Inverse medium problems for spherical scatterers in the low-frequency region

The interior low-frequency dipole excitation of a spherical scatterer is motivated by various applications, arising mainly in biomedical engineering. In this paper, we investigate the near-field direct and inverse scattering problem corresponding to the interior electromagnetic excitation of a dielectric sphere by a magnetic dipole. The near-field quantity of interest is the secondary electric field at the dipole's location, which is, under the low-frequency assumption, expressed in closed form. Then, this derived low-frequency near-field expansion is utilized in the development of a simple inverse medium scattering algorithm concerning the determination of the sphere's dielectric permittivity.