  We calculate the self-force acting on a charged particle on a circular
geodesic orbit in the equatorial plane of a rotating black hole. We show by
direct calculation that the dissipative self-force balances with the sum of the
flux radiated to infinity and through the black hole horizon. Prograde orbits
are found to stimulate black hole superradiance, but we confirm that the
condition for floating orbits cannot be met. We calculate the conservative
component of the self-force by application of the mode sum regularization
method, and we present a selection of numerical results. By numerical fitting,
we extract the leading-order coefficients in post-Newtonian expansions. The
self-force on the innermost stable circular orbits of the Kerr spacetime is
calculated, and comparisons are drawn between the electromagnetic and
gravitational self forces.
