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A variational proof of Thomson's theorem
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-0130-9643
2016 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 380, no 35, 2703-2705 p.Article in journal (Refereed) Published
Abstract [en]

Thomson's theorem of electrostatics, which states the electric charge on a set of conductors distributes itself on the conductor surfaces to minimize the electrostatic energy, is reviewed in this letter. The proof of Thomson's theorem, based on a variational principle, is derived for a set of normal charged conductors, with and without the presence of external electric fields produced by fixed charge distributions. In this novel approach, the variations are performed on both the charge densities and electric potentials, by means of a local Lagrange multiplier associated with Poisson's equation, constraining the two variables.

Place, publisher, year, edition, pages
Elsevier, 2016. Vol. 380, no 35, 2703-2705 p.
Keyword [en]
Classical electromagnetism, Electrostatics, Thomson's theorem
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Other Physics Topics
URN: urn:nbn:se:kth:diva-192396DOI: 10.1016/j.physleta.2016.06.039ISI: 000380597100001ScopusID: 2-s2.0-84978066504OAI: diva2:969049

QC 20160913

Available from: 2016-09-13 Created: 2016-09-12 Last updated: 2016-09-13Bibliographically approved

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Essén, Hanno
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