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 \(0<q \le 2\) . Analogous results are developed for Newtonian capacity in higher dimensions and logarithmic capacity in 2 dimensions. Open problems are raised for Riesz equilibrium moments.
