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Is it possible that there can be no such thing as a uniform magnetic
field that is uniformly increasing? The reason I ask is:
Suppose there were such a region and you wanted to know the electric
field at a point in that region. This is a typical textbook problem:
if there were a wire loop, use Faraday's law to find the induced
voltage and set that voltage equal to E x circumference. This is an
example problem in many texts. My question is about the direction of
the induced electric field (hard to explain without a diagram)
presumably it is in the direction of the induced current. But if you
were to move the wire loop, say one diameter to the right, it would
still be in the same uniformly increasing uniform field. So if the
current was clockwise (say) before, it would still be clockwise. But
now the electric field direction at the leftmost point is in the
opposite direction of what it was when that location was the
rightmost point of the as-of-yet-untranslated wire loop. But that
means the direction of the induced electric field caused by a
uniformly increasing uniform field varies with t he orientation of a
wire loop placed in that field!