Energy conservation for a radiating charge in classical electrodynamics

Abstract

It is shown that the well-known disparity in classical electrodynamics between the power radiated in electromagnetic fields and the power-loss, as calculated from the radiation reaction on a charge undergoing a non-uniform motion, is successfully resolved when a proper distinction is made between quantities expressed in terms of a "real time" and those expressed in terms of a retarded time. It is shown that the expression for the real-time radiative power loss from a charged particle is somewhat different from the familiar Larmor's formula, or in a relativistic case, from Li\'{e}nard's formula.