Series solution of an eddy-current problem for a sphere with varying conductivity and permeability profiles

Two-parameter families of analytical solutions are found for a single-turn coil symmetrically located above a two-layer sphere. Several cases are considered where the conductivity and relative magnetic permeability of the outer spherical layer are functions of the distance ρ from the sphere´s center. The change in impedance of the coil is obtained in terms of a series containing Bessel functions. Computational impedance results are presented for different values of the parameters of the problem and the exact conductivity and permeability profiles are given diagrammatically for comparison with the impedance results