The Cherenkov effect for non-rotating extended charges

Abstract

In this work we analyse the Cherenkov effect for non-rotating extended charges. We obtain the energy radiated per unit path length per unit frequency by the charge facing the Cherenkov effect as a radiation reaction problem. The underlying idea is to consider that the power radiated by the charge is equal to the work done by the radiation reaction force. Our results are equal to those obtained using other methods (see Buskirk F. R. and Neighbours J. R., Phys. Rev., 28 (1983) 1531

Smith G. S., Am. J. Phys., 61 (1993) 147

Jackson J. D., Classical Electrodynamics (Wiley, New York, N.Y.) 1962, pp. 494-499, 783). In the limit of point particle we recover the usual results of the Cherenkov effect.