Abstract
Summary The paper deals with equilibrium distributions of n electrons (point charges −1) on plane conductors in the shape of a simple closed curve. For Jordan curves γ of class C 3+e and a certain roundness, a precise formula is obtained for the asymptotic behavior of equilibrium sets of n points. The results extend and refine the sophisticated work of Pommerenke on the asymptotic distribution of Fekete points (and other equilibrium points) on “strongly analytic” Jordan curves. They enable one to obtain a close estimate for the field due to n electrons in equilibrium (Faraday cage effect). The basic tool in the paper is a quantitative Tauberian result to the effect that if for a given distribution of n electrons on a smooth, roundish Jordan curve, the tangential forces are small, then the electrons are close to an equilibrium configuration, except possibly for a conformal rotation.
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