OK now we're getting somewhere, i think (i hope!). If I understand you correctly, you believe that

*Faraday's law implies a violation of conservation of energy*!

"you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's." I would call this a strawman, unless you can point me to where Lewin said that Maxwell's equations require ignoring conservation of energy.

It's his KVL that violates conservation of energy in his experiment because it can't possibly account for the source of energy as it knows nothing about magnetic flux!

I'm not sure I'm going to be able to bring you over without repeating things I've already said in the past few posts, but I'll try.

The point there is that something can't be simultaneously zero and non zero.

It can - when "something" is one thing in one case and completely different in another.

but.. it's not. int E•dl is int E•dl is int Ed•dl. It has the same meaning in both Lewin's KVL and Faraday's law. It means you go around a loop adding up each incremental bit of E field you encounter along your path. It doesn't matter whether it's an E field from a battery or an E field in a resistor or an E field arising from a changing magnetic flux. Do you believe that int E•dl has somehow a different meaning in the two equations?

Take following as my objection you asked for: you cannot take in account law of conservation of energy in KVL case but ignore it in Maxwell's.

Shall I repeat & emphasize : Integral E.dl part of Kirchoff's circuit rule includes *both* EMF source and load. Integral E.dl of Maxwell's equation includes/describes only EMF *source*.

I would say that as applied to this experiment, Faraday's law equates Int E•dl with the source (negative time rate of change of magnetic flux through the loop) of energy. It seems like you are unwilling to accept an EMF that doesn't arise from a source that is clearly related to an E field being maintained between two points, and that's what's causing you trouble, but that's the reality that Faraday describes.

You simply can't equal two (integrals), because they "look the same" (your words BTW).

I think you are misunderstanding my point. Let's use completely different symbols to hopefully make it clear. Let's look at two equations:

Y = 0

Y = F(x)

In equation one, we are saying that Y = 0. In equation two we are saying Y is equal to some function of x. There is only one way both can be valid and that is the case where F(x) = 0 for any value of x. But we are asserting that F(x) also takes on non-zero values. Therefore Y = 0 is not a universal relation but just one possible point on the real general case of Y = F(x). 0 is just one possible value in the range of the function.

If it helps, think of Y as your height above the ground, and F(x) as a function that gives your current height above the ground. You might spend days, weeks or months walking around thinking that F(x) always equals 0 because you're always firmly on the ground. Then you get in an elevator, or an airplane for the first time. F(x) is no longer zero, and you must conclude that Y = 0 is a special case and not a general relation. This is mathematically, logically the same argument with different symbols.

Following equation describes circuit of Dr.Lewin's experiment inner loop:

Don't you find it similar to equation of KVL you wrote?

I assume you agree to both. Me too.

Yes, and I had to use Faraday's law to get there. Lewin's KVL could not have done it. That is one of his points.

[Edit: few clarifying words]

[Edit2: fix broken quoting]