ACTION OF A COIL OUTSIDE THE AXIS. 93 



738. Disregarding terms above the second order, we find for the 

 components X and Y, and their partial differentials in respect of x, 



c) Y 



- 



c) 2 Y tfx 



- = ATT/ , y = - i CTT - 

 ~dx 2 J J b u 6 



The value of X decreases continuously from the plane of the 

 circle to infinity. The first differential which is zero for x = 0, is 

 constantly negative; the position of the point, for which it is a 

 maximum, varies with y, but is always near the plane of the circle. 



The value of Y, which is at first zero for x = 0, attains its 

 maximum for x = - , and then decreases to zero. The second 

 differential is zero for # = 0, and for 4x^ = ^a 2 . This latter value 

 of x corresponds to the maximum negative of the first differential. 



739. ACTION OF A COIL OUTSIDE THE Axis. In order to 

 obtain the action of a regular coil, containing n^ windings for unit 

 length, it will be sufficient to calculate that of a uniformly magnetised 

 cylinder, the intensity of whose magnetisation is n lt or that of two 

 magnetic surfaces A and B of constant densities + n l and - n^ 

 which covered the bases. 



After what has been said (736), the potential V of a circular layer 

 of radius r and density n v at a point P, the co-ordinates of which in 

 respect of the centre of the circle are x and y, has the value 



r- 



