ON THE RADIATION BY A CHARGE IN A MATERIAL MEDIUM

Abstract

In this work we obtain the exact non linear equation of motion, including radiation reaction, for a charge moving in an isotropic, homogeneous and linear medium. From this equation we recover the known results for the dynamics of charges in vacuum and discuss the involved approximations. Using the hypothesis of uniform motion in the exact non linear equation we obtain the usual results of the Cherenkov effect. Also we analyze several conceptual points in order to get a better understanding of the Cherenkov effect. We study the energy balance and show explicitly the existence of an external force to avoid a contradiction with the electromagnetic theory

we show that, in this case, the charge behaves as a transducer transforming completely mechanical work into radiation. We also discuss the physical origin of the Cherenkov radiation, giving an explanation why there is radiation even when the charge is in uniform motion.