  In a recent paper by Giuliani and Rothman \cite{GR}, the problem of finding a
lower bound on the radius $R$ of a charged sphere with mass M and charge Q<M is
addressed. Such a bound is referred to as the critical stability radius.
Equivalently, it can be formulated as the problem of finding an upper bound on
M for given radius and charge. This problem has resulted in a number of papers
in recent years but neither a transparent nor a general inequality similar to
the case without charge, i.e., M\leq 4R/9, has been found. In this paper we
derive the surprisingly transparent inequality
$$\sqrt{M}\leq\frac{\sqrt{R}}{3}+\sqrt{\frac{R}{9}+\frac{Q^2}{3R}}.$$ The
inequality is shown to hold for any solution which satisfies $p+2p_T\leq\rho,$
where $p\geq 0$ and $p_T$ are the radial- and tangential pressures respectively
and $\rho\geq 0$ is the energy density. In addition we show that the inequality
is sharp, in particular we show that sharpness is attained by infinitely thin
shell solutions.
