Eddy currents in an infinite slab due to an elliptic current excitation

The magnetic flux density and the eddy-current density induced in a conducting plate of finite thickness by an elliptic filamentary current loop parallel to the slab are calculated. The system of coordinates used is the Cartesian one, and as a result, the method can be applied to any filamentary excitation parallel to the slab interface once the excitation is expressed in the Cartesian system of coordinates. The solution of the partial differential equations describing the problem is achieved by 2-D spatial Fourier transformation, and the final inverse transformation is performed by applying the 2-D fast inverse Fourier transform. The displacement current is not neglected, and therefore the method can be applied to low and high excitation frequencies. The method can be easily extended to cover the case of multiple layers, and it can be applied to problems ranging from power applications to eddy-current nondestructive testing.