124
II
INDUCTION IN ROTATING SPHERES
and hence the heat generated is (§ 6)
2πR5 T²²
W=
=
15 K
If F be the moment of inertia of the sphere, wo its velocity
at time t = 0, and if it rotate under no external forces, the
equation of its motion is
Fw2 2π T2R5
Fw
+
w2dt
2 15 K
2
30
or
2π T2R5
-t.
15 F
w=w。.ε
experi-
ment.
thus
If q be the mass of 1 cub. cm. of the material,
@=
F
wo. E
=
-
8
159πR³,
T²
-t.
4qk
An analogous law holds when the sphere is set in motion
by the action of rotating magnets.
Spheres of different radii and spherical shells are set in
Matteucci's motion and brought to rest with equal velocity. This in
fact corresponds with an experiment made by Matteucci.¹
The angle which the sphere traverses after excitation of
the electromagnet amounts to
wdt
=
49K
T2
Javit - 108 109-
0
For strongly magnetic spheres we find
wdt = 4qk wo⋅
9T2
1 Wiedemann, Galvanismus, § 878; Lehre von der Elektricität, 1885, vol.
iv. § 386, p. 322.