Open Access
2016 A Rigorous Framework for the Landau and Lifshitz Approach to Thomson Electrostatics
Michael Grinfeld, Pavel Grinfeld
J. Geom. Symmetry Phys. 41: 69-75 (2016). DOI: 10.7546/jgsp-41-2016-69-75


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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Michael Grinfeld. Pavel Grinfeld. "A Rigorous Framework for the Landau and Lifshitz Approach to Thomson Electrostatics." J. Geom. Symmetry Phys. 41 69 - 75, 2016.


Published: 2016
First available in Project Euclid: 31 May 2017

zbMATH: 1359.35187
MathSciNet: MR3585166
Digital Object Identifier: 10.7546/jgsp-41-2016-69-75

Rights: Copyright © 2016 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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