Electrostatics and Riemann Surfaces
General Physics
2020-09-21 v2
Abstract
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions when their argument is complex-valued. The underlying connections between these techniques and the theory of Riemann surfaces are also explained. Our goal is to provide students and instructors a quick reference article for an extraordinary topic that is not included in the standard books.
Cite
@article{arxiv.2006.07149,
title = {Electrostatics and Riemann Surfaces},
author = {Spencer Tamagni and Costas Efthimiou},
journal= {arXiv preprint arXiv:2006.07149},
year = {2020}
}
Comments
Slightly expanded version: three subsections added. Accepted for publication in the Eur. J. Phys