Quaternion form of the electromagnetic reciprocity theorem

Abstract

In this paper, the general forms of quaternion electromagnetic field mutual energy-momentum equations (QEMF-MEME) and quaternion electromagnetic field energy-momentum reciprocal equations (QEMF-EMRE) in frequency domain are derived based on the quaternion-electromagnetic-field equations. It has been discovered that QEMF- EMRE is a reflection of the electromagnetic interaction between lagging and leading waves. The real and imaginary parts of scalar, the real and imaginary parts of vector of QEMF-EMRE correspond to the Feld-Tai reciprocity theorem, Lorentz reciprocity theorem, and the two sets of momentum reciprocity theorems, respectively. While, QEMF-MEME reflects the electromagnetic interaction of two sets of lagging waves, and its real scalar, imaginary scalar, real-vector, and imaginary-vector parts are the Feld-Tai reciprocal energy theorem, the reciprocal energy theorem, the two sets of reciprocal momentum theorem.