The electromagnetic field in conductive slabs and cylinders submitted to a harmonic longitudinal magnetic field

Abstract

The analysis of the induced current distribution in conducting wires subjected to a harmonic axial voltage is important in designing many electrical devices such as transformers and transmission lines. The azimuthal magnetic field induces axial electric currents and therefore the impedance of the wire depends on the excitation frequency. The current density is increasingly confined to a thin layer at the boundary of the wire as the frequency increases. To minimize this effect at higher frequencies it is necessary to enhance the surface-to-volume ratio by using thin high-conductivity wires. The study of induction phenomena in conducting samples subjected to a harmonic longitudinal magnetic field has attracted less attention. The time-varying magnetic flux induces eddy currents, which flow perpendicularly to the axis of the sample. We study the electromagnetic field in samples of simple geometry, making the usual approximations in good conductors. The validity of our calculations extends to several GHz and allows us to propose a method for determining the electrical conductivity by measuring the phase angle of the complex mutual inductance between a primary coil, responsible for the external magnetic field, and a secondary winding around the sample.