Motion of extended charges in classical electrodynamics

The Lorentz–Dirac theory of radiation reaction on the motion of point charges is beset by the well known problems of runaway solutions and preacceleration. We examine the classical theory of extended charged particles and obtain a differential-difference type equation of motion. Analysis of this equation reveals that the theory is internally consistent (i.e., no runaways or acausality) whenever the size of the particle exceeds the classical radius (defined as the radius for which the electrostatic self-energy equals the mass of the particle). A specific example is presented which explicitly shows the different character of the extended and point charge solutions.