an inductor, resistor and capacitor in one physical piece of material, just that the inductance part tends to be vastly larger than the other two. But everything theoretical is not necessarily realizable physically.

Belcher concludes:
Quote
Many introductory texts on electromagnetism are not precise about what exactly they mean by the voltage drop across the inductor, and many students come to incorrect conclusions about what this actually means. The most common misconception is that the  - LdI/dt voltage read by the voltmeter just above represents a −∫abE⋅dl through the inductor. But if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires.

So, replacing perfectly conducting wires with batteries, or generators, is a noob mistake. It's a trap for young players. This means that the circuit below is not modelling Lewin's circuit.

In fact, Lewin's circuit is not lumpable, because we do not have anywhere inside the loop where we don't have varying magnetic fields, where we could replace the EMF with a battery and get away with it. The voltages that you can measure at the terminals of the resistors of the internal loop are the result of electric fields that are being generated along the very same path where the resistors are.

The failure to understand this basic principle of electromagnetism leads to all kinds of wrong conclusions.

Well in terms of being unlumpable i still don't see how my lumped transformer model is wrong here:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg2138140/#msg2138140

It does fill a lot of criteria:
- It contains all fields inside the lumped transformer
- All other elements are not enclosed in a magnetic field so circuit analysis methods should work on them.
- It behaves exactly like the real experimental circuit, so in terms of functionality it is an accurate mesh model
- All parts of the mesh model belong to some physical part of the real circuit, no magical added components just to make it work.

This does NOT magically prove anything about KVL working in real circuits with magnetic fields in them. My claim is that this particular circuit can be reasonably lumped and mesh modeled to sufficient accuracy that circuit analysis predicts its behavior within a reasonable margin of error.

No need to tell me that a mesh model is not exactly the same as a real circuit. I know its not! No mesh model is, because we can't create these ideal circuit components in real life, but when modeling is done right it acts just like the real thing despite being simplified.

#### Sredni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #713 on: January 30, 2019, 10:17:44 pm »
- All other elements are not enclosed in a magnetic field so circuit analysis methods should work on them.

When applied to the Romer-Lewin circuit, this is wrong and false.

The Romer-Lewin circuit encloses a net nonzero variable magnetic field.
Your lumped circuit is a different circuit for the very reason that by forcing the field to be confined inside the four arcs, you create a field-free zone inside the circuit connecting them.

As I said before, until you realize that, there is nothing I can do to help.

EDIT: heres a little help

« Last Edit: February 13, 2019, 07:35:14 am by Sredni »
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#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #714 on: January 30, 2019, 11:07:10 pm »
Well in terms of being unlumpable i still don't see how my lumped transformer model is wrong here:
https://www.eevblog.com/forum/chat/does-kirchhoffs-law-hold-disagreeing-with-a-master/msg2138140/#msg2138140
[snip]
No need to tell me that a mesh model is not exactly the same as a real circuit. I know its not! No mesh model is, because we can't create these ideal circuit components in real life, but when modeling is done right it acts just like the real thing despite being simplified.

Your model says you will find 250mV across all wires. Theory says it is zero. You measure, it is zero. Nature agrees with theory. What do you think is wrong? Nature? Theory? Perhaps both? Or your model?

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #715 on: January 31, 2019, 06:10:35 am »
I said in my last post that i know its not the exact same circuit.

But the real life circuit that the mesh model represents is very similar and behaves exactly the same as Dr. Lewins circuit.

And yes my model says that you will measure 250mV across the wires, but only if you use probes traveling outside the field to connect your voltmeter! If the voltmeter is hooked up with wires that go trough the same field inside the transformer you get 0V. So how is that 0V different?

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #716 on: January 31, 2019, 10:14:03 am »
I said in my last post that i know its not the exact same circuit.

So end of story. Theory, practice, and now your brain are saying that your circuit is not a model of Lewin's circuit. Listen to them.

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #717 on: January 31, 2019, 05:39:55 pm »
So then all cirucit mesh models are flawed because they don't exactly replicate every detail of a cirucit such as parasitic capacitance between all conductive materials, parasitic inductance in every piece of wire and models the magnetic field produced even by picoamps of current passing trough wires? And so we should throw away circuit analysis as a whole and stop using it because it never represents the exact circuit?

#### Berni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #718 on: February 01, 2019, 07:00:11 am »
But where do you draw the line.

Real transformers also leak fields, especially if run close to saturation in a badly designed E core. So anything around them is now un-lumpable?

Or maybe the design has one of these non shielded inductors: https://si.farnell.com/coilcraft/pcv-2-564-08l/inductor-560uh-7a-10-power/dp/2457700
These things spew bunch of the returning field out around them, so anything around that part on your board is now un-lumpable?

Or just running two parallel traces on a circuit board creates coupling between them, this is actually how RF couplers are made most of the time. So at what length do the two traces go from being lumpable to un-lumpable?

Or do we need to go to something that really makes strong use of magnetic coupling like for example a resonant loop antenna? Like this: http://webclass.org/k5ijb/antennas/Small-magnetic-loops-FAQ.htm

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #719 on: February 01, 2019, 01:12:45 pm »
But where do you draw the line.

That's your most significant question up to now.

Feynman's chapter 22 is all about drawing that line. Literally. He even names it Γ (gamma).

#### Sredni

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #720 on: February 01, 2019, 02:05:52 pm »
But where do you draw the line.

Where most---

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
« Last Edit: February 13, 2019, 07:36:40 am by Sredni »
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#### ogden

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #721 on: February 01, 2019, 05:55:19 pm »
Your model says you will find 250mV across all wires. Theory says it is zero.

Which exactly theory says it is zero?

Are you saying that for EMF voltage to appear - full winding is necessary? In your understanding there is no 1/4 * EMF voltage on the 1/4 winding (tap)?

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #722 on: February 01, 2019, 06:55:40 pm »
Your model says you will find 250mV across all wires. Theory says it is zero.

Which exactly theory says it is zero?

Since 19th century electromagnetism is explained by Maxwell's equations.

Quote
Are you saying that for EMF voltage to appear - full winding is necessary? In your understanding there is no 1/4 * EMF voltage on the 1/4 winding (tap)?

Where have you been lately? Have you followed our discussion since Jan 23rd?

#### ogden

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #723 on: February 01, 2019, 07:59:00 pm »
Are you saying that for EMF voltage to appear - full winding is necessary? In your understanding there is no 1/4 * EMF voltage on the 1/4 winding (tap)?

Where have you been lately? Have you followed our discussion since Jan 23rd?

If I missed your answer to exact same question I just asked - feel free to copy/paste it (again) here.

#### bsfeechannel

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##### Re: Does Kirchhoff's Law Hold? Disagreeing with a Master
« Reply #724 on: February 01, 2019, 08:06:23 pm »
Read Feynman's book chapter 22, "verses" 1 and 2. The answer to your question is there. I can't do better.

Smf