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Proof of Thomson's theorem of electrostatics
Journal article   Peer reviewed

Proof of Thomson's theorem of electrostatics

Ezzat G. Bakhoum
Journal of electrostatics, Vol.66(11-12), pp.561-563
11/01/2008
DOI: https://doi.org/10.1016/j.elstat.2008.06.002
Web of Science ID: WOS:000261814200002

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Abstract

A 100 years old formula that was given by Thomson [Footnote on p. 154 of J.J. Thomson, Maxwell's Treatise on Electricity and Magnetism, Dover, New York, NY, 1954.] recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson [Classical Electrodynamics, Wiley, New York, NY, 1962, p. 51] and later published by Pappas [Differential geometric solution of a problem in electrostatics, SIAM Rev. 28 (1986) 225]. Unfortunately, Differential Geometry, being a specialized branch of mathematics, is normally inaccessible to the majority of scientists and engineers. This paper provides for the first time a proof that does not depend on Differential Geometry.

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