Equation of motion in classical electrodynamics

Abstract

It is proposed that an equation derived as a first-order iteration of the Lorentz-Dirac equation be considered as the exact equation of motion for classical electrodynamics. The added force term which is quadratic in the applied field is shown to be equivalent to a Poynting-like momentum being transferred to the particle. We apply this equation to the motion of a particle in a uniform magnetic field and also in a uniform electric field. In both cases the particle trajectory exhibits the essential physical behavior, while the accompanying electromagnetic radiation is supplied by the interaction with the external field.