  The electromagnetic field around a Kerr black hole inside a current loop is
sometimes used as the basis of a toy model for discussing the properties of
particle orbits near astrophysical black holes. The motivation for the present
paper is to correct the published solution to Maxwell's equations with a
charged current loop. Dipole approximations and closed-form expressions in the
extreme Kerr limit are also presented. Using the corrected solution, it turns
out that imposing a vanishing electromotive force produces a loop with a
potential which is finite everywhere outside the black hole. Ring solutions can
be combined into solutions with multiple rings or current discs.
