Application of the argument principle to Maxwell's Conjecture for three point charges

Author： Peretz Ronen  

Publisher： Taylor & Francis Ltd

ISSN： 1747-6933

Source： Complex Variables and Elliptic Equations, Vol.58, Iss.5, 2013-05, pp. : 715-725

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Abstract

J.C. Maxwell conjectured that if n positive charges, ξ j , 1 ≤ j ≤ n, are located in ℜ3 at n points , 1 ≤ j ≤ n, then the number of equilibrium points of the electrostatic potential they generate is finite and contains at most (n − 1)2 points [J.C. Maxwell, A Treatise on Electricity and Magnetism, Vol. 1 (Republication of the 3rd revised edition) Dover Publ. Inc., New York, 1954].

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