96
H
INDUCTION IN ROTATING SPHERES
II
and hence
e very
large.
2n+1
Y = 。 + 1 + 1 14π0 ( 1 − ( 2 ) 2 +¹) vo
2n+1
Απθ
-
Thus the current intensity is unaltered at the inner surface
of the spherical shell; in other portions it is always increased
when is positive. The increase is directly proportional to 0.
In diamagnetic spheres the intensity is everywhere less than in
neutral ones. The rotation of magnetic spheres absorbs more
work, that of diamagnetic ones less work than that of neutral
ones.
2. Let be very great and e not nearly equal to unity.
Then we have
A =
=
2n+1
4π0n(1 − €²²+¹)'
-
2n+1
2n+1
B =
4π0(n + 1)(1 − €²n+1)'
-
and hence
Thin spher-
ical shells.
2n+1
1
2n+1
n
-
R
2n+14o.
Thus the current in the innermost layer is here zero:
thence it increases rapidly outwards and becomes (2n+1)/n
times as great at the outer surface as for the neutral sphere.
If is at all large the increase of current is almost independent
of its absolute value.
3. Let e be infinitely nearly equal to unity.
Then
Thus
A =
=
(2n+1)(1 + 4π0) — 4π0n
B
=
-
(2n+1)(1 +4π0)
Απθη
(2n+1)(1 + 4π0)
y = Yo.
In infinitely thin spherical shells the magnetic perme-