  We present a partial differential equation describing the electromagnetic
potentials around a charge distribution undergoing rigid motion at constant
proper acceleration, and obtain a set of solutions to this equation. These
solutions are used to find the self-force exactly in a chosen case. The
electromagnetic self-force for a spherical shell of charge of proper radius $R$
undergoing rigid motion at constant proper acceleration $a_0$ is, to high order
approximation, $ (2 e^2 a_0/R) \sum_{n=0}^\infty (a_0 R)^{2n}
((2n-1)(2n+1)^2(2n+3))^{-1} $, and this is conjectured to be exact.
