The electromagnetic field (EMF) of a bunch moving uniformly and traversing a dielectric plate located in a waveguide is investigated. The main attention is focused on the case when Cherenkov radiation is generated in the plate. Analysis of the field components of the mode is performed with methods of the complex variable function theory. An algorithm of computation using the exact expressions for the EMF is also presented. Consideration of the EMF structure for different time moments is given. It is shown that Сherenkov-transition radiation (CTR) is generated in the vacuum area after the plate under certain conditions. Results obtained might be of interest for development of new methods of generation of electromagnetic radiation.