Conducting Sphere on Magnetic Induction. 177 



dv 



f 



e-^J n (X/))J n (\/)rfX = 



cos nu . e?u 



^ Jo Vd 2 + p 2 +f 2 + 2pfcosv 



Differentiate the first of these equations with respect to/. 

 Since 



. (19) 

 (20) 



j x<?- Arf J (\p)J 1 (V') (/A - 



_7r Jo 



(d 2 + p 2 +/ 2 + 2,3/ cost;)* 

 Differentiate again with respect to d. 



(21) 



i 



X 2 e~^J () (\p)J l {Xf)d\ 



1 /»* 3d(f+p cosv)dv 

 =r ^) (d 2 + P 2 +f' 2 + 2pfcosv)^ 



(22) 



Differentiate (20) with respect to d. 



(-) 1 



'f 



d . cos nv . dv 



~ 7T J Q (d 2 + /> 2 +/ 2 + 2pfC0Sv)* 



Differentiating again with respect to d. 



X 2 e-^Jn(X/3)J„(X/)^X 



_ (-)* pj- {p 2 +f + 2pf cos v-2d 2 ) cos ww rfv 



7T .'ft 



(23) 



7T Jo (d 2 + p 2 +./ 2 + 2p/co S *;)i 



therefore, for a point in the dielectric just outside the plate, 



; (24) 



27/*/ / . "tt 



T<* = — ±y f cos pt 



) Jo (* 



Sd(f+pcos v) dv 



* + p 2 +f 2 + 2pf cos u)* 

 rf . cos y^y 



{d 2 + p 2 +f 2 + 2pfcos v)* 



>- (25) 



^cos jtf f {p2 +/2 + 2 ^ C0S v ~ 2c?2) cos u dv 



(d 2 + p 2 +f 2 + 2pf cos »)* 



