Testing radiation reaction by simple charge distributions

TL;DR

This paper investigates the validity of approximating a uniformly charged spherical shell by a point charge in the context of radiation reaction, revealing that such substitution is not generally valid.

Contribution

It demonstrates that the field of a uniformly charged spherical shell cannot be accurately replaced by that of a point charge, using a reference frame free approach and generalized functions.

Findings

The field of a charged spherical shell differs from a point charge.

Substituting a shell with a point charge is invalid for radiation reaction analysis.

The approach simplifies calculations and clarifies the limitations of point charge models.

Abstract

A point charge is frequently approximated by various charge distributions deriving the Lorentz-Abraham-Dirac (LAD) equation. Here a rigid spherical shell is treated from this point of view. This particular continuum model is excellent to investigate whether some hidden expectations are true or not. It is shown here that the field of a uniformly charged rigid spherical shell cannot be substituted by the field of a central point charge. The related calculations are short and transparent due to a reference frame free representation of spacetime and the mathematical theory of generalised functions. %Here it is shown that the field of a uniformly charged rigid spherical shell cannot be substituted by the field of a central effective point charge. The related calculations are short and transparent due to a reference frame free representation of spacetime and the mathematical theory of generalised functions.