The field of a coil between two parallel metal sheets

Abstract

This paper solves the problem of a circular coil of any radius with its plane parallel to two infinite and perfectly conducting planes separated by any distance. It is shown that if the distance between the planes is less than half a wavelength, then the output of work from the coil is zero; this corresponds to the well-known “cut off property” of the more conventional form of wave guide. The radiation resistance per unit arc of a single-turn coil is found to fluctuate, according to the radius of the coil, between zero and twice the resistance per unit length of a straight wire between the same planes. Equation (12) of the paper gives an exact expression for the field when the sheets are close together, and thus gives the absolute calibration for an “attenuator” of this form: also the parameters are calculated for a current transformer consisting of a pair of concentric circles between metal sheets. The solution is attempted for a single turn surrounding a metal tube (such as a steel mast): this succeeds formally and a numerical solution in any particular case is feasible. It may thus be said to have solved the two extreme cases of a circular girdle round a biconical metal sheet, a problem whose general solution remains very cumbersome so far.A particular form of solution of great practical interest is a coil enclosed in a cylindrical screening-can with closed ends. This solution turns out to be simple, and by its help the extensive experimental work of Mr. A. G. Bogle can now be completed analytically and extended to cover the change of high-frequency resistance of a coil due to enclosing it in a screen.