Spherical Conducting Shell on Dielectric Induction. 15§ 



Again, (J K' is very small (it is of the order 10 -21 ), hence, 

 unless p is very large, we may neglect \' 2 . Hence in the 

 dielectric 



V 2 P=0, 

 we may therefore assume 



p =(4-*|) x ^> 



where X„ is an arbitrary solid spherical harmonic, so that in 

 the dielectric we must put -»/r n (X/r) = 1, and, consequently, 

 cj) n (\'r)=n + l. 



Therefore in the dielectric 



<^tHx n e^. 



n + 1 dX n 

 tpr dd 



e** J 



> (8) 



The inducing system is in the dielectric inside the shell. 

 Hence in the dielectric inside the shell 



„__«fe±a C x„ + x - _ 1 w i 



vpr i 



(9) 



In the dielectric outside the shell 



n(n + l) g 



ipr 



""l, 



(10) 



: e ipt 



w= — - , a e^ 



tpr du J 



where Z_ n -i is an arbitrary solid spherical harmonic of 

 degree — n— 1. 



In the conducting shell 



■- - n -^r L * .Mx.*" 



1 *y 



The boundary conditions are (1) that the normal magnetic 

 induction, (2) that the tangential magnetic force is to be 



continuous. The tangential magnetic force = — in the con- 

 ductor, and =« in the dielectric. 



