The mutual inductance of two circular coaxial coils of rectangular section

Abstract

Various formulae have been proposed from time to time for calculating the mutual inductance of coaxial coils. All of them are approximate formulae and in most cases the approximation is closer if the coils are not near each other. The degree of approxi- mation is not, however, shown by the formulae themselves, and it is therefore highly important to critically examine and compare all the formulae available, and to ascertain which are most accurate and what the magnitude of the residual error is likely to be in any given case. A practical question, for example, is to determine what limitations as to size of section, radius, and distance apart must be placed on two coils in order that their mutual inductances may be computed to one part in 50,000. If such coils are to be used in the absolute measurement of resistance, the formulae employed for computing the mutual inductance must be justified beyond question. We propose in this paper to examine these formulae and to compare them by numerous numerical calculations. We shall show which are the more accurate formulae, point out where some of them fail, and shall derive some new expressions more convenient to use than some of those which have heretofore been employed. We shall also give a number of examples to illustrate and test the formulae, and curves to show the relative accuracy of various formulae for par- ticular coils at varying distances. 359