Electromagnetic Field inside a Current-Carrying Region

Abstract

The improper integrals, appearing in the course of evaluating the vector potential A and the electric field E inside a current‐carrying region, are carefully examined. It is found that the integrals exist and have a well‐defined meaning only when the current density function satisfies a Hölder condition. A definite and precise way of evaluating them is derived and A, E are shown to satisfy the usual inhomogeneous equations.