  The $q$-th moment ($q>0$) of electrostatic equilibrium measure is shown to be
minimal for a centered ball among $3$-dimensional sets of given capacity, while
among $2$-dimensional sets a centered disk is the minimizer for $0<q \leq 2$.
Analogous results are developed for Newtonian capacity in higher dimensions and
logarithmic capacity in $2$ dimensions. Open problems are raised for Riesz
equilibrium moments.
