Eddy-current induction by an air-cored coil located inside a long cylindrical bolthole in an isotropic conductive medium is examined using a second-order vector potential formalism. Closed-form expressions are presented for (i) the induced electromagnetic fields and currents, and (ii) the change in coil impedance, Δ Z , due to eddy-current induction in the surrounding conductor. In these expressions, the coil characteristics enter via a source function, D s . Two alternative methods for computing D s are described: in one, D s is computed directly, and in the other, D s is computed using a knowledge of the source magnetic flux density at the surface of the hole. The strengths and weaknesses of the two approaches are discussed. The non-axisymmetric case of a cylindrical coil with its axis perpendicular to the hole axis is examined in detail because of its significance in eddy-current non-destructive evaluation using bolthole probes. An explicit closed-form expression for Δ Z in terms of the coil and bolthole parameters is derived for this important geometry. The validity of the theoretical calculations was tested by comparing the theoretical results with experimental measurements of Δ Z as a function of frequency for a series of air-cored coils inside 10.0 and 6.4 mm diameter boltholes in Al alloy specimens. The theoretical and experimental results are in excellent agreement.
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Burke et al. (2004) studied this question.
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