Impedance of a single-turn coil due to a double-layered sphere with varying properties

This paper presents an analytical solution for the change in impedance in a coil due to the presence of a conducting double-layered sphere symmetrically situated with respect to the coil. In the case where the relative magnetic permeability, μ(r)=r^α, of the outer sphere is a function of the distance r from the center of the sphere, where a is an arbitrary real number, the solution is expressed in the form of a series containing Bessel functions and can be used to compute the change of impedance. Numerical results for the case α=-2 are presented