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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.

An analytical model of an axisymmetric eddy current ferrite-cored probe above a multi-layered conducting half-space has been developed using a procedure in which the domain of the problem is truncated radially. This means that solutions can be expressed in the form of generalized Fourier-Bessel series. The expansion coefficients are found by matching the field across the interfaces between the subregions of the problem. Initially, the magnetic vector potential of a simple circular current filament is expanded in a series form. The solution is then modified to accommodate an infinitely long coaxial ferrite core, and the principle of superposition is invoked to derive a coil field from the filament field in the presence of the core. Next, we consider a semi-infinite core and then one of finite length. Finally, the effects of a multi-layered conductor are included. Numerical predictions of probe impedance have been compared with experimental data showing excellent agreement.

Eddy-current induction due to a thin conformable coil wrapped around a long conductive cylinder is examined using a second-order vector potential formalism. Compact closed-form expressions are derived for the self- and mutual impedances of curved rectangular spiral coils (i) in free space and (ii) when wrapped around the surface of the cylindrical rod. The validity of these expressions was tested against the results of a systematic series of experiments using a cylindrical Al-alloy rod and conformable coils manufactured using flexible printed-circuit-board technology. The theoretical expressions were in very good agreement with the experimental measurements. The significance of the results for eddy-current nondestructive inspection using flexible coils and flexible coil arrays is discussed.

The electromagnetic field of a cylindrical eddy current probe coil near the open end of a borehole in a conductor has been calculated analytically accounting for edge effects. Calculations of the coil impedance as a function of position and excitation frequency have been made allowing theoretical results to be compared with experimental measurements. Comparisons have been carried out for special cases in which a cylindrical coil has its axis either perpendicular or parallel to the axis of the hole. In the approach used, the field is expressed in terms of transverse electric and transverse magnetic potentials defined with respect to the axis of the hole. The domain of the problem is truncated in the axial direction in order to express the solution in the form of eigenfunction expansions. The truncation modifies the original unbounded domain problem, but the additional boundaries can be made as remote from the coil as desired so that they have a negligible effect on numerical estimates of the coil field. Th...