We came across an odd EM problem involving the
electric field induced by time varying magnetic
field. If it makes you happy, let it be large or
infinite in exten. Let it point vertically down,
be uniform, and be increasing in magnitude. For
any given loop in the horizontal plane it is easy
to calculate the induced EMF around the loop and
from that you think you could figure out the
electric field at any point on the loop and thus
one could calculate the electic field at any spot
for a given time.
But here is the problem, first consider a loop
in the horizontal plane with radius of 1 meter and
located 1 meter to the right of the origin ( the
center is at (1,0,0) and use this loop to find
the electric fiel at the origin. Next calcuate
the electric feld at the orign by consider a
similar loop but with its center at (-1,0,0). In
one case the electric field seems to point in the
positive y direction while in the other it points
in the negative y direction.