Abstract
Consider n point charges, each with charge 1/n, in electrostatic equilibrium on the surface S of a conducting sphere. It is shown that as n tends to infinity, the distribution of the total charge 1 on S tends to the uniform distribution on S. Though this is an entirely deterministic result, the proof is probabilistic in nature.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Korevaar, J. (1972). Prijsvraag wiskundig genootschap 1972–2. Nieuw Arch. Wiskunde, (3), 20, p. 73.
Korevaar, J. (1976). Problems of equilibrium points on the sphere and electrostatic fields. Technical Report 76–03, Department of Mathematics, University of Amsterdam.
Landkoff, N.S. (1972). Foundations of Modern Potential Theory. Springer-Verlag, Berlin.
Robbins, H.E. (1975). Lecture presented at the Fourth Lunteren Meeting on Probability and Statistics.
Van Zwet, W.R. (1976). Solution Prijsvraag Wiskundig Genootschap, Amsterdam.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag New York, Inc.
About this paper
Cite this paper
van Zwet, W.R. (1994). The Asymptotic Distribution of Point Charges on a Conducting Sphere. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics V. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2618-5_32
Download citation
DOI: https://doi.org/10.1007/978-1-4612-2618-5_32
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7609-8
Online ISBN: 978-1-4612-2618-5
eBook Packages: Springer Book Archive