CURRENTS IN INFINITE PLATES AND SPHERICAL SHELLS. 
341 
Infinite solid bounded by plane face. 
§ 16. Let the axis of z be chosen to coincide with the axis of revolution and the 
origin on the face, and revolve along dp, pdp, dz ; 
U = 0, V =cop, W=0 
• (4) 
oj being the angular velocity supposed uniform. 
The components of electromotive force are 
P = 
Q= 
li= 
dp 
“PV-Tp 
dp 
P d 4> 
dp 
° J P a ~dh' 
( 5 ) 
The external magnetic force may be represented by 
0 _ dP 0 r\ _dP 0 _ 
dz ’ pdfi dp ’ ±1 ° _U ’ 
and all the conditions of the problem are satisfied by taking for the vector potential 
of the currents in the solid 
F=~~, G=~ H=0. 
p(t(p dp 
The total magnetic force is the sum of the parts due to the currents in the sheet 
and the external force : it is therefore given by 
a 
_dfi P + P 0 ) _ cd(P + P n ) _1 dj <Z(P + P 0 ) \ 1 d\ P + P 0 ) 
“ dpdz 5 1 pd<j)dz 5 y P dp\P dp / > 2 dp 2 
The currents may be denoted by 
d<4> d<t> 
u = v =Tp’ w=0 ’ 
4tt<P= — V °-P 
( 6 i) 
If we now substitute for P, Q, R their equivalents cru, crv, 0, the second of 
equations (5) becomes 
d<t> dp . . 
