Dynamics of a charged particle

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 allows for that by imposing a basic condition on the external force. That condition ensures that the particle’s finite size charge distribution appears as 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 agreement with the results by [H. Spohn, Europhys. Lett. 50, 287 (2000)] and by others. An example, uniform acceleration, demonstrates what the above basic condition entails. For clarity of the argument, I discuss the nonrelativistic case before the relativistic one.