II
125
INDUCTION IN ROTATING SPHERES
From the above the following table is calculated.
=
In it
T is taken 5000, which corresponds to an electromagnet of
medium strength. The initial velocity is taken to be one turn
(2) per second. The angles described are given in turns.
The relative values hold for every T and every w。
Material.
Jwdt
0
Aluminium
0.14
Iron.
0.16
Silver
0.27
Copper
0.31
German silver
3.90
Graphite
27.2
Conc. sol. of copper sulphate
about 544,000
7. Damping in a galvanometer.
ometer.
Consider a magnet swinging inside a conducting spherical Damping in
shell;
and suppose it to be very small, or to have approxi- a galvan-
mately the form of a uniformly magnetised sphere. If M be
its moment, then in the spherical shell'
Thus
X
M
ρ
sin cos w.
ω Μ
↓ =
= -
sin sin w,
K P
and the heat generated per second is
8π M²²/1 1
W
=
3 K
R
where, as before, denotes the inner and R the outer radius of
the spherical shell.
Let now be the deflection of the needle from its position
of rest, and F its moment of inertia; then its vibrations are
determined by the equation
d² MT
+
dt² F
+2€-
dt
аф
=
0,