  We extend the Wald solution to a black hole that is also boosted. More
specifically, we derive analytic solutions for the Maxwell equations for a
rotating black hole moving at constant speed in an asymptotically uniform
magnetic test field. By adopting Kerr-Schild coordinates we avoid singular
behaviours at the horizon and obtain a complete description of the charge and
current distributions in terms of the black-hole spin and boost. Using this
solution, we compute the energy losses expected when charged particles are
accelerated along the magnetic field lines, improving previous estimates that
had to cope with singular electromagnetic fields on the horizon. When used to
approximate the emission from binary black holes in a uniform magnetic field,
our estimates match reasonably well those from numerical-relativity
calculations in the force-free approximation.
