Excerpt from Tables for the Calculation of the Inductance of Circular Coils of Rectangular Cross Section
Formulas for calculating the inductance of circular coils of rela tively small rectangular cross section, as compared with the mean radius of the coil, have been known for... many years. Of these, that of Perry 2 is empirical and of no great accuracy. Maxwell's 3 for mula replaces the coil by two circular filaments of radii equal to the mean radius of the coil, separated by a distance equal to the geometric mean distance of the points of the rectangular cross section. The inductance of the coil is assumed equal to the mutual inductance of these filaments, multiplied by the square of the num ber of turns. This method gives good results when the cross sec tion is small compared to the mean radius, but fails for cases where the distance between the filaments is so great that their curvature can not be neglected.
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