MIT Professor vs. all college physics books

[Feynmanfan]

Hi there!

I'm a first year student and found quite interesting the MIT on-line video lectures on electromagnetism.
http://ocw.mit.edu/OcwWeb/Physics/8...tures/index.htm

In one these lectures given by Dr. Walter Lewin it is explained how all college books and teachers wrogly use Kirchhoff's 2md law in order to calculate the current through a RL circuit.

That is emf-IR-L (dI/dt)=0. Dr.Lewin says that this is the right answer but physically the procedure is not. In his lecture he states that Faraday's law is misinterpreted and not taken into account. He thinks that everybody knows that that's the differential equation, and just because they see a zero automatically we are using Kirchoff's law.

Lewin follows saying that Kirchoff tells us that the sum of V through a closed loop is 0, but how can it be zero if we have a change in magnetic flux. and therefore the closed integral of E.dl =-dflux/dt.

I couldn't convince my teacher. I am totally confused and don't know what to think.

What do you guys think? Is Lewin right? How can I convince my teacher?

Yours,

Santiago

 

[turin]

Well, there are two inductances: the intended inductance of the inductor and the inductance of the circuit mesh (which can essentially be considered as a loop of current). I personally disagree with the author of the accusation.

In an introduction to circuit analysis, there are certain physical aspects that one defers to a more advanced treatment (or possibly never to be treated). The back-emf of the inductor can most certainly be treated in KVL just as any other voltage in the loop, since to remove it therefrom would break the circuit. KVL does not stipulate any origin to the constituent emfs. The two salient assumptions in this case, for pedagogy's sake, are:
1) the non-trivial portion of the circuit is << λ
2) the inductance of the mesh itself is negligible

Of course, in reality, the inductance of the mesh is always present. In other words, KVL should really be considered as an approximation when dealing with time-dependent circuits. Faraday's Law can then be considered as a degree of violation of KVL. In fact, the inductance of the mesh itself is actually sometimes incorporated as an essential part of the design which cannot be ignored (i.e. microstrip circuits). However, this is far beyond an introduction to the theory of passive circuits. Perhaps the professor is not targetting introductory level instruction. I do not agree with the reason the professor gives to qualify his/her position.

 

[Feynmanfan]

Thanks a lot for your opinion.

 

[turin]

Thanks a lot for your opinion.

Would you like to discuss it? Can I assume that you agree with the position that Faraday's Law is being misinterpretted? Where (physically) do you think the L di/dt comes from in the diff. eq.? Do you think that the inductor should not be considered as a cicuit element in the mesh? For what level of instruction is this intended (context)?

 

[Feynmanfan]

Well,

I'm a first year student and feel still a little bit confused. You argued as my teacher did, that the inductor can be considered just as any other voltage in the loop.
However, this MIT professor whom I read on the net takes the "ideal" RL circuit and he considers the inductor made of a superconducting material. Therefore E=0 across the inductor.

You are right when you say that all this theory is just an approximation, because we're dealing with time-dependent circuits.

The level of intstruction is not high, we're talking about a first year course of electromagnetism. After having studied Kirchhoff's law and how it works in conservative fields, to me (and to this professor) it doesn't make sense when we use the same law that states the total voltage around a closed loop must be zero.

In this circuit we have non-conservative fields so (despite getting the right solution) it is not physically correct to use this Voltage loop law. It is true that you have the Modified Kirchhoff law for inductors, that's the same and it works right but is it physically correct. That's what confuses me.

WHat measures a voltmeter when we put it parallel to the inductor (the ideal inductor with 0 resistance, cause if it had some we'll put it with all the other resistance)? Well, the voltmeter doesn't measure a drop in potential but a change in magnetic flux, that due to Faraday's law and the high resistance of the voltmeter an emf is induced. Kirchhoff's 2nd law doesn't apply in this non-conservative field. That's still my opinion.

I'd very gladly learn from what you think, as an experienced physicist or student.

Thanks again

 

[turin]

I think I am starting to see this professor's point. I should probably follow that link.

You argued ... that the inductor can be considered just as any other voltage in the loop.

Yes.

... this MIT professor ... considers the inductor made of a superconducting material.

It may surprise you to learn that I basically agree with this idea, except, instead of convoluding the pedagogy with superconducting material (which has its own quirks), I merely require my theoretically ideal inductors to have 0 resistance. An introduction to circuit analysis is mathematically abstract. This has it's advantages, as the basic analysis does not restrict application to electrical systems.

Therefore E=0 across the inductor.

Only in DC steady state. For the transient analysis, the L di/dt term gives an actual voltage difference between the terminals of the inductor. This is the case for an ideal (perfectly conducting) inductor. If the inductor had some resistance, this would, to first order approximation, simply act like another R in series with the inductor.

You are right when you say that all this theory is just an approximation, because we're dealing with time-dependent circuits.

Do you realize that the entire circuit loop is itself an inductor? For introductory circuit analysis, you just assume that this inductance is negligible. In other words, you assume that d&Phi;/dt << V (of the circuit voltage source).

The level of intstruction is not high, we're talking about a first year course of electromagnetism. After having studied Kirchhoff's law and how it works in conservative fields, to me (and to this professor) it doesn't make sense when we use the same law that states the total voltage around a closed loop must be zero.

In this context I agree with you. As an electrical engineer you would not even worry about the origin of KVL. As a physicist, even in an intro course, the origin of KVL is more important to learn than the application. I don't understand why your teacher is treating it differently. I agree with you that it doesn't make sense in light of Faraday's Law unless you explicate the approximation.

In this circuit we have non-conservative fields so (despite getting the right solution) it is not physically correct to use this Voltage loop law. It is true that you have the Modified Kirchhoff law for inductors, that's the same and it works right but is it physically correct. That's what confuses me.

The issue is not the fact that you are treating an inductor; it is the fact that the current in the circuit is changing. To underline this point, consider just a simple R circuit with a voltage source (like a lightbulb attached to a battery). The issue is the same in this case. If source voltage varies, then Ohm's Law says that the current will vary through the resistor. But KCL says that the current will then vary throughout the circuit. This will induce a non-trivial (though usually negligible) back-emf around the circuit described by Faraday's Law, and therefore, KVL will not be strictly correct, but only an approximation, which can be corrected by introducing the back-emf. This is the case regardless of whether or not there are intentional inductors in the circuit.

WHat measures a voltmeter when we put it parallel to the inductor (the ideal inductor with 0 resistance, cause if it had some we'll put it with all the other resistance)? Well, the voltmeter doesn't measure a drop in potential but a change in magnetic flux, that due to Faraday's law and the high resistance of the voltmeter an emf is induced. Kirchhoff's 2nd law doesn't apply in this non-conservative field. That's still my opinion.

If you had an "ideal" voltmeter (one that does not affect the circuit in any way) then the theory says that you will measure a potential difference across an inductor if the current is changing. Faraday's Law says that this potential difference is a back-emf, but it is still an electrical potential. The potential is higher on the side of the inductor into which the current is increasing (using the convention of positive current being the opposite of the direction of electron flow and high potential corresponding to a deficit of electrons).

 

[robphy]

http://ocw.mit.edu/NR/rdonlyres/Physics/8-02Electricity-and-MagnetismSpring2002/C29636DB-AB80-49E0-BFAB-BCE00159F00E/0/lecsup41.pdf is a detailed lecture supplement on this topic. I just recently viewed that lecture myself. Time-permitting, I will study these notes.

By the way, the link to that course is
http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/CourseHome/
(It seems the URL is truncated in the first post in this thread.)
and the video lecture is #20
http://ocw.mit.edu/OcwWeb/Physics/8-02Electricity-and-MagnetismSpring2002/VideoLectures/index.htm