264: General Solution of the Electromagnetic Relations. 



Again, 



Be B . a sin 6> B 



^— =r — -^ (?> sin 0) — (ar 2 . 



Be 

 The portion o£ ^— involving the constant A has the value 



A d 



— -r- (?'*J) . (h)cos fm&> + e), 

 r dr 



where 



n.n + 1.0 = ^ . (l-fj?^\-n.n + l.Y™dn$ 



??1 npMl 



sin C7 



Thus 



~ = . - . +- . r*J . ! V cos ( W2G) + e ) 



0&> n . n + 1 r ar sin 



— ^ -. . Jsin^-j — sin (m&) + o), . . . (^1) 



V n .n + 1 da 



from which c follows at once. 



The calculation of y and z is now immediate. 

 Writing 



A = n . n + 1 . C» 



(22) 



where (C* D?)" are arbitrary, the components of magnetic 

 force become 



fl=n . n + 1 . (Jr^J . P™(/*) cos (mo> + e£) 



h = _ c: 1 r- * £ (rU) . sin 6 =± cos (mo> + eg) 

 clr K ' dfi 



- m jy^r-hJ . £» sin (7*101 + 8?) 

 sin u 



c = Dlf-tJ . sin 0^cos (mo) + ST) 



- 0? • r- 1 ~ (**J) . -^rz • sin ( ma > + f ") ; * (23) 



ar sm (7 



