Foundations for the computation of the inductance of thin-wire loops in the presence of cylindrical cores and shells

摘要

In this paper one finds an analysis which can serve as the basis for computing inductance of thin-wire loops and helices in the presence of cylindrical shells and cores. Computation of inductance involves time-invariant magnetic fields that, in principle, are not influenced by nearby ideal conductors, yet inductance itself plays a role in circuits only in the case of time varying voltages and currents. To obtain a boundary condition needed to solve for the static magnetic field near a perfect conductor due to a time-invariant current, one appeals to a Rayleigh series analysis. With this needed condition in hand, one fashions a Fourier integral representation of the magnetic field due to stationary sources near cylinders and thereby determines inductance of loops near conducting shells and cores. Inductance is measured in the laboratory and the results are compared with those found theoretically.