Surface currents, scattering, and applications in the Rayleigh region

Extended Maue integral equations for determining the surface magnetic fields and currents are developed and applied for points of discontinuous and continuous surface normal. Methods using the associated integral operators are shown to be useful in obtaining solutions which otherwise might not be tractable. Application is made to evaluate the total surface current on a perfectly conducting sphere for general plane wave incident fields. The dyadic result becomes, at normal incidence, proportional to the incident surface current, which, in all cases of field incidence, has a Rayleigh region limiting value of 3/2. The nature of the dyadic result is examined and the behavior of the limiting current ratio is briefly treated for nonspherical shapes including its deviation from 3/2 for near-spherical shapes.