Theory of eddy currents induced by a nonsymmetric coil above a conducting half-space

Abstract

A solution is presented for the boundary value problem posed by a current-carrying coil of arbitrary shape in air above the plane surface of a conductor of semi-infinite extent. Two special cases are also treated: a circularly-symmetric coil at an arbitrary tilt angle with respect to the surface normal, and an infinitesimal coil, a magnetic dipole, also at an arbitrary tilt angle. Numerical results are presented for dipole orientations parallel and perpendicular to the surface.

Calculation of Eddy Current Fields for Coils of Arbitrary Shape

“…3. In that work, it is shown that the components of the current density can be written as derivatives of a Hertz potential.…”

Eddy Current Response to Three-Dimensional Flaws by the Boundary Element Method

“…It should be noted that none of these approximations are essential to the application of the boundary element method; they are introduced only as a way of saving computer time in these illustrative examples. [5], and, when necessary, a two-dimensional generalizat ion of that theory [6]. Figure 3 shows the absolute value of the complex impedance of an absolute probe as a function of probe position; the flaw is located at the center of the pattern and the response shows the expected symmetry for a circular coil over a cubic flaw.…”

“…Our approach makes use of the boundary element method (BEM) [4] for solving the boundary integral form of Maxwell's equations for the current density and tangential magnetic field on the surface of a flaw in a known incident field. Incident field data, i.e., the current density and magnetic field in the material in the absence of a flaw, are provided by analytic solutions [5,6] for simple part geometries, or by an additional boundary element calculation if the part geometry is complex. Probe response is then calculated by means of the reciprocity theorem [7], with receiver field data provided again by analytic or boundary element calculations for the unflawed part.…”

High Sensitivity AC Field Measurement Using Rhombic Inducer

“…The derivation of the FD scalar magnetic potential can be achieved using a technique in [6]. Based on the solution, a computer program has been developed.…”