Formulae and Tables for the Calculation of Mutual and Self-Inductance #268065

A great 'many formula have been given for calculating the mutual and self-inductance of the various cases of electrical circuits occurring in practice. Some Of these formula have subsequently been shown to be wrong, and Of those which are correct and appli cable to any given case there is usually a choice, because of the greater accuracy or greater convenience of one as compared with the others. For the convenience Of those having such calculations to make we have brought together in this paper all the formula with which we are acquainted which are of value in the calculation of mutual and self-inductance, particularly in nonmagnetic circuits where the frequency Of the current is low enough to assure sensibly uniform distribution of current. A considerable number of formula which have been shown to be unreliable or which have been replaced by others that are less complicated or more accurate have been omitted, although in most cases we have given references to such omitted formula. Where several formula are applicable to the same case we have pointed out the especial advantage Of each and indicated which one is best adapted to precision work. In the second part of the paper we give a large number of exam ples to illustrate and test the formula. Some Of these examples are taken from previous papers by the present authors, but many are new. We have given the work in many cases in full to serve as a guide in such calculations in order to make the formula as useful as possible to students and others not familiar with such calcula tions, and also to facilitate the work Of checking up the results by anyone going over the subject. We have been impressed with the advantage Of this in reading the work Of others. In the appendix to the paper are a number of tables that will be found useful in numerical calculations of inductance. In most cases we have given the name Of the author of a formula in connection with the formula. This is not merely for the sake Of historical interest, or to give proper credit to the authors, but also because we have found it helpful to distinguish in this way the various formula instead of denoting each merely by a number. The formula of sections 8 and 9, which are taken largely from a paper by one of the present authors,1 are, however, not so designated, although the authorship Of those that are not new is indicated where known.