Abstract
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 C3+ε 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
