Computation of the electric field within a region of uniform current density

It is commonly accepted that the calculation of the electric field inside a current-carrying region by the Green's dyadic method requires that the normal Green's dyadic be modified to take into account the principal value of the Green's dyadic. For the special case of a uniform current density, commonly encountered in the application of the method of moments when pulse functions are used as sub-sectional basis functions and Dirac delta functions are used as testing functions, the Green's dyadic method can be successfully used to evaluate the electric field inside the current density without invoking the concept of principal values. This result is non-rigorous in the sense that it cannot be generalized for an arbitrary current density and is of interest primarily from a computational standpoint.