ELECTROMAGNETIC-FIELD GENERATED BY A MOVING POINT-CHARGE - A FIELDS-ONLY APPROACH

There are various methods for obtaining the electromagnetic field gene rated by an arbitrarily moving point charge in free space. If one deco mposes the total electric field in terms of its transverse and longitu dinal components, one must deal with the fact that the longitudinal co mponent is propagated instantaneously. In this paper we deal with this in a novel manner. In the Fourier transform domain we solve for the t ransform of the transverse electric field in terms of expressions whic h involve the transforms of the current density and the longitudinal e lectric field; we thus view these expressions as ''sources'' of the tr ansverse electric field. By inverse Fourier transforming we directly o btain the space-time transverse electric field, which is shown to cont ain a term which exactly cancels the instantaneous longitudinal electr ic field, so that the total electric field is propagated in a retarded fashion. Our approach does not make use of intermediate vector and sc alar potentials, and thus dispenses with the need for gauge conditions .