The electric field in space and time of a source moving in a lossless, isotropic, and dispersive medium is obtained from the inhomogeneous wave equation combined with the charge continuity equation. The Fourier transform method is employed together with the theory of functions of complex variables to express the causality condition. The existence of two retarded times is pointed out for the case of a pointlike source moving in a nondispersive medium faster than the propagation velocity of the electromagnetic field. The Čerenkov as well as the polarization radiation is obtained for a dispersive isotropic medium.

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