  In this paper we consider a rotating black hole with electric and magnetic
monopole charges that moves in a static homogeneous electromagnetic field. We
assume that both the charges and the fields are weak, so that they have no
effect on the spacetime geometry, which is described by the Kerr metric. We
present exact solutions to Maxwell's equations describing the field of a
charged rotating black hole moving in an external field background. We use
these solutions to calculate the energy, momentum, and angular momentum fluxes
of the electromagnetic field into the black hole. Using these results, we
obtain expressions for the torque and force acting on the moving charged
rotating black hole arising as a result of its interaction with the external
electromagnetic field. We calculate these quantities both in the frame comoving
with the black hole and in the frame of the external background field. We use
this result to derive the equations that govern the change in the black hole's
mass and spin, as well as the motion of the black hole. We provide exact
solutions for specific cases which illustrate the role of charge and spin on
the motion of the black hole.
