An equivalence theorem based on the use of electric currents radiating in free space

The most common formulations of the equivalence principle use both electric and magnetic currents radiating in free space or only electric (magnetic) currents radiating in presence of a perfectly magnetic (electric) conductor. In this paper, a formulation is provided for equivalent currents of only electric (magnetic) type as a function of the tangential total fields of the original problem over the equivalence surface. The formulation of these equivalent currents becomes simple for some canonical surfaces, like a plane, a cylinder and a sphere. Explicit expressions of the equivalent electric currents on a spherical surface are provided in terms of spherical wave functions.