Field of Circular Current* 



425 



Hence, writing $ = 7r — 2cj>\ we get by (6) after a little 

 reduction 



Similarly 

 "where 



lY^-^-E + F 



M 



v 2* tan / a 2 + r" -^ ,-A 1 



(12) 



2 „2 



+ r 2 + 2arcos0, 

 a 2 + *-*-2ar cos 0, 



and the modulus k of the elliptic functions is given by 

 F=l-?' 2 2 /;- 1 2 . 



If R and T be the component magnetic forces along and 

 perpendicular to OP (fig. 1), we have 



R=Zsm0+Xcos0=^^E, 



and 

 T=ZGos0-Xsm0=^r 



a 2 cos 20 



cos 6 



I 



E + 



cos^ J J 



(13) 



In rectangular coordinates, we have 

 2i V'laz 



'lL'2 tl J 



Z= |'p^ipL) E + (F _ E )] ) 



(14) 





The magnetic force at P due to the circular current is the resultant of 

 the forces 2/(F— E)/(r 1 cos0) and ±ia~E )\?' 2 acting at right angles 

 to OP and AP respectively. 



If <f> be the angle APB (fig. 2), OP=r, the angle POA = 0, 



and OA = OB = a, we ha\ 



-e AP = / 



andPB = n. 



