94
II
INDUCTION IN ROTATING SPHERES
Here Χ denotes the total potential; but this consists—
(a) Of the given external potential of the inducing
magnets.
(b) of the potential x. of the magnetised sphere itself.
This last satisfies the conditions:—
Inside
=
as follows from equation (2) and (4); at the surface-
4πθΝ, = (1 + 4πθ)
охо
-
i
др
- (3x);
(6),
(7),
Self-
where Np is the radial force exerted by the external magnetism
and the induced currents.
In words we may thus express the effect of the magnetis-
ability of the medium :-
The magnetisation firstly alters the internal magnetising
force in the manner shown by the general theory of magnetism,
and secondly increases the effects of the magnetising force in
the ratio 1+ 4π0 : 1. The two effects are opposed, and the
result is that the action is found to be increased in only a
finite degree even for large values of 0.
Let us again, to begin with, neglect self-induction.
induction to be remarked that this is allowable only when
neglected.
It is
4πω(1 + 4πθ
R
K
is very small.
When and R are large, a must be very
small absolutely to satisfy this condition.
If the external potential be
Xn = Ap"Y₂,
the potential of the spherical shell itself may be expressed in
the form
Xe
+5)='
Br2n+1\
C+
p2n+1 Xn›
and the total potential therefore in the form
2n+1
x = (A + B (1) ***) x
Xn⋅