Cherenkov radiation from a charge of finite size or a bunch of charges

A point charge moving in a medium with a constant speed greater than the speed of light in the medium produces Cherenkov radiation. When the medium is nondispersive, the potential functions and electromagnetic field for the point charge are singular along the surface of the Mach cone, and the spectrum (Fourier transform) of the field increases indefinitely with frequency. The purpose of this paper is to present a simple extension of the results for the point charge to a charge of finite size or a bunch of charges. The model adopted allows an analytical description of the potential functions and electromagnetic field near the surface of the Mach cone. The aforementioned singularities associated with the point charge are absent, and the spectrum for the field is bounded and given by a simple expression. The graphical displays presented for Cherenkov radiation from a charge of finite size clearly show the similarity to other familiar physical phenomena, e.g., the wake of a boat moving in shallow water. In addition, they provide physical insight into the process of radiation that should be useful for instruction.