The dynamics of a charged particle

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.