The electromagnetic self-force of a Lorentz-contractible spherical shell of radius $R$ in rectilinear arbitrary motion: the terms of order $1/R$ and $R^0$

TL;DR

This paper derives the electromagnetic self-force on a Lorentz-contractible spherical shell in arbitrary rectilinear motion, expanding in powers of radius R, and compares the results with previous studies.

Contribution

It introduces a new method based on a velocity-dependent volume charge density to calculate the self-force, avoiding previous difficulties.

Findings

Calculated the first two terms of the self-force series expansion in R.

Validated the method by comparison with existing literature.

Performed the analysis entirely in the laboratory frame.

Abstract

We write the electromagnetic self-force of a Lorentz-contractible spherical shell of radius $R$ in arbitrary rectilinear motion as a series expansion in powers of $R$, and calculate the first two terms of this series. The method we use, which is based on the description of the particle in terms of a velocity-dependent volume charge density, avoids some important difficulties of the previous approaches from the literature. We compare our results with the results obtained by other authors. The whole calculation is done in the laboratory frame of reference.