A model of eddy-current probes with ferrite cores

A model of a three-dimensional axisymmetric probe coil with a ferrite core in the presence of a conducting half-space (the workpiece) is developed. The half-space is accounted for by computing the appropriate Green's function by using Bessel transforms. Upon introducing equivalent Amperian currents within the core, we derive a volume integral equation, whose unknown is either the magnetic induction field, or induced magnetization, and whose kernel is the Green's function that was previously derived. The integral equation is transformed via the method of moments into a vector-matrix equation, which is then solved using a linear equation solver. This allows the computation of the magnetic induction field within the core, the driving-point impedance of the coil-core combination, and the induced eddy currents within the workpiece.