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.