On the Self-induction of Solenoids of Appreciable Winding Depths
S Butterworth · Proceedings of the Physical Society of London · 1914
The existing formulae for coils of this type - viz., those of Rosa and Cohen - are shown to be inaccurate, the error amounting to one-fifth of 1 per cent. for the best formula when the winding depth is one-tenth the diameter of the coil. For greater winding depths the error is larger. The inaccuracy in Rosa's formula is due to the neglect of curvature in correcting for thickness, while in Cohen's formula the error is due to the approximate method of development. New formulae are developed by methods which are free from such approximations, and which apply to any coil for which the length is greater than twice the diameter, and the winding depth is less than one-tenth the diameter. These formulae are capable of giving eight-figure accuracy. Simplified formulae are also given which are suitable when only four-figure accuracy is required.