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I will take a swing at rephrasing this question. First, let me modify
the question slightly. I am thinking of it in terms of a horseshoe
magnet that is spinning about its symmetry axis. The magnetic field
lines are basically confined to the region between the poles or inside
the magnet itself the electron is sitting on the axis between the center
of the poles.
That is the E-field lines form a loop around the x axis. From what
I can figure, the electron does not respond to this field, but I am not
sure.