Vector Monochromatic Diffraction Fields and Fields of Charges in Electrodynamics

Abstract

In previous works, the electromagnetic field in an arbitrarily chosen volume is represented in vector form including surface and volume integrals using the found vector Green’s function. Surface integrals describe the diffraction of the field created by charges external to the volume, and volume integrals describe the fields created by charges moving inside the volume. In this work, passing to the Fourier transforms in the previously found vector formulas of the field, expressions for a monochromatic electromagnetic field are obtained. Integro-differential equations are also obtained for a monochromatic electromagnetic field in a non-magnetic medium, in the presence of charges with a given motion. Because both diffraction fields and the fields of charges with a given motion, as well as the fields of charges induced in the medium, are considered together, these equations are obtained for the first time.