QUASI‐STATIC TRANSIENT RESPONSE OF A CONDUCTING PERMEABLE SPHERE

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Abstract
When a conducting body is immersed in a time‐varying magnetic field, eddy currents are induced. These, in turn, produce a secondary magnetic field which may be detected by an observer external to the sphere. It has been demonstrated that a measurement of the external field can be used to estimate the conductivity of the body if certain assumptions are valid. For example, Ward (1953) has shown that the conductivity and permeability of geological core specimens from diamond drill holes may be determined by examining the frequency dependence of the time‐harmonic response of the specimen. In principle, the same information should also be available from the time response of the specimen for a suddenly applied magnetic field (Wait, 1951). In this paper, we wish to discuss the transient solution when a homogeneous conducting sphere is under the influence of a transient magnetic field. Also, as suggested earlier by Wait (1951), the actual time‐domain electromagnetic response of a massive sulfide body should exhibit features akin to this transient solution. Thus, the results should have application in mining geophysics. We consider both a nonpermeable and a permeable sphere, using a different approach for each. Because the former is a special case of the latter, a consistency check is obtained.

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