Electric dyadic Green´s functions in the source region

A straightforward approach that does not involve delta-function techniques is used to rigorously derive a generalized electric dyadic Green\´s function which defines uniquely the electric field inside as well as outside the source region. The electric dyadic Green\´s function, unlike the magnetic Green\´s function and the impulse functions of linear circuit theory, requires the specification of two dyadics: the conventional dyadic G^-eoutside its singularity and a source dyadic L^-which is determined solely from the geometry of the "principal volume" chosen to exclude the singularity of G^-e. The source dyadic L^-is characterized mathematically, interpreted physically as a generalized depolarizing dyadic, and evaluated for a number of principal volumes (self-cells) which are commonly used in numerical integration or solution schemes. Discrepancies at the source point among electric dyadic Green\´s functions derived by a number of authors are shown to be explainable and reconcilable merely through the proper choice of the principal volume. Moreover, the ordinary delta-function method, which by itself is shown to be inadequate to extract uniquely the proper electric dyadic Green\´s function in the source region, can be supplemented by a simple procedure to yield unambiguously the correct Green\´s function representation and associated fields.