Accurate determination of the electrical resistivity from mutual inductance measurements

摘要

When a conducting specimen is placed inside a coil, the coil impedance changes. For simple coil and specimen geometries, the impedance change can be related to the electrical resistivity of the specimen. This paper describes a variety of methods for the accurate determination of the resistivity of a cylindrical specimen from the measured change in mutual inductance of a cylindrically symmetric coil assembly. The useful range of resistivity extends from about 3nOHgr;sdot;cm to above 100 mgr;OHgr;sdot;cm. Using the calibration methods that are described, 1percnt; absolute accuracy is not difficult to obtain even when using a coil system only five coil diameters in length. When compared with calculations for the corresponding infinite specimen and coil problem, the measurements are in disagreement by much more than 1percnt;. Approximate calculations and numerical estimates show that axial field gradients are responsible for these differences when the specimen is more than about twice as long as the coils, and that end effects in the specimen are responsible for the differences when the specimen is short compared to the coil length. The effect of losses other than those in the specimen being studied has also been investigated extensively. We find that in many important experimental circumstances, the conventional procedure of subtracting coil system losses with the specimen absent from those with specimen present can be seriously in error. For instance , if the tail of a metal Dewar, a vacuum can, or the pole faces of an electromagnet are placed so that they intercept some of the return flux of the primary coil, the system losses may not be additive. This occurs because the magnitude of the return flux depends upon the screening currents in the specimen (and hence on the presence or absence of the specimen). This problem is discussed from both an analytical and experimental point of view. An experimental system having very small background losses is described and numerous results on specimens of different lengths and diameters are presented. It can be shown that a radial conductivity variation of about 50percnt; or more can be determined by making measurements at a few frequencies, but that the results are not very sensitive to the functional form of the conductivity variation.