In the above figure, we have a rod moving with some speed in $v$ in a magnetic field $B$, it is said that when at equilibrium the rod generates a surface charge density such that the magnetic field must be cancelled off.
However, I do not understand why this must be the equilibrium state, so this leads to my question, How do you prove that the equilibrium condition for the system is that a charge density is developed on the body of conductor such that the electrostatic force on conductor cancels the magnetic force?
Addendum: Ignore fringe effects and Eddie currents
