2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57811We 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.Latex, 29 pages, 6 figuresMathematical PhysicsPrimary 31B05; Secondary 58E05text