Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 54

In Section 7-4 we indicated that E and B can be determined from the potentials V and A, which are related by the Lorentz condition, Eq. (7 - 98}, in the time-harmonic case. The vector potential A was introduced through the relation B = x A because of the solenoidal nature of B. In a source-free region, • E = 0, we can define another type of vector potential A., such that E = x A e Assuming harmonic time dependence:
a) Express H in terms of A e
b) Show that A. is a solution of a homogeneous Helmholtz's equation.