  Recently, we derived an improved universal upper bound to the entropy of a
charged system $S \leq \pi (2E b-q^2)/ \hbar$. There was, however, some
uncertainty in the value of the numerical factor which multiplies the $q^2$
term. In this paper we remove this uncertainty; we rederive this upper bound
from an application of the generalized second law of thermodynamics to a
gedanken experiment in which an entropy-bearing charged system falls into a
Schwarzschild black hole. A crucial step in the analysis is the inclusion of
the effect of the spacetime curvature on the electrostatic self-interaction of
the charged system.
