Reactance of a Sinusoidally Driven Antenna

This problem is based on the overoptimistic claim in [1] that the reactance of an antenna can be decomposed into capacitive and inductive reactances. Deduction of antenna reactance via so-called complex Poynting theorem (sec. 13.14 of [2], sec. 2.20 of [3]) goes back at least to sec. 5 of [4]. See also chap. 8 of [5]. We consider only media with unit relative permittivity and permeability. For any system in which the charges and currents have time dependence e it is convenient to consider fields as complex vectors, of which only their real parts have physical meaning. For example, the real part of the complex Poynting vector,