Dumbbell model for the classical radiation reaction

Abstract

In his treatise on electron theory, Lorentz showed that the classical radiation reaction is attributable to the breakdown of Newton’s Third Law within the structure of an accelerating charge. But Lorentz’s calculation, based on a spherical model, is so difficult as to obscure the underlying physical principle, and requires that the charge be instantaneously at rest. Noting that the answer must be structure independent, in the point-charge limit, we develop Lorentz’s theory in the context of a more tractable model: the dumbbell. We also compute the self-torque on a rotating dumbell.