Radiation from and force acting on a point charge moving through a cylindrical hole in a conducting medium

The radiation from and the force acting on a point charge, moving with relativistic velocity through a cylindrical hole in a conducting medium, is determined. It is shown that a Cerenkov effect occurs if the conductivity of the medium is sufficiently small. Explicit results are given for the time dependence of the field demonstrating the existence of a Cerenkov cone. The dragging force on the moving particle due to radiation losses is examined in detail. The proposed method also applies to dispersive media.