On the Cherenkov radiation from extended charge distributions

In this work the Cherenkov effect for extended charge distributions isanaly zed using two different methods. In the first method, the Poyntingvector is employed to determine the energy radiated, whereas in the secondone, we ap ply the idea of generating time-dependent elementaldipoles, induced by a ch arge distribution moving withconstant velocity, inside a material medium. A n explicit expression for the Cherenkovradiation generated by some differen t kinds of spherically symmetric charge,travelling inside a medium, is obta ined.