Abstract
The study of the influence of the speed of motion of various emitters of electromagnetic waves on the created electromagnetic fields is one of the urgent engineering and technical problems. Mathematical modeling of such processes is associated with the solution of the system of Maxwell's equations under the action of moving charges and currents, the speed of which can be different. The speed of propagation of electromagnetic waves in a medium-light speed is critical when constructing such solutions. At light and superluminal speeds, shock electromagnetic waves with a intensities jumps on the wave fronts arise. In this paper, Green's tensors and generalized solutions of the transport system of Maxwell's equations are constructed in the entire range of speeds, from subluminal to superluminal. To construct solutions, the Fourier transform of generalized functions and scalar potentials were used, the form of which is significantly different at subluminal and superluminal speeds of movement. Conditions for jumps of tension on the wave fronts are obtained. Analytical formulas are obtained for calculating the vectors of electric and magnetic intensity of the electromagnetic field for emitters of different shapes. In particular, for ring, spherical and spherical emitters. A computer implementation of Green's tensor and an analysis of the effect of the speed of movement on the nature of the radiation are carried out. The results of the research are presented in the form of graphs of the behavior of scalar potentials in wide range speeds of electromagnetic wave radiation emitters.