Scattering of electromagnetic waves by a charged sphere

The problem of scattering of electromagnetic waves of arbitrary frequency by a homogeneous, isotropic sphere which carries excess surface charges can be solved under the assumption that there exists a linear relation between surface current density and electric field. The scattering coefficients so obtained are formally different from those in the standard Mie–Debye theory. Whether or not there is any observable difference between scattering by a charged and otherwise identical uncharged sphere depends upon the value of a phenomenological surface conductivity or, equivalently, surface dielectric function. For sufficiently small particles the effect of surface charges is merely additive, the effective dielectric function is the sum of bulk and surface dielectric functions.