II
47
INDUCTION IN ROTATING SPHERES
Similar calculations may be performed for the case of n
negative, where the inducing magnets are inside. They lead
to this result :-
:-
If the inducing potential is
then
R
n+1
Xn
=
-
Y'n'
Y.
=
=
=
Ω; =
Ωρ -
=
-
-
4πR2
ωρ
(2n+1)n h\R
4πR2
n
w/R\n-
Y'
n
(2n+1)n X (2) ""'Y'..
k
4TR(n + 1) w P
n
(2n+1)n (1) 'Y'
4πR
R
W
-
2n+1 h\p
k ρ
=
@
- Ry'
k n
R
n+1
ης
1 @ OY'
n
I'n'
n
n
u =
n k dwx
1 w dy'₂
v =
W =
-
n k dwy
1 waY'
n k dw₂
n
10
=
@R sin e
ƏY
n
до
Of the magnitudes here given, y, u, v, w, o are got from
their preceding values at once by interchanging n with
n - 1.
-
On the solution obtained I make the following remarks:-
1. When a spherical shell of finite thickness rotates under
the influence of the potential Xn (n positive or negative), the
induced currents are
SCIENCE ENGINEERING LE