# Is MIT Prof. Lewin wrong about Kirchhoff's law?

by sarumonkee
 P: 802 @Studiot: I guess the 'old' definition of emf has something to do with the supply - things that propel electricity? So on the other side of the equation, what is the voltage drop of, say, a power supply V? @yungman: I think when it comes down to nano seconds, Kirchhoff's laws don't even hold. The characteristic length = speed of light x time = around 10cm, significant enough for the set-up in Prof. Lewin's experiment (he has quite a big coil obviously!). And yes, during the time after he switched on the coil and the current goes up *instantaneously* to 1mA, wires are no longer "nothing". However, during this period, no conclusion can be drawn. But the point is that, after this period, when dB/dt decreases, the period is about mili-seconds. The current also decreases from 1mA to zero during this period, so di/dt is no longer that large. The graph of V1 and V2 during this period can be seen, and they are not the same. And one more point: Though personally I also want to see with my own eyes the set-up of the experiment, I think even if no conclusion can be drawn from this experiment, what Prof. Lewin said is based on the fundamental - Faraday's law or Maxwell-Faraday equation. He is NOT making a new theory. The subtlety is that, accepting KVL (provided that the characteristic length >> dimensions of the circuit) does give out correct final results, though KVL is not true in this case. @cabraham: The term "potential" should be redefined in your #2 statement. IMHO, strictly speaking, this term should NOT (and does NOT, as mathematics says) exist for non-conservative field. Prof. Lewin tried to avoid the term in his papers.
 P: 5,462 hikaru and those here who don't use megaphone diplomacy may find this thread from another forum interesting. http://forum.allaboutcircuits.com/sh...light=kirchoff
 P: 192 I would like to point out that kirchoff's law cannot have anything to do with an electric field being conservative. As a current passes through any resistive material it will expend energy in the form of heat. If one tried to drive a closed circuit with a conservative field there would in fact never be any current because no electron could ever make it back to the starting point (simple conservation of energy). So saying kirchoffs law doesn't apply because it is not a conservative field is not valid. If that were a valid argument then kirchoff's law would in fact never apply.
 Sci Advisor P: 7,410 Any time a scalar potential is used to derive all the physics, it is being assumed that the electric field is conservative. In situations where the electric field is not static, a scalar potential may still be useful if only approximate. This is the quasistatic approximation. KVL uses a scalar potential, and is closely related to conservative fields.
P: 697
 Quote by hikaru1221 I'm interested in the other version of KVL. Is it "sum of voltage drop = sum of emf"? Anyway, how do we define the term "voltage" in the case of varying magnetic field?
Voltage can still be defined when there are time varying fields. You can research the well known vector potential A. The scalar potential (which is voltage) and the vector potential can be combined into a 4-vector in relativity theory, and a complete field description (including time varying fields) can be provided by scalar and vector potentials. But, this goes a little beyond the thread topic.

The "other" version of KVL could also be called the original version. I say this because Kirchoff's original experiments were with batteries and resistors. The experiments revealed that the sum of EMFs from batteries in a loop equals the sum of the currents times the resistances in the loop. The word potential does not even come up, but it's clear from a modern perspective that resistance times current is a potential drop. Maxwell quotes this version of KVL and gives credit to Kirchoff in his famous Treatise on Electricity and Magnetism. Actually, he mentions both Kirchoff's voltage law and his current law, which nobody argues about at all.

For some reason, this other simplified version of KVL (sum of potentials equals zero) has cropped up in the literature. I'm not sure why, but it is very common to see it in text books. So, it's not too surprising to see Prof. Lewin quoting this as the definition. Again, this is all just semantics, but it is certainly instructive to study and understand the original intent of KVL.

Now it should be said that the original experiments were with EMFs from batteries and not from time changing magnetic flux, but the concept is basically the same. Non-conservative EMFs can be grouped together and used with a very straightforward definition of KVL which says that the sum of EMFs around a loop equals the sum of potential drops around the loop (or some variation on that). Kirchoff and Maxwell define it without reference to potential at all, which can avoid the confusion of what potential means. However, modern theory uses the concept of potential, so it's perhaps better not to avoid it.

To help answer your question, I've attached a copy of Kraus' description of the classical definition of KVL. (Electromagnetics by John D. Kraus, 3rd ed. 1984). Note the footnote at the bottom which mentions time varying fields. As I mentioned above, this is the version of KVL I carry around in my head and use in my professional work. I really don't know why anyone would be interested in the other version of KVL that we commonly see, but who am I to judge?
Attached Files
 KVL1.pdf (222.7 KB, 46 views) KVL2.pdf (235.7 KB, 36 views)
 Sci Advisor P: 7,410 Hmmm, so the original KVL is really Faraday's law (no mention of potential, only line integral of E and includes dB/dt)? Faraday's law is of course a defining equation of electrodynamics, from which what I normally think of as KVL is derived via some quasistatic approximation. I suppose various forms of KVL have cropped up, since circuit theory is an approximation anyway, as long as one uses concepts like capcitance and inductance that are assumed to be properties of the circuit elements.
P: 697
 Quote by atyy Hmmm, so the original KVL is really Faraday's law (no mention of potential, only line integral of E and includes dB/dt)?.
In a sense, you can say that Kirchoff's statement is a general version of FL applicable to circuits. But, keep in mind that Kirchoff did experiments with batteries and not generators, and KVL makes no direct reference to time changing flux being a source of EMF. That fact is one of the many great discoveries of Faraday. So, Faraday's law still is a separate statement, in my view.
 P: 802 @stevenb: So the term voltage is not equivalent to electric potential? Interesting. No wonder, my high school textbook changes from "electric potential" in electrostatics chapter to "voltage" in AC circuit chapter. Then if we apply the original version of KVL, we have to redefine "voltage" / emf of all components?
P: 697
 Quote by hikaru1221 @stevenb: So the term voltage is not equivalent to electric potential? Interesting. No wonder, my high school textbook changes from "electric potential" in electrostatics chapter to "voltage" in AC circuit chapter. Then if we apply the original version of KVL, we have to redefine "voltage" / emf of all components?
My understanding is that the term voltage can be either potential difference or EMF. Usually we can use KVL sloppily and get the right answer, but strictly you would want to classify each component as having either EMF or potential. Or, for nonideal components such as an inductor that likely has significant resistance, both types of voltage can be relevant.
 P: 802 Okay, for the original version of KVL (sum of emf = sum of ohmic drop IR), we don't even need the term voltage. I'm still thinking about how we define emf here. Emf, in the common sense, is somewhat like a "charge pump". Then how should we explain the "emf" of a capacitor?
P: 3,799
 Quote by hikaru1221 @yungman: I think when it comes down to nano seconds, Kirchhoff's laws don't even hold. The characteristic length = speed of light x time = around 10cm, significant enough for the set-up in Prof. Lewin's experiment (he has quite a big coil obviously!). And yes, during the time after he switched on the coil and the current goes up *instantaneously* to 1mA, wires are no longer "nothing". However, during this period, no conclusion can be drawn. But the point is that, after this period, when dB/dt decreases, the period is about mili-seconds. The current also decreases from 1mA to zero during this period, so di/dt is no longer that large. The graph of V1 and V2 during this period can be seen, and they are not the same. And one more point: Though personally I also want to see with my own eyes the set-up of the experiment, I think even if no conclusion can be drawn from this experiment, what Prof. Lewin said is based on the fundamental - Faraday's law or Maxwell-Faraday equation. He is NOT making a new theory. The subtlety is that, accepting KVL (provided that the characteristic length >> dimensions of the circuit) does give out correct final results, though KVL is not true in this case.
So far everybody here only concentrated on each small theory and law, looking at this in the microscopic point of view. I am not even trying to argue on the formulas the professor put out and the validity of non conservative field and Kirchhoff's law. My whole point is I question his experiment and his arrogance of calling this one wrong and that one wrong.

It is so obvious that there is a transformer effect when he created a loop with the two resistors that is like 4” diameter. You can generate 5 to 6 volt per turn on a transformer!!! How do I know? Because we actually design transformer like this in our products and we were selling them!!! I design electronics systems for various mass spectrometer systems. I put a whole micro controller system floating on over 10KV. I need to provide 24V 4A power float to 10KV. I had one of my engineer design a DC to DC converter that have isolation voltage over 10KV. The way I want him to do it is by using HV wire on the secondary and get the efficiency by jacking the switching frequency to over 100KHz to reduce the size of the core and minimize the number of turn on the secondary winding ( HV cable that is 1/8” diameter). We can get something like 6V per turn. I don’t know the detail calculation because my engineer did that. We only had a few turns on the secondary.

My whole point is what the professor did is nothing special, and he mis-represented himself in the experiment and start calling this one is wrong and that one is wrong where in reality his experiment is fraud. If he has any real life experience, he would not have talk so loud and put it on Youtube. His mistake of calling point A and D in the first video show he has no idea of the transformer effect that the voltage measured really depends on where on the wire you measure. As I said, as a real life engineer, only take me but 3 minutes to see the problem, that I can generate about 6V in one single turn and we did it and we beat out each and every competitor at the time because we put so much control floating on high voltage.

Bottom line, I am not nor am I interested in arguing with all of you whether Kirchhoff's law is true of not, the whole point is he use a fraud experiment and blow out hot air and get you guys argue two pages of this. In my "not highly educated" opinion, Kirchhoff's holds in his experiment. KVL say nothing but the voltage over a complete loop is zero. In this case, if you consider the transformer effect as a voltage source and put it in as part of the loop, it WILL be zero around the loop. That is the "moon" that the professor is missing by going microscopic.
 Sci Advisor P: 7,410 In general, capacitor (C=Q/V) cannot be defined.
P: 697
 Quote by hikaru1221 Okay, for the original version of KVL (sum of emf = sum of ohmic drop IR), we don't even need the term voltage. I'm still thinking about how we define emf here. Emf, in the common sense, is somewhat like a "charge pump". Then how should we explain the "emf" of a capacitor?
Good question.

If we follow the modern description of Kraus, then it makes sense to view the electric field in the capacitor as a conservative field in the context of providing a potential drop, albeit a negative one sometimes. You could also call this a positive EMF without offending too many people. The math works out either way.

If we used the original definition from Maxwell, we would be forced to call this potential an EMF, since the concept of potential (which Maxwell was of course well aware of) is not mentioned in this particular definition. It is an EMF because it is a negative potential drop capable of driving the movement of charges and EMF is anything that looks like voltage and can provide energy to separate opposite charges or force like charges together.
 P: 5,462 If I hold a PP3 battery in my hand there is EMF, but no magnetic flux and therefore Faraday's Law is not applicable. There is, of course, no circuit at this stage either. If I now connect two identical batteries ( or carefully adjusted power supplies) in opposition in a circuit, perhaps including resistance, there is still no magnetic flux as there is no current. Kirchoff's law can be applied to this situation as we can sum the opposing EMFs meaningfully.
 P: 802 @yungman: Thanks. The point I would like to point out is, the wire has little effect compared to the resistors, and this is why though we have 1 volt around the loop, this 1 volt is mostly on the resistors. @stevenb: Okay, so original KVL is equivalent to Faraday's law. Kirchhoff was brilliant to put everything in a closed-loop form.
P: 5,462
 Okay, so original KVL is equivalent to Faraday's law. Kirchhoff was brilliant to put everything in a closed-loop form.
Is it?

P: 3,799
 Quote by hikaru1221 @yungman: Thanks. The point I would like to point out is, the wire has little effect compared to the resistors, and this is why though we have 1 volt around the loop, this 1 volt is mostly on the resistors. @stevenb: Okay, so original KVL is equivalent to Faraday's law. Kirchhoff was brilliant to put everything in a closed-loop form.
I look at the wire as a Voltage source induced by the magnetic field. If you consider the voltage source in the loop, KVL held.
Mentor
P: 15,618
 Quote by cabraham I meant time varying fields present in the circuit loop. Time varying fields on the interior of the inductor is modeled by circuit theory, w/o the need to consider fields.
That is a good way to put it (better than my number 3). If you had written this then I would not have objected.

 Quote by cabraham The Lewin paper explicitly stated the field inside the circuit loop, not that on the interior of an inductor. Did you read the paper by Dr. Lewin?
Yes, I read it. In the paper, despite how he drew it, he is considering the field inside an inductor. The example in the video is better on that count.

 Quote by cabraham As far as a cap having " no net charge", this is very semantical. "Charge" as used by the science community implies "differential". An "uncharged cap" has lots of charge, but zero difference. A "charged cap" has the same total absolute charge but is displaced forming a differential. If you define "net charge" as total charge on both plates, then of course there is no "net charge" in either case, energized or not. Whan I say "charge" in ref to a cap, I infer the differential quantity, not the absolute total which you define as "net charge". Dr. Lewin is correct on all counts. He simply illustrated how non-conservative fields differ from conservative. You're trying to look for reasons to poke holes in his case by bringing in arbitrary arguments based on your own semantics.
It is not my own semantics, it is the standard meaning of the term "net charge". Your objection here is a little excessive.

 Quote by cabraham In the final analysis Dr. Lewin states the following. 1) With conservative E fields, KVL holds, & the potential from a to b is independent of the path. 2) With non-conservative E fields, KVL does not hold, & the potential from a to b is dependent on the path. Introducing hyperbole does not alter this basic tenet. Is there any issue with the above 2 statements?
Yes, they are wrong for the same reason as above. As written they would apply to the apply to the fields within the interior of an inductor and not only to fields in the circuit loop.

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