ACTION OF A CIRCULAR COIL ON THE AXIS. 



79 



to the magnetic induction of a uniformly magnetised cylinder (495), 

 the intensity of magnetisation of which is r 



If a and p are the angles under which we see the extreme wind- 

 ings of the coil, from the point P, and if x is the distance from the 

 point P to the median plane (373), the value of the action G of the 

 bobbin at the point P is 



(l l) G 



^ (COS /? COS a) = 2TTH 



Suppose now that the coil is made up of several layers com- 

 prised within a channel of length 2b and thickness zc^a" -a', the 

 coiling being uniform. 



A layer of thickness dr contains a number n\dr of turns for unit 

 length. Replacing n : by this value in the preceding expression, 

 and integrating between the limits a' and 0", we shall have for the 

 action of the coil 



which gives 



(12) 



At the centre of the bobbin, where x = 0, the action reduces to 



(13) G = 

 We may write 



putting 



277 



= n 

 a. 



