The dynamics of a charged particle

TL;DR

This paper derives physically accurate equations of motion for a classical charged particle by modifying the Lorentz-Abraham-Dirac equations, accounting for finite charge size and external force conditions, aligning with previous research.

Contribution

It introduces a new derivation of particle dynamics that corrects the LAD equations by incorporating finite size effects and specific external force conditions.

Findings

Derived equations match known results for finite-sized charges.

Imposed conditions prevent unphysical solutions of point charges.

Illustrated the approach with a uniform acceleration example.

Abstract

Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can classically not be a point particle because of the Coulomb field divergence, my derivation accounts for that by imposing a basic condition on the external force. That condition ensures that the particle's finite size charge distribution looks like a point charge to the external force. Finite radius charge distributions are known not to lead to differential equations of motion. The present work is in agreemnent with the results by Spohn and by others. An example, uniform acceleration, demonstrates what the above basic condition entails. For clarity of the argument, I discuss the non-relativistic case before the relativistic one.