CALCULATION OF THE RETARDED ELECTRIC FIELD FOR AN ARBITRARY CHARGE AND CURRENT DISTRIBUTION.

In the Lorentz gauge, the solutions to the scalar and vector potential equations free space are the retarded potentials, which are integrals of charge and current distributions over all space, subject to the retardation condition. It is shown that if the charge and current are turned on in the finite past, integrals over a finite region result, in particular, over an expanding sphere of radius ct, centered at the field point. The limits of integration, which are time and space dependent, have been obtained. Author