[en] In the study of beam-cavity coupling effects, one must solve Maxwell's equations for the fields produced by a given beam shape and given cavity geometry. A recent paper that treats the effect on the bunch shape has considered the longitudinal electric field in a pill box cavity produced by a step function charge pulse traveling at the speed of light. In order to obtain a clear physical picture of how the fields are produced in the cavity, we treat the problem of a point charge traveling at the speed of light, c, between two infinite plates. This must, of course give the same result as the closed pill box cavity for values of time t such that ct is less than the cavity radius. In this paper, the longitudinal and radial electric field components and the azimuthal magnetic field component are derived from Maxwell's equation for this idealized case. We use the eigenmode expansion method and include some details of the tricks used in the computation of the sums. We also discuss the physical picture of the electromagnetic fields that were derived. 5 refs., 3 figs