Cherenkov radiation in vacuum. 1

After discussing some historical aspects of the Cherenkov effect from electrodynamic and quantum theoretical points of view a methodically clear and simple theory of the Cherenkov effect is presented in which an arbitrary shaped rigid charge distribution is considered and which is based only on essential knowledge of Fourier transformations and cylindric functions. The Cherenkov effect is derived as a consequence of the structure of the potentials and the influence of the geometric shape of the charge distribution on the spectral distribution of the radiation intensity is taken into account in a general form. The educational value of such a representation of the Cherenkov effect in textbooks is emphasized