Low frequency electromagnetic radiation

The field scattered by a dielectric body irradiated by a low frequency electromagnetic wave can be expressed, to a first approximation, in terms of a scattering tensor. Variational principles are obtained for the elements of this tensor. Bounds based on these principles permit estimates of the rate of change of the tensor with dielectric constant and shape. In particular, it is shown that the trace of the tensor is stationary for the sphere among shapes of equal volume. For scatterers possessing rotational symmetry the longitudinal component can be related to the transverse component of the adjugate problem. 1