A variational proof of Thomson’s theorem

Authors: Essén, H., Fiolhais, C. N., Gouveia, M. T.
Document Type: Article
Pubstate: Published
Journal: Physics Letters A
Volume: 380   2703–2705
Year: 2016


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, constrainingthe two variables.