Impedance changes in a coil due to a nearby small conducting sphere

Abstract

An expression for the impedance change in a coil carrying a low-frequency alternating current due to the presence of a small conducting sphere is derived. The expression is the product of two separate factors: one depends on the properties of the coil via the magnetic induction, and the other depends on the properties of the sphere. As a consequence, the phase of the impedance change depends only on the ratio of the skin depth to the sphere radius. The calculated impedance is found to be in good agreement with experimental results for the specific case of a circular, air-cored coil of rectangular cross section and an aluminium alloy sphere. The possibility of using a small sphere for mapping the magnetic of an alternating magnetic field is described.