OK, I've asked a lot of pointed questions, so it's time for me to stick my neck out and say something. First, when I first saw this debacle, I didn't really understand it, but it seemed like a non-issue to me. Still, such debates should be about learning and discovery, not belittling, name-calling and all the sorts of ugly pettiness that have shown up. It doesn't help that both Lewin and Mehdi are of the attention-seeking type. What struck me as interesting is that of all the stuff that has been posted here, Youtube, wherever, it never becomes clear what the disagreement is about. People say Lewin is 'wrong', others say he is 'right'. What does that even mean? Did he rig his demonstration? Here's my interpretation of the disagreement (warning: there's no real resolution), anyone who differs please be specific about which point we depart at!
So here's a drawing just like the myriads of others we've all seen:
I think we all agree that in this diagram, both V1 and V2 will read the same voltage. I think both camps also agree that voltages V(A0-A2) and V(A0-AV2) are the same. The point of departure is that the 'KVLers' would say that the two voltages are some number and they cancel each other out, so the both voltmeters read just the voltage across R2. That number, of course, would vary with the position of R2 because it posits the existence of a continual voltage gradient on the wire. The 'Lewinites' seem to be asserting that both voltages are zero and that the position of A0 doesn't matter.
Using the definition of voltage as being the work required to move a test charge along a path, it seem pretty clear that going from A0 to D0 through R1 takes a different amount of work than going through R2. Thus they have different voltages and of opposite sign. However, when we are measuring with a voltmeter, neither of those paths is what we are referring to--it is the path of the test leads going to the voltmeter. (I initially stuck on this point!) I haven't seen any mathematical proof, but it appears that things work out so that even though there are infinitely many paths to arrange those test leads, if you stay in-plane (or possibly even not, but I haven't thought about that) and don't cross the ring, your voltmeter will always read either the voltage across R2 or R1, without any intermediate results. Again, either there is no induced voltage on the test leads nor (A0-A2) and (D0-D2), or they always add up to the same number and cancel.
Some have tried probing out-of-plane perpendicular to the ring and gotten different results, but the counter is that this method somehow 'ignores' something--the induced EMF field--and thus is wrong. It has been asserted here that you can't have a voltage on a conductor that is a partial turn or a partial ring. Again, there are two apparent explanations, one that until the loop is complete there is no voltage and the other that there is a voltage, but you can't measure it because any probe you use will either cancel or complete the loop.
I earlier had alluded to the concept of 'absolute' voltage. It might sound silly, but I checked to make sure that Lewin had actually taught this earlier in the course. In electrostatics, you learn and then apparently promptly forget that a conductive sphere of radius
r will have a capacitance of C=4*pi*E
0r. And, since Q=CV, V=Q/C. There's a perfectly legitimate definition of voltage derived directly from fundamental constants. Now before the howls of protest start, please remember I'm trying to resolve the issue of
what the disagreement is about, not who is right.
So now I'm going to measure voltage in a different way, one that is never path dependent--brass balls. I'm going to take two hollow brass balls of a precisely known radius r hanging from an insulated string. Since I know r, I know C. I'm going to arrange a partial turn or partial ring or even a straight rod, going through a changing magnetic field, then extend the ends out to the point where the fields are negligible. Then while the field is in state of linear change (call this the MQS period, or Magneto-Quasistatic period) I'm going to touch the brass balls to the ends of the rod so that they accumulate a charge, keeping them there until equilibrium is reached. Then I will separate them from the rod before the MQS period ends. Next I will take the brass balls back to my Couloumb meter lab where I will proceed to precisely determine what the charge was on each ball, then I will know each voltage from V=Q/C. The difference between the two is my voltage, by this definition, between the two points. If I use this method on the Lewin ring, I think the results will match the perpendicular probing method.
So that, IMO, is the nature of the disagreement. As others have said, in a conductor in a varying field, there will be two forces E
IND and E
COUL that will will balance out in the MQS domain, because that is what conductors do--there can be no electric field in a conductor. However, that doesn't negate the fact that there is a charge imbalance over the conductor. When it comes to partial turns, I think the mathematical types here have done themselves a disservice by insisting that we only consider full loops because any voltage measurement will make a complete loop. The complete loop doesn't matter if the gap is beyond the non-negligible area of flux. If you took the rod in my example and bent it into a U-shape and then extended it far enough out so that the flux from the torus was negligible, you would get the same reading from a voltmeter as you would from the brass ball technique. Completing the loop satisfies the math, but doesn't matter in the real world because the work has been done locally in the area near the torus.
So that post wasn't as long as I thought it would be. Lewin is not 'wrong'. But Lewin is wrong! According to my absolute definition, it is not KVL that fails in a varying magnetic field, it is the definition of voltage being the integral of E dot dL (sorry--I can't find notation symbols) that fails in a non-conservative field. I can hear howls of protest. But think about it!
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