114
II
INDUCTION IN ROTATING SPHERES
See Fig. 11.
Magnetic
pole above
a rotating
disc.
Thus in this
form as the lines of flow.
$
case the equipotential lines have the same
For very large velocities we have
=
K
2π
(axn
K En
=
d
2π r(p² - n²)
which formula is not applicable at infinity.
The formulæ here developed are illustrated by Fig. 11,
pp. 112 and 113. The assumptions on which the diagrams
are based are the following:-
x
The plate is made of copper (thus = 227,000) and has
a thickness 2 mm. (thus k = 113,500). The distance of the
pole from it is 30 mm. The values of marked give absolute
measure when the strength of the pole is 13,700 mm¹mgr/sec.
In Fig. 11, a and b, p. 112, the velocity of the pole is
5 m/sec (a = 5000); here a represents the phenomenon when
self-induction is neglected, b when it is taken into account.
Fig. 11 c represents the phenomenon for a velocity of
100 m/sec, calculated by means of the formula for large values
of 2walk. It is true that for the value chosen the approxima-
tion is not very close. Fig. 11 d, p. 113, corresponds to an
infinite velocity of the pole. The electric equipotential lines
are also shown in this diagram. The values of the electric
potential marked are in millions of the units employed by us.
The connection between the various states is clearly shown
by the diagrams themselves.
2. A magnetic pole at rest is placed above a rotating
infinite disc. Let the xz-plane be taken so as to pass through
the pole. In addition to xyz we introduce coordinates n 5,
of which the origin is the foot of the perpendicular let fall
from the pole on the disc. Further, let
thus
ૐ =
= x -α,
n =y,
y=2;
a
a
მა
=
a
a
+ &
-
a is the distance of the pole from the axis of rotation; let c be
its distance from the plate. Then
1
x = √ E² + n² + (5+c)²