Applications of potential theoretic mother bodies in Electrostatics

TL;DR

This paper explores the application of potential theoretic mother bodies, originally from mathematical physics, to electrostatics for computing electric field potentials, offering a novel approach to potential calculation.

Contribution

It introduces the use of mother bodies in electrostatics, bridging a gap between potential theory and electric field analysis with new computational methods.

Findings

Demonstrates the feasibility of mother bodies in electrostatic potential computation

Provides a new framework for analyzing electric fields using potential theoretic skeletons

Suggests potential for improved efficiency in electrostatic calculations

Abstract

Any polyhedron accommodates a type of potential theoretic skeleton called a mother body. The study of such mother bodies was originally from Mathematical Physics, initiated by Zidarov and developed by Bj\"{o}rn Gustafson and Makoto Sakai. In this paper, we attempt to apply the brilliant idea of mother body to Electrostatics to compute the potentials of electric fields.