Impedance of an induction coil at the opening of a borehole in a conductor

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Theodoulidis, Theodoros
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Bowler, John
Professor Emeritus
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Center for Nondestructive Evaluation

The Center for Nondestructive Evaluation at Iowa State has been involved in the use of nondestructive evaluation testing (NDT) technologies to: assess the integrity of a substance, material or structure; assess the criticality of any flaws, and to predict the object’s remaining serviceability. NDT technologies used include ultrasonics and acoustic emissions, electromagnetic technologies, computer tomography, thermal imaging, and others.

In October of 1985 the CNDE was approved by the State Board of Regents after it had received a grant from the National Science Foundation (NSF) as an Industry/University Cooperative Research Center.

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The electromagnetic field of a cylindrical eddy current probe coil near the open end of a borehole in a conductor has been calculated analytically accounting for edge effects. Calculations of the coil impedance as a function of position and excitation frequency have been made allowing theoretical results to be compared with experimental measurements. Comparisons have been carried out for special cases in which a cylindrical coil has its axis either perpendicular or parallel to the axis of the hole. In the approach used, the field is expressed in terms of transverse electric and transverse magnetic potentials defined with respect to the axis of the hole. The domain of the problem is truncated in the axial direction in order to express the solution in the form of eigenfunction expansions. The truncation modifies the original unbounded domain problem, but the additional boundaries can be made as remote from the coil as desired so that they have a negligible effect on numerical estimates of the coil field. The truncated region approach has proved to be accurate and computationally efficient but more significantly, it allows new solutions to be found for problems that are otherwise analytically intractable. The results model eddy current inspections of boreholes including edge effects at the opening of the hole.


The following article appeared in Journal of Applied Physics 103 (2008): 024905 and may be found at

Tue Jan 01 00:00:00 UTC 2008