COIL OF MAXIMUM SELF-INDUCTION. 



153 



It will be seen that a given /^ only depends on the ratio - = m. 

 We might therefore calculate it by means of the following table : 



The value of the coefficient of induction of the coil with a 

 rectangular channel will then be obtained by the formula* 



(58) L = 



783. COIL OF MAXIMUM SELF-INDUCTION. We may solve the 

 following problem as an application : Given a wire, as well as 

 the section of the channel which should be similar to itself, to 

 find the conditions which make the coefficient of self-induction a 

 maximum. The geometrical mean distance R 2 varies in the linear 

 dimensions of the section of the channel ; the number n\ of windings 

 for unit surface being the same, the total number of windings varies 

 as the square of these dimensions. 



As, on the other hand, the total length of the wire is constant, 

 we have the equations of condition 



2-iran = const. , 



which give 



dn 



da 



n R 9 a 



* STEFAN. Sitzungsberichte der Kaiserl. Akad. der Wissensch. Vol. LXXXVIII., 

 p. 201. 1883. 



