  We revisit the problem of a spinning black hole immersed in a uniformly
magnetized plasma within the context of force-free electrodynamics. Such
configurations have been found to relax to stationary jetlike solutions that
are powered by the rotational energy of the black hole. We write down an
analytic description for the jet solutions in the low black hole spin limit,
and demonstrate that it provides a good approximation to the configurations
found dynamically. For characterizing the magnetospheres of rapidly spinning
black holes, we find that the current sheet which forms in the black hole
ergosphere plays an essential role. We study the properties of the current
sheet, and its importance in determining the jet solution and the rate at which
energy is extracted from the black hole.
