RF Engineering for Wireless Networks

Appendix 4 The Lorentz Gauge

1. No Royal Road

In Chapter 5 we showed that ideal dipoles did not couple along their axes. In this appendix we demonstrate that this result is not peculiar to the ideal dipole but is an inevitable consequence of the conservation of charge. To simplify the derivation, we consider only plane waves far from a spatially limited clump of charges and currents. We first demonstrate that the scalar and vector potentials are related to one another: the Lorentz gauge. We then show that as a consequence of the Lorentz gauge, only the transverse part of the vector potential A couples to a distant receiver.

This appendix assumes the reader is familiar with typical vector notations, Gauss’ law (the divergence theorem), the chain ...