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A model of an axisymmetric probe coil with a cylindrical ferrite core in the presence of a layered conducting half space is developed. The boundary value problem is formulated in terms of the magnetic vector potential, which is expanded in a series of appropriate eigenfunctions. The corresponding eigenvalues are the real roots of a function with the radius and the magnetic permeability of the core as parameters. The unknown coefficients of the series are computed by solving a matrix system, which is formed by applying the usual interface conditions. Expressions are derived for the induced eddy current density and the impedance of the coil. Numerical results for the latter are in good agreement with experimental data. © 2003 American Institute of Physics.