11
121
INDUCTION IN ROTATING SPHERES
solid
spheres and
Figs. 14 and 15, pp. 122 and 123, are intended to illustrate Rotating
the distribution of current in solid spheres rotating under
the influence of a constant force perpendicular to the axis of constant
rotation.
force.
Here the closed circuits are all circles whose planes are
parallel to the axis of rotation. Hence if we know the
current-density in the equatorial plane it is very easy to deter-
mine it at all other points. But in our case u = 0, v = 0 in See Figs.
the xy-plane, and thus the current-density w. The diagrams 14 and 15.
represent the density of the current in the plane in question
by means of the curves
w = const.
=3
The values of w marked give absolute values when the
influencing force
T= 289
mgr
mnm sec
The size of the spheres is that drawn (R = 50 mm.).
In Fig. 14 a copper sphere is illustrated making five
turns a second (in a neglecting self-induction).
In Fig. 15 a the same sphere is illustrated when making
fifty turns a second.
Fig. 15 b shows the currents in an iron sphere making five
turns a second. Here the resistance of iron is taken to be six
times that of copper, and 470 200. We see that even with
the very moderate speed chosen an approximate representation
could not be obtained if we neglected self-induction.
=
magnet.
6. There is a well-known experiment in which a conduct- Stoppage of
rotating
ing sphere rotating between the poles of an electromagnet is spheres by
brought to rest by suddenly exciting the latter. The theory electro-
of this experiment is very simple if we assume the magnetic
field to be uniform, neglect self-induction, and at every instant
treat the currents as steady. If T be the magnetic force
parallel to Ox, the external potential is
x= - Tp sin 0 cos w;
thus
¥
=
W
2K
-Tp² sin 0 sin w,