Electronic – Assigning a notion of voltage even when there is a changing magnetic field

magnetic fluxvoltage

In Walter Lewin's lecture, he finds depending on how you keep the lead of the voltmeter for a circuit in a changing magnetic field, you will measure different values]. This experiment is discussed from 49:34 of this lecture and then infers that this is why a notion of voltage is no longer possible in the case of changing magnetic field.

According to Mr.Boom, Lewin's result had a correct result, given his setup, but his conclusion was incorrect. To demonstrate this Mr.Boom experiments (see from 7:24 of this video before disagreeing), where he creates a modified version where Lewin's concluded principle must be equally applicable, however in Mr. Boom's equivalent experiment, Lewin's ideal fails. Hence, the premise of Boom was demonstrated. Particularly speaking, Mr.Boom says that, and I quote from after 10:45 of the second video, he concludes the real reason for Lewin's result was bad probing (*)

however, Mehdi(Mr.Boom) does an experiment in his second video and gets a result against Lewin's theory, so what was wrong with the experiment for falsifying Lewin? I have read this answer by Sredni Vashtar on this but I am not able to use their answer to answer this doubt I have put in the sentence right before.

I think that there is a definite voltage for a circuit even with a field passing through because even though the voltage depends on the line integral, there is only one physical path where current can go through feasible in a circuit!.


Understanding Mr.Boom's arguments

The original experiment of Lewin involved the following circuit:
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Now, using an oscilloscope ( I think?) he measures top and bottom point of circuit at same time (For Boom's discussion)

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And finds that each scope shows different readings:

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Mr. Boom repeats the experiments and finds the same results here, but he disagrees with the conclusion which Lewin made that this leads to KVL not be applicable in the case of circuits with varying magnetic field effects.

To illustrate his point, he does an experiment with a similar set up:

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Since Lewin's theory must be independent of how resistors are arranged, Mr.Boom rearranges the resistors (1k and 10k )and then measures the voltage of each side. He begins by measuring on the 10k side:

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This results into:

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And then he measures through opposite side:

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Which results in the reading:

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He then measures the reading across both the resistor:

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This resulting graph is the some of voltage graph of each resistor measured in individual case. Now, he says the sum voltage is the same voltage across the loop. Hence, there is indeed only a single voltage associated with the two points across the circuit. Now, to double check, he discusses the measurement if the sense wires the other way (path without resistor)

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In this way, it seems that the voltage of the sense wire is zero.. and again we with multiple voltage values. Now, boom's explanation is that the problem is that the voltage is not single-valued but rather an accurate reading can not be taken as the induced field effects the measuring device as well. (see from 8:55 )

Note: All of the above is my understanding of boom's video, if there is a mistake please point out.


Physicists and Electronic engineers divided?

To be frank, I couldn't easily understand Mr. Boom's video, so I searched for other videos by people in electronic engineering-related fields for perhaps a more 'dumbed down' version of it to understand. This led me to this video by Mr. Bob Duhamel, in which he states that Lewin is wrong see from around 23:00 and agrees with Mr. Booms's result.

Now, here is the weird part, people in physics stack exchange and such seem to agree with Mr. Lewin's result that different measurements give different values see this answer by knzhou. So, it seems the answer is entirely different depending on wether you study EE or physics.


Romer's paper

So, now I saw the paper which roomer wrote on the issue (Mr.Boom cites this in 2nd video response). The paper is quite interesting and introduces a concept of 'pseudo potential' which can be assigned even in case of changing magnetic field and he explains this new idea with concepts of topology and such. He specifically finds that though the line integral of E*dl is indeed path-dependent, there are only two or three discrete values it can take.

I haven't fully understood the paper's significance here, I'll add in this part as I read through it more.


Some related questions on this aren't easily findable, so I will link all here:

  1. Does Kirchhoff hold even when there is changing magnetic field?
  2. Can two voltmeters connected to the same terminals show different values? Circuit with induced EMF ( See Sredni vashtar's answer)
  3. What would a voltmeter measure if you had an electromotive force generated by a changing magnetic field?
  4. Are Kirchhoff's Laws violated in case of varying magnetic fields?
  5. Kirchhoff's Voltage Law in a General Electromagnetic Field

Hopefully, I got all the related posts, please comment if I have missed any because I want to bring a 'clear' to make myself completely clear what was going on here.

P.s: I have no formal education in Electronics engineering, only some basics I learned from high school. So please comment if I have made mistakes in understanding the situation in my post, I will correct them.

Further, apologies if this post seems a bit messy, I tried my best to make sense of everything I read from multiple resources and put in a neat summary here but I hope it makes sense.

Best Answer

In Walter Lewin's lecture, he finds depending on how you keep the lead of the voltmeter, you will measure different values. Supposedly he discusses it in this video according to Mr.Boom, and then infers that this is why a notion of voltage is no longer possible in the case of changing magnetic field.

That's nonsense. Of course there's a notion of voltage in presence of a changing magnetic field. In fact, Maxwell's equation, which describe all electricity (unless you start looking at quantum levels), specifically describe that relationship!

So, cutting this discussion quite short:

Kirchhoff's equation holds for the circuit notation you know, as it's a direct result of the very math that holds together the basics of reality (Ampère's circuital law says: you take any closed loop and calculate the current density along that. Then you get a value proportional to the integral of the magnetic field that goes through the surface enclosed by that line.

Now, that circuit notation you know, with nodes, and lines representing conductors, assumes these conductors are infinitely short, have zero resistance and no current is induced in them (otherwise, you wouldn't just draw a line, but a resistor and/or a current source, right). If no current is induced, then *there can't be a net magnetic field permeating the loop formed by any conductors in a classical circuit.

I.e. the pure application of Kirchhoff's law states your magnetic fields are zero. If they aren't, you need to extend your network with current sources, representing what that magnetic field does to the conductors (again, in these linear network circuits, the conductors, and all elements, are assumed to be zero in size, so that a magnetic field can't have any effect, speed of light doesn't matter etc pp).

So, yes, Kirchhoff's law and changing magnetic fields, thereby induced currents, and hence voltages across any resistive elements, are compatible – if you know the limits of where to apply Kirchhoff's law. The circuit schematics that you're used to are, as a model of a circuit, not sufficient to define things like length, position of conductors to a magnetic field, so obviously, they themselves aren't appropriate to demonstrate this.