about the lecture on electromagnetic induction and non-conservative faraday's law. Prof W. Lewin said, the voltmeter would have different readings when connected to the same pair of nodes because the current was caused by changing magnetic field which is nonconservative, if this is the case, then the concept of a uniform potential surface does not hold in this example.?

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anonymous · Answer

No, it doesn't. In a nonconservative field, the concept of the "potential" at a point does not hold any more. Go back to the definition of the "potential" at a point. It is the amount of work you do to bring a test charge from infinity to that point.  In a nonconservative field, this work that you do will depend on the path you've taken to get there. So, the "potential" at a point is not explicitly defined anymore(because, for a million paths, there will be a million different potentials associated with that point). And therefore, the concept of equipotential surfaces will also not hold :)