AbstractA piecewise homogeneous spherical medium is excited by an external or internal electric dipole with arbitrary location and polarization. The dyadic Green's function of the medium is determined analytically. Then, the vector electric fields and far‐field patterns are obtained. Low‐frequency approximations of the far‐field patterns are subsequently derived, which encode the dipole's locations coordinates and polarization components in the different orders of the associated expansions. This fact enables the establishment of far‐field inverse scattering algorithms referring to the electromagnetic interior or exterior excitation of a small sphere by an arbitrary dipole. Inverse medium and inverse source problems are considered concerning, respectively, the determination of the scatterer's material parameters and the dipole's characteristics. The developed inverse algorithms determine exactly the unknown parameters of problems fulfilling the low‐frequency assumption, which is indeed the case in most relevant applications, like, e.g., in biomedical imaging.