46
II
INDUCTION IN ROTATING SPHERES
be the inducing potential, then
Yi
Y₁ =
y.-
n
ωρ
Y'
n
4πR2
(2n + 1) (n + 1) k\R
4πR2
w/R
n+ly!
n
(2n + 1) (n + 1) k
ய R
Y' n
kn+1
4πR W
Ω =
ATTRO (R) "Y".
2n+1k R
Ω.
=
4πRn
w/R
n+ly
(2n + 1) (n + 1) k
Again, from the relations
1 a
au, au
U
=
Y,
4πu,
R მა, др др
and the corresponding ones for V and W, we find
u =
v =
w=
1 dy 1 w JY' n
=
R dwx n + 1 k dwx
1 ay
=
1 w dy'
R dwy n + 1 k dwy
1 ay 1 w dy'
=
Row, n+1k dw,
dw₂
n
n
Lastly, the expression for the electric potential in the
material of the spherical shell may be transformed. Write for
the moment p' = p sin 0, then
$
=
W
n+1
p
2
-
Xn
Əz
nzxn
W
P
p sin eXn
n+1
ae
and at the surface of the shell
@R
ay
φ
-
sin
n
n+1