120
II
INDUCTION IN ROTATING SPHERES
See Fig. 13.
Rotating
spherical
shells.
In Fig. 13 two particular cases are represented. In a the
straight wire cuts the axis of rotation at a sufficient distance
from the disc, and in this case the second term above vanishes.
In b the wire lies in the plane of the disc, and in fact at the
distance from the disc at which it is represented in the figure
itself.
4. If measurements are to be made in experiments on the
rotatory phenomena of induction, very thin spherical shells
should be used; for in their case the calculations can be
easily and exactly performed. The simplest form of experi-
ment would be one in which such a spherical shell is made
Execution to rotate under the influence of a constant force. The
of experi- rotation of the current planes might be demonstrated either
by the effect of the currents on a very small magnet, or better
by a galvanometric method.
ments.
As an example I shall calculate the angle of rotation and
the magnetic moment of the rotating spherical shell.
Suppose the shell to be of copper, let its radius be 50 mm.,
its thickness 2 mm.; since n = 1, i = 1, we have
4π Rw
tan 8:
=
3 k
and if T be the inducing force, we find the moment of the
shell to be
M = T
R³ sin &
2
If q is the number of revolutions per second,
@= 2πq,
and since k = 113,500, we find
tan 80.0116 q.
From the above the following table has been calculated:—
M
q
T
q
T
ΣΙΕ
M
5
3°19'
3,614
80
42°51'
42,500
10
6°27'
7,178
90
46°13'
45,100
20
13°3'
14,110
100
49°13'
47,310
30
19°10'
20,520
200
66°40'
57,360
40
24°53'
26,290
500
80°15'
61,570
50
30°6'
31,340
60
34°49'
35,680
8
90°
62,500
70
39°4'
39,380