  The equilibrium measure of a compact plane set gives the steady state
distribution of charges on the conductor. We show that certain moments of this
equilibrium measure, when taken about the electrostatic centroid and depending
only on the real coordinate, are extremal for an interval centered at the
origin. This has consequences for means of zeros of polynomials, and for means
of critical points of Green's functions.
  We also study moments depending on the distance from the centroid, such as
the electrostatic moment of inertia.
