Studies on polarizabilities and scattering behavior of small spherical particles

It is possible to relate the response of a sphere to an applied uniform sta tic electric field with the scattering from a small spherical particle due to plane wave incidence. The limits up to which these relations between the polarizability and the extinction, scattering, and radar cross sections of a sphere are valid in the dynamic range are presented here. From the obser vations it can be concluded that radar cross section is a very good measure in predicting the polarizability. A related aspect studied here is the eva luation of the effective permittivity of a sparse mixture of spherical incl usions using a generalized Maxwell Garnett mixing rule. This is compared wi th extinction of a plane wave by a slab of n spherical inclusions sparsely located. The extinction by such a slab is calculated using the quasistatic approximation to Mie theory, and also using the full Mie theory, as the siz e of the inclusions is increased, The studies have been carried out for bot h lossless and lossy inclusions. The generalized mixing rule was found to b e quite accurate in predicting the value of effective permittivity up to si ze parameters of 0.5 at least for small epsilon(r) of the inclusion.