AND Tf' LINES OF FORCE OF A CIRCULA-R CURRENT. 



/ 



we find after a^i^P^e calculation, that 



a 



-71 I r^f (I 



2a)i 



~V„K 



~ ,2 '^^ ^ '2^ \ So 3 So ' 



Since So ' *^»'2' ^^'® generally small quantities, the second term 



will be^Gî'y small as compared with the first. Further we notice that 



V a.'^ \ „ — Van 



i\rj a— «1 (a) 



■ 



TV \e '^ + e 



2 [p:^''^^ -.f.—'^i^ 





■q e 



Thus the calculation of the solid angle subtended by a circle can be 



sasily undertaken without the use of special tables. 



§ 6. Evaluation of M or the coefficient of mutual induction of two 

 poaxial coils. — As has already been noticed, J/= const, gives magnetic 

 lines of force about a circular current, or stream lines about a circular 

 vortex ring of infinitely small section. Reverting to (B'), (9), (10), 

 and (11), we find that 



M =4: TT ax 



■{- 



cos d dd 

 ^dr' + x^ + z- — 2 ax cos 6 



=47: ax AJ\a ^ {ii)+B) du (16) 



"s 



Thus the expression for M can be written in either of the 

 following^ forms : — 



or 



M=47r ax-^l'-^-rj, co, ) {B^ 



Wj \ 2 ' 



