Low Frequency Electromagnetic Scattering. The Impedance Problem for a Spere

Abstract

We consider the low-frequency scattering problem of a plane electromagnetic wave by a small sphere, of the boundary of which an impedance condition is satisfied. The impedance boundary condition was introduced by Leontovich (1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. Il provides a method to simulate the material properties of the surface of highly absorbing coating layers. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first order while in the far field we derive the leading non-vanishing terms for the scattering amplitude, the scattering and the absorption cross-sections.