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(1) How can there still be an emf in the loop if it's not closed?
Theoretically, I don't know how to calculate the flux and use Faraday's Law
in its integral form because there is no closed loop. It doesn't even make
sense to me: what if I made two cuts in the loop - would I still get an
emf? How about if I made a really big cut? Experimentally it doesn't make
sense either - I would make different measurements with a voltmeter
depending on how I connected the leads to the loop (eg. if they snaked
around backwards around the outside of the loop), so how can one speak of a
definite emf as though it were a battery?
(2) A different issue. Let's suppose the loop is made of real wire and
hence is actually three-dimensional. I can then draw closed loops all over
the inside of the wire. So won't there be gazillions of eddy currents on
all length scales inside the wire? Won't each individual valence electron
be driven every which way at once? Exactly what will happen? I can't
visualize it. Will the internal currents cancel, leaving net currents
flowing like a skin near the surfaces of the wire? I don't recall having
heard of that, so I think there's something basically wrong with my
reasoning here.
(3) A more basic issue. What exactly is an "emf"? Given that, "The
(nonconservative) electric fields produced by induction cannot be described
by an electric potential" (bottom of p. 791), what is emf, if not a
potential?