Contribution to the Theory of the Cherenkov Effect

The rigorous solution is given for the field of a uniformly moving point charge which, coming from vacuum, enters at $t=0\mathrm{}$ through a plane surface into an ideal, macroscopic, homogeneous dielectric medium ($\epsilon =\mathrm{const}.\mathrm{}$). The solution represents a characteristic transition radiation, as the velocity of motion approaches $\frac{c}{{\left(\epsilon \right)}^{\frac{1}{2}}}$ and furnishes information about the formation of the characteristic cone if $v=\frac{c}{{\left(\epsilon \right)}^{\frac{1}{2}}}$.