  We discuss the problem of finding an upper bound for the number of
equilibrium points of a potential of several fixed point charges in R^n. This
question goes back to J.C.Maxwell and M.Morse. Using fewnomial theory we show
that for a given number of charges there exists an upper bound independent on
the dimension, and show it to be 12 for three charges. We conjecture the exact
upper bound for a given configuration of nonnegative charges in terms of its
Voronoi diagram, and prove it asymptotically.
