Some Equivalence Theorems of Electromagnetics and Their Application to Radiation Problems

HE usual methods of calculating the power radiated by an electric circuit depend upon a determination of the electromagnetic field from the electric current distribution in the circuit. The best known of these methods consists in integrating the Poynting vector over the surface of an infinite sphere surrounding the circuit. This method has been used exclusively until recent years; to facilitate its application, John R. Carson obtained a compact general formula for the radiated power.1 Another method 2 consists in calculating the work done against the forces of the field in supporting a given current distribution in the circuit. Theoretically either of the two methods is sufficient for solving any radiation problem. Practically, aside from inherent difficulties involved in the calculation of the electric current distribution in the first place, the preliminary integration for determining the field components E and H may be rather complex. Thus in obtaining the power radiated by a semi-infinite pair of perfectly conducting coaxial cylinders this preliminary integration has to be extended over the infinite surfaces of the two conductors. And yet by the Maxwell-Poynting theory, no energy can flow through the walls of the outer cylinders since the electric intensity E and hence the Poynting vector vanish there. Any energy which is radiated away must pass through the open end and it is natural to expect that there must be a method for calculating this energy from the conditions at the open end.