Electromagnetic response of two crossing, infinitely long, thin wires

The electromagnetic coupling of two crossed thin wires of infinite length is considered. Two coupled integral equations are obtained, given in terms of generalized impedance functions, for the spectral currents flowing in each wire. The wires may be in a homogeneous medium or over a half-space. The numerical implementation focuses, however, only on the former. The numerical solution may be obtained by either applying moment or multiple scattering methods. The solution obtained from the method of moments is applicable for any wire spacing. Obversely, the multiple scattering method leads to a convenient matrix series solution, which shows that the coupling between wires is proportional to 1/d ² (where d is the wire separation) plus higher order scattering terms