Mystery of point charges

Details Mystery of point charges Mystery of point charges

2004-09-03

arxiv.org/abs/math-ph/0409009v1

Physics

Mathematical Physics

Latex, 29 pages, 6 figures

Scientific paper

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.

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