The fields and self-force of a constantly accelerating spherical shell

TL;DR

This paper derives a PDE for electromagnetic potentials of an accelerating charge distribution, finds solutions, and calculates the self-force for a spherical shell undergoing constant acceleration, providing high-order approximations and conjecturing exactness.

Contribution

It introduces a PDE for electromagnetic potentials of accelerating charges, solves it, and computes the self-force for a spherical shell, advancing understanding of self-interactions in accelerated systems.

Findings

Exact solutions to the PDE for electromagnetic potentials.

High-order approximation of the self-force on a spherical shell.

Conjecture that the derived series expression is exact.

Abstract

We present a partial differential equation describing the electromagnetic potentials around a charge distribution undergoing rigid motion at constant proper acceleration, and obtain a set of solutions to this equation. These solutions are used to find the self-force exactly in a chosen case. The electromagnetic self-force for a spherical shell of charge of proper radius $R$ undergoing rigid motion at constant proper acceleration $a_0$ is, to high order approximation, $ (2 e^2 a_0/R) \sum_{n=0}^\infty (a_0 R)^{2n} ((2n-1)(2n+1)^2(2n+3))^{-1} $, and this is conjectured to be exact.