AND THE LINES OF FORCE OF A ClßCÜLAK CURRENT. 5 



Remembering that 





 



we lind by simple substitution 



^^J±Z^^^A d-^a ,h-^^o'% e (5) 







and 



TT 



/ A r COS 6 dd ,c. 



é^iaxl ^== (6) 







But we easily find that 



IT 



f(a—x cos d)dd __ TV 







whence by (5) 



<p = ^r.-2azf- {a-xcosd)dd ^^,^ 



J (a- + x' — 2ax cos d) AJd? + x^ + z^ —'2ax cos 6 







The above expression gives the solid angle subtended by the disc 

 at point (x, o, z). 



Evidently the coefficient of mutual induction M of two parallel 

 coaxial coils is connected with ^ by the relation 



7r</> = M. (7) 



Consequently, (6) gives 



TT 



,, 4 r cos d dd ,T,/\ 



./ v^a'^ + X' + z'—2 ax cos 6 



