Abstract
A semi-analytical solution for evaluation of field distributions around the surface of a conductive half space which contains a hidden long crack and excited by a three-dimensional (3D) current-carrying inducing coil at arbitrary frequency is presented. The governing Helmholtz equation is solved in three dimensions by separation of variables. The solution is obtained by developing a two-dimensional (2D) Fourier series model and using exponential functions in the third dimension. To expand all possible field components in the problem, we assume the conductor as a lossy material. The displacement current in the crack mouth is regarded to have a nonzero value accordingly. After imposing boundary conditions and using the mode matching technique, a linear system of AX=B is solved to obtain the unknown coefficients. The accuracy of the proposed modeling technique is demonstrated by comparing our results with those obtained numerically for a 3D inducing coil.
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