Three-component, two-dimensional analysis of the eddy current diffusion problem

In many electrical engineering applications, one is required to solve the electromagnetic field problem taking into account the effect of induced currents in conducting parts. Since the geometry of the structure is complex and the source distribution, in many cases, is multidimensional, a truly three-dimensional analysis is required to obtain the eddy current distribution in the volume of the conducting structure. This 3D analysis not only is difficult and cumbersome, but also yields a field distribution that is difficult to comprehend. It is, therefore, necessary to construct simpler two-dimensional models as a step in understanding and validating three-dimensional models. Previously, 2D analyses concentrated on a one-component formulation of the eddy current diffusion problem in a 2D geometry. These techniques are inadequate to obtain the eddy current distribution in the presence of a flaw, as occurs in nondestructive evaluation applications. In this paper, a new three-component formulation is presented to represent source current and eddy current fields accurately. The method is validated by comparison with closed form solutions for simplified geometries.