Computation of a quasi-static field induced by two long straight parallel wires in a conductor with a rough surface

This paper deals with the computation of the quasi-static electromagnetic field due to an eddy current probe scanning a conductive half-space. Two homogeneous media are separated by a cylindrical metallic surface characterized by an arbitrary aperiodic profile. The eddy current induction problem with a rough surface is rigorously tackled by a semi-analytical approach based on Maxwell's equations written in a non-orthogonal coordinates system adapted to the geometry of the profile. The choice of a two-dimensional eddy current probe (a long coil carrying an alternating current) is carried out in order to simplify the presentation, for the first time, of a specific semi-analytical approach which will be in fine dedicated to the simulation of EC testing of conducting magnetic test pieces of complex shapes without resorting to pure numerical methods.