  We study the effects of an external magnetic field, which is assumed to be
uniform at infinity, on the marginally stable circular motion of charged
particles in the equatorial plane of a rotating black hole. We show that the
magnetic field has its greatest effect in enlarging the region of stability
towards the event horizon of the black hole. Using the Hamilton-Jacobi
formalism we obtain the basic equations governing the marginal stability of the
circular orbits and their associated energies and angular momenta. As
instructive examples, we review the case of the marginal stability of the
circular orbits in the Kerr metric, as well as around a Schwarzschild black
hole in a magnetic field. For large enough values of the magnetic field around
a maximally rotating black hole we find the limiting analytical solutions to
the equations governing the radii of marginal stability. We also show that the
presence of a strong magnetic field provides the possibility of relativistic
motions in both direct and retrograde innermost stable circular orbits around a
Kerr black hole.
