Some Electromagnetic Equivalence Theorems Unifi ed by a Single Theorem and Generalized to a Nonlinear Case

Abstract

Love's theorem, the induction theorem, and the physical equivalence theorem are combined into a single theorem, and then proven in terms of the previously known electromagnetic principles and theorems. From the proof, the new theorem is seen to be applicable even in the inhomogeneous and nonlinear case. We also suggest some procedures for utilization of the new theorem in practice, for engineers having little experience with the equivalence theorems. We demonstrate that the new theorem not only unifies the conventional equivalence theorems, but is also versatile in obtaining equivalent problems in alternative forms. Some forms of the equivalent problems established in examples do not exist in the literature.