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 cons idered where the conductivity and relative magnetic permeability of the out er spherical layer are functions of the distance rho from the sphere's cent er. The change in impedance of the coil is obtained in terms of a series co ntaining Bessel functions. Computational impedance results are presented fo r different values of the parameters of the problem and the exact conductiv ity and permeability profiles are given diagrammatically for comparison wit h the impedance results.