532 MAGNETIC INDUCTION. 



If S is the section of the cylinder, which we will assume to 

 be circular, I the strength of the current, and n^ the number of 

 turns for unit length, the flow of force or of magnetic induction 

 is equal to 47r 1 IS (495) ; and, when the current is equal to unity, 

 the value of this flow is 



= 471-^8. 



Suppose that ri additional turns of any given diameter are 

 wound on the cylinder, the flow of force of the first circuit 

 traverses ri times the surface of the second ; the coefficient of 

 mutual induction is then 



(49) M = '^=4irXS. 



The same flow traverses the surface of the first circuit n times 

 for unit length, so that the coefficient of self-induction of the 

 solenoid for unit length, is 



(50) L 1 = 1 ^=4ir!S. 



The values found for the coefficients M and Lj are a maximum, 

 for the true flow of force is less than 47r 1 IS, and this flow 

 diminishes as we come near the ends of the solenoid, where it 

 becomes even less than 27r 1 IS. For the magnetic induction in 

 the uniformly magnetised cylinder, which is the equivalent of a 

 solenoid (373), is equal to the resultant of the force qn-nj. parallel 

 to the axis, and of the action of the two terminal layers of uniform 

 densities <r = 1 I, which is in trie contrary direction. But in a 

 section near the positive surface, this surface sends towards the 

 interior a flow of force equal to 2ir 1 IS, to which must be added, 

 in order to obtain the true flow, the portion of the flow from the 

 negative surface which traverses the same edge. 



Suppose that the ri turns in question form a solenoid, concentric 

 with the first and of the same length /. Let us denote by r^ and r^ 

 the two radii, and by n^ and n 2 the number of turns in unit length 

 of each of them. Disregarding the action of the ends, we may write 



M = n% Ig N" = 

 putting 



