Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/344

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312
CIRCULAR CURRENTS.
[706.

If the transverse section of the coil is circular, of radius , then, by Art. 692,

,

and ,

whence
;

or, the mean radius of the coil should be times the radius of the transverse section of the coil in order that such a coil may have the greatest coefficient of self-induction. This result was found by Gauss[1].

If the channel in which the coil is wound has a square transverse section, the mean diameter of the coil should be times the side of the square section.

  1. Werke, Göttingen edition, 1867, vol. v. p. 622.