SCATTERING BY FINITE WIRES

For a conducting wire of finite length illuminated by an incident electromagnetic wave, induced surface current is represented as the sum of a driven term and resonant traveling waves, for which free-space propagation behavior is slightly modified by a perturbation m. Requiring current to vanish at the ends of the wire, both m and the resulting amplitude are obtained for normal incidence by applying Galerkin's method to the resulting trial function. In the Rayleigh limit cross sections are expressed analytically. For wires up to one-half wavelength long, we find equivalence with Tai's variational results [J. Appl. Phys. 23, 909 (1952)]. Beyond this point, the driven term goes over to the infinite cylinder current, as wire length increases. At the same time, for highly conducting wires one finds an explicit formula for m, in which \m - 1\ much less than 1; for moderate conductivity, m reduces to the attenuated propagation behavior found by Sommerfeld [J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941), pp. 524ff] for infinite-length wires.