On the electrostatic equilibrium of charges and cavities in a conductor
Abstract
We consider a charged conductor of arbitrary shape, in electrostatic equilibrium, with one or more cavities inside it, and with fixed charges placed outside the conductors and inside the cavities. The field inside a particular cavity is then only due to charges within that cavity itself and to the surface charge induced on the surface of the same cavity. A similar statement holds for the exterior of the conductor. Although this is an elementary property of conductors, it is not a trivial statement, as explained in this article. Undergraduate texts in electrodynamics do not discuss at length or provide a complete argument for an important problem such as this. Two simple and complete proofs are provided in this note with the help of the standard electrostatic uniqueness theorems.
Cite
@article{arxiv.1609.04248,
title = {On the electrostatic equilibrium of charges and cavities in a conductor},
author = {Aritro Pathak},
journal= {arXiv preprint arXiv:1609.04248},
year = {2016}
}
Comments
Accepted for Publication in a forthcoming issue of European Journal of Physics, as listed in the link below. http://iopscience.iop.org/journal/0143-0807/page/forthcomingArticles