98 PROPERTIES OF CIRCULAR CURRENTS. 



y 



The series converges then whenever the ratio - is smaller than 



a 



unity, for the factor which multiplies the successive powers of 



2 



this ratio tends towards - . 



7T 



741. ACTION OF A COIL AT A GREAT DISTANCE. We shall in 

 like manner consider what the value X becomes when the distance x 

 of the point P from the plane of the coil is very great compared with 

 the radius. We may in this case, in the expression for the action of 

 a circular current, expand the value of u in respect of increasing 



A 



powers of the ratio - . 



We have then 



du 



du_ = i r* 1.3 r 4 1.3.5 r6 J -3-5-7 >' 

 dx~ 2* 2 2.4*4 2.4.6 x 6 2. 4.6.S* 



and consequently 



X = 27rr *\ l 3^^3-5^ 3-5-7^ 



X 3 [ 2 X 2 2.4* 4 2.4.6 X 6 



(40) 



