II
97
INDUCTION IN ROTATING SPHERES
ability is without effect on the induced currents (though the
magnetisation is not zero, and the magnetic forces in the shell
are altered). It may here be noted that this result holds also
when self-induction is taken into account.
4. Let e = 0, which is the case of a solid sphere. The Solid
sphere.
term with a negative power of p vanishes, and we get
1
A=-
Απθη
1+
2n+1
1+ 4π0
N
1+
Απθ
2n+1
For large values of we have
2n+1
↓
=
n
The quantity 2n+1/n lies between 2 and 3.
Hence in iron spheres the currents are from two to three
times as strong as in a non-magnetic metal of equal resistance;
the heat generated, the work used up, and the damping pro-
duced are from four to nine times as great as in such a metal.
5. Plane plates.
A very thin plane plate may be looked upon as portion of Plane
plates.
a very thin spherical shell, hence for such a one
Y = 4o.
A very thick plate may be regarded as portion of an in-
finitely large solid sphere; since n is to be put very large we
have for such a plate
Ý
=
1+470
2 + 2πθ
In both limiting cases the total current-function remains
unaltered; in the last case for large values of the intensity
is doubled by the permeability.
For medium thicknesses of the plates intermediate values
M. P.
H