Kelvin transformation and inverse multipoles in electrostatics
Classical Physics
2017-02-01 v1
Abstract
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are obtained through the mapping from simple highly symmetric systems. In particular, the concept of multipole expansion is revisited from a point of view opposed to the usual one: the sources are distributed in a region far from the origin while the electrostatic potential is described at points close to it.
Keywords
Cite
@article{arxiv.1611.05942,
title = {Kelvin transformation and inverse multipoles in electrostatics},
author = {R. L. P. G. Amaral and O. S. Ventura and N. A. Lemos},
journal= {arXiv preprint arXiv:1611.05942},
year = {2017}
}
Comments
19 pages, 4 figures