SELF-INDUCTION OF A COIL. 



As the product Jw represents the total number of windings, 

 if we put 



<Jl.^ = lllll.rdxdydx'dy', 

 we get 



(57) L 



The coefficient of self-induction L of the coil is then equal to 

 the product by ?z 2 of the coefficient of mutual induction of two 

 concentric circles of radii a and + R 2 , or of two equal circles 

 having as radius the mean radius of the coil, and placed at a dis- 

 tance R 2 , which is the geometrical mean distance of the surface w. 



781. For a coil with a rectangular section of mean radius a, 

 of breadth 2/^, and depth 2t, the value of the quantity in brackets, 

 which we shall represent by X, is (758) 



2 Tc b b 

 - arc tan - + - arc tan - N 



3L* c 



If we put 



b c~\ i 



- arc tan - N 



c bA 12 



we see that the quantity A, only depends on the ratio m = - of the 



b 



two dimensions b and c, and does not alter when these quantities 

 are interchanged ; we have 



2f 



, = \ 



3i_ 



II 



m arc tan I arc tan m 

 3_ mm 



