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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