328 
PROFESSOR C. NIVEN ON THE INDUCTION OF ELECTRIC 
Induction of currents in a solid sphere at vest. 
§ 8. When a solid sphere of radius a is influenced by an external magnetic system 
whose potential is fi 0 , we may express the vector potential of the latter by taking 
o J= -(P 0 r), F 0 =0, G 0 
<0*0 TT 
15 do ■ 
sin 6 dp 
dx, dy, dz being now coincident with dr, rd6, rsin 6dp. 
The equations of electromotive force, viz. : 
d(F+ F 0 ) 
dp 
dt 
dr 
d( G + G 0 ) 
dp 
dt 
rdd 
d {H + H 0 ) 
dp 
dt 
r sin ddcf) 
}> • 
and all the conditions of the problem may be satisfied by taking 
p= 0, F=0, G= 
dP _ dP 
sin ddcf)’ dd 
d<$> 
U = (), V— 
4tt<P= — V 2 P 
sin 6dp’ dd 
y 
P satisfies the characteristic equation 
01 
more fully. 
a o-r> dP 
S v ' p =^’ 
,ZT 2rfP 1 df. <fP\ 1 .;’l' df 
<W“ P r irhsiii# <y snl °<w) + r-sm 2 e d^r~ a- dt 1 
• (50) 
(51) 
(52) 
(53) 
outside the sphere P satisfies the equation 
V 2 P = 0 ; 
and we must have the further condition that F, G, H and their differential coefficients, 
or (which is the same thing) 
r/P 
P and —. 
dr 
(54) 
