Impedance of a Coil in the Vicinity of a Crack

Calculations are presented for the impedance of a coil as it is moved in the vicinity of a v-groove crack in the surface of a metallic slab. The coil is modeled as a pair of parallel wires, oriented parallel to the crack, carrying equal and opposite currents. The inhomogeneous electromagnetic fields in the air above the slab and in the metal are determined by the boundary integral equation (BIE) method. This approach leads to a pair of coupled integral equations for the tangential components of the electric and magnetic field vectors on the surface of the slab containing the crack. The solutions, which are obtained by standard methods of discretization, are valid for arbitrary ratio of crack or coil dimensions to skin depth. Illustrations are presented of the Poynting vector distribution over the surface of the metal, including the crack faces. A plot of the complex impedance is given in the form of a coil scan across the crack.