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A RIGOROUS FRAMEWORK FOR THE LANDAU AND LIFSHITZ APPROACH TO THOMSON ELECTROSTATICS
Journal article   Open access   Peer reviewed

A RIGOROUS FRAMEWORK FOR THE LANDAU AND LIFSHITZ APPROACH TO THOMSON ELECTROSTATICS

Michael Grinfeld, Pavel Grinfeld and Marin Drinov Academic Publishing House
Journal of geometry and symmetry in physics, v 41
01 Jan 2016
DOI: https://doi.org/10.7546/jgsp-41-2016-69-75
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
https://projecteuclid.org/euclid.jgsp/1496196040View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Physical Sciences Physics Physics, Mathematical Science & Technology
Landau and Lifshitz [7] proposed a novel formulation of the famous Thomson theorem, also known as the Thomson variational principle. In an attempt to explain, rather than postulate, the distribution of electrical charge exclusively on the surface of the conductor, Landau and Lifshitz allow the admissible variations in the electrical charge to penetrate the interior of the conductor. This is a valuable generalization of their predecessors' work, as well as a step towards basing more of the analysis on first principles. Landau and Lifshitz' approach has not received the attention it deserves because it was not formulated as a rigorous technique, but rather as a slight of hand to arrive at a known result. In this paper, we construct a rigorous mathematical framework based on the Landau and Lifshitz idea. In particular, we prove that surface distribution of charges corresponds to the absolute minimum of electrostatic energy.

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Collaboration types
Domestic collaboration
Web of Science research areas
Physics, Mathematical
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