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

 

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

$\log {\frac {R}{c}}=-{\frac {1}{4}}$,

and $\log {\frac {8a}{c}}={\frac {13}{4}}$,

or, the mean radius of the coil should be $3.22$ 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 $3.7$ times the side of the square section.

 

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