Radiation reaction from electromagnetic fields in the neighbourhood of a point charge

Abstract

From the expression for the electromagnetic field in the neighborhood of a point charge we determine the rate of electromagnetic momentum flow, calculated using the Maxwell stress tensor, across a surface surrounding the charge. From that we derive for a `point charge' the radiation reaction formula, which turns out to be proportional to the first time-derivative of the acceleration of the charge, identical to the expression for the self-force, hitherto obtained in the literature from the detailed mutual interaction between constituents of a small charged sphere. We then use relativistic transformations to arrive at a generalized formula for radiation reaction for a point charge undergoing a relativistic motion.