- Does Faraday's Law of Induction assume the changing magnetic flux exists over the entire area of a current loop?
Suppose there is an almost infinitly long but narrow solenoid with an AC current surrounded by a much larger loop such that there is no magnetic field except in the solenoid. I had always thought it didn't matter what part of the outer loop the flux changed in, there would be an induced electric field and thus a current in the outer loop. Now, I'm reading about the Maxwell-Lodge controversy which makes a big deal over the fact that there is no magnetic field outside the solenoid and none at the outer loop. So, 1) Does Faraday's Law still give the correct result by itself? 2) Is the issue mainly about the role of the Vector potential in mediating Faraday's law? Thanks.