Interaction of an Eddy-Current Coil With a Right-Angled Conductive Wedge

A fundamental problem in eddy-current nondestructive evaluation is one of finding the quasi-static electromagnetic field of a cylindrical coil in the vicinity of the edge of a metal block. Although the field can be calculated numerically, an effective analytical approach can potentially provide a better understanding of the edge fields and form the basis of a procedure for solving a whole class of related edge problems including edge structures that contain corner cracks. One can represent the metal block as a conductive quarter space in an unbounded region. However, it has been found that the analysis is more straightforward if the problem domain is truncated in two dimensions. With the domain boundaries far from both the coil and the corner, the truncation has a negligible effect on the solution near the edge but the field calculation becomes much easier. A double Fourier series representation of the field is used, as in the case of a rectangular waveguide problem. The field in the conductor is then matched at the interfaces with that in air to determine the expansion coefficients that are used to represent the field in different parts of the domain. In this way we have derived expressions for the magnetic field, the induced eddy-current density and the coil impedance at arbitrary position and orientation of the coil.

I. Introduction

An important problem in electromagnetism is to determine the quasi-static field of an induction coil in the presence of an electrical conductor. In the case where the conductor is an infinite plate [1], an infinite tube [2] or a uniform sphere [3], exact expressions can be found for the field using analytical procedures starting with the separation of variables. Such results, once found are invaluable since they are part of a timeless, readily accessible resource for the engineering community to use. Analytical solutions are naturally limited in scope but they often have a role in solving part of a more complex problem. For example in the general area of measurement science where accurate numerical results are needed but also in cases where purely numerical models continue to be used [4], [5].