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Since the rod is moving at constant velocity, the net field in the metalMe too, sort of. I can imagine a thick rod where the end charges take on a
would be zero. The only way to get that is to allow a charge
distribution to occur which would cancel the induced field. It
certainly wouldn't be just charges at the end, since the induced field
is constant, and the field due to the charges would, in the extreme be 1
over r squared.
Anyway, thats the way I imagine it.