The Calculation of the Mutual Inductance of Circular Filaments in Any Desired Positions

The calculation of the mutual inductance of circular coils whose cross-sectional dimensions are small, compared with their distance apart, depends upon basic formulas for the calculation of the mutual inductance of circular filaments. The case of coaxial circular filaments has been quite thoroughly treated and any desired accuracy is attainable. However, the available formulas for more general cases such as circles with parallel or inclined axes are slowly convergent for considerable ranges of the parameters and for such cases admit of only rough accuracy. The present paper is concerned with providing formulas and tables capable of giving a moderate accuracy, with a moderate amount of labor, even in complicated cases. The tables apply to calculations for equal circles with parallel axes, and to circles of nearly equal radii having inclined axes which intersect at the center of one of the circles. This latter case enters in the design of a variometer composed of two coils of small cross sections; the former is applicable to the calculation of a variometer with coils having eccentric axes. A general formula is derived, which allows of a fairly simple method of computation for any desired case, by the employment of a chart of the flux distribution about a circular filament carrying current. An accuracy of a few parts in a thousand is readily attainable.