On the Cherenkov radiation from extended charge distributions

Abstract

In this work the Cherenkov effect for extended charge distributions isanalyzed using two different methods. In the first method, the Poyntingvector is employed to determine the energy radiated, whereas in the secondone, we apply the idea of generating time-dependent elementaldipoles, induced by a charge distribution moving withconstant velocity, inside a material medium. An explicit expression for the Cherenkovradiation generated by some different kinds of spherically symmetric charge,travelling inside a medium, is obtained.