A standard textbook problem says: Assume a uniform magnetic field (B)
pointing into the page inside a circular region of radius R (and zero
outside of it) and increasing in magnitude at a constant rate
(dB/dt). Find the induced electric field (E) everywhere in space.
For specificity, assume the B field is produced by an ideal solenoid.
One finds by symmetry that E is azimuthal in direction, increasing
linearly from zero for r<R up to (R/2)(dB/dt) in value, and then
dropping off as the inverse square outside the solenoid.
Fine, now what happens if the solenoid is square in cross-section?
(This question was asked by a student.) Say length L on a side, and
still ideal so B uniform inside and zero outside with constant rate
of increase of strength.
Regardless of whether I try the differential or the integral form of
Faraday's law, I don't seem to make much progress. Who can help me
out? If this variation is done in some reference, that would be
helpful too. -Carl
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Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/