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I like to visualize the electric field in a moving conductor as a smooth
gradient which will support a current if connected to a stationary return
path, but which will exhibit the field regardless (i.e. beyond the 'rails'
the field in the rod survives...)
I am uncomfortable with the conceptual model of electrons or charge
'piling up'. The force due to a very minor difference in electron
density is considerable.
Brian
When a conducting rod is moving in a uniform magnetic field (rod,
magnetic field, velocity mutually perpendicular) charge
accumulation establish at the ends of the rod.