Diffraction by an imperfectly conducting right-angled wedge

Abstract

ABSTRACTA new and exact solution is given for the diffraction of the field of an electric line current by an imperfectly conducting wedge of exterior angle . Previous attempts at solving this problem assumed that the solution could be expressed as a series in inverse powers of the conductivity of the wedge, but this approach can only be applied to wedges of exterior angle less than π as the solution obtained is singular at the edge of the wedge for angles exceeding π. It is shown that in the present case no such expansion is uniformly valid; at large distances from the wedge, however, the present solution agrees with that obtained by assuming an expansion in inverse powers of the conductivity, even though this latter solution is singular at the edge, to order (conductivity of the wedge)−1; the next term in the expansion of the present exact solution is O(conductivity). The case of an incident plane wave may be obtained by letting the source tend to infinity.