Charge Densities for Conducting Ellipsoids

TL;DR

This paper derives simple geometric formulas for charge densities in conducting ellipsoids and hyperellipsoids, providing explicit expressions for surface and line charge densities in various dimensions.

Contribution

It introduces straightforward geometric expressions for charge densities in conducting ellipsoids and hyperellipsoids across multiple dimensions, extending known results.

Findings

Explicit formulas for volume charge density in ellipsoids

Derivation of surface charge density expressions

Generalization to hyperellipsoids in any dimension

Abstract

The volume charge density for a conducting ellipsoid is expressed in simple geometrical terms, and then used to obtain the known surface charge density as well as the uniform charge per length along any principal axis. Corresponding results are presented for conducting hyperellipsoids in any number of spatial dimensions.