In Example 7.3.2, a three-dimensional dipole current source drives circulating currents through a…
In Example 7.3.2, a three-dimensional dipole current source drives circulating currents through a uniformly conducting material. This source is so slowly varying with time that time rates of change have a negligible effect. Consider first the power flow as pictured in terms of the Poynting flux density, (3).
(a) Show that
(b) Show that
(c) Using these results, show that (11.1.3) is indeed satisfied.
(d) Now, using the alternative EQS power theorem, evaluate S as given by (23) and again show that (11.1.3) is satisfied.
(e) Observe that the latter evaluation is much simpler to carry out and that the latter power flux density is easier to picture.