XVII
275
FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
1. Suppose a ring-magnet, whose cross-section we shall
for simplicity take as small compared with its other dimen-
sions, to lose its magnetism. Then it will exert a force on all
electricity in its neighbourhood which causes this electricity
to circulate round the body of the magnet. The magnitude
of this force is proportional to the rate of loss of magnetisa-
tion, and may be constant during a short but finite time, if
during this time the magnetisation diminishes at a constant
rate. The distribution of force in space is precisely the same
as that which would be produced by a current flowing in the
body of the magnet. Like the latter the electric force con-
sidered has a potential which is many-valued, and, apart from
its multiplicity, is the same as that due to an electric double
layer of uniform moment bounded by the axis of the magnet.
The potential of the ring-magnet on an electric pole can, apart
from its multiplicity, be represented by the potential of the
double layer on the pole; or, taking the multiplicity into
account, it can be represented by the solid angle subtended by
the magnet at the pole, multiplied by a suitable constant.
Now this potential determines the action of the magnet
on the pole as well as of the pole on the magnet. If we have
not a single pole but a whole system of electric charges, the
potential of the diminishing magnetisation on it can be found
by a simple summation. In particular, when the electric
forces which act on the ring-magnet are due, not to electric
charges, but to a second ring-magnet of diminishing moment,
their distribution is the same as if they were due to an electric
double layer. Hence, according to our assumption of the unity
of electric force, interaction occurs between our two ring-
magnets of diminishing moment; and the potential determin-
ing this interaction is the mutual potential of two electric
double layers which are bounded by the bodies of the magnets.
As in electromagnetics the mutual potential of two magnetic
double layers is reduced to an integral to be taken along their
boundaries, so here we can bring into the same form the
potential of the electric layers, that is, of the two magnets of
diminishing moment. We thus find that this potential is the
product of the factor A2 of the rates of diminution of the
1A is, as usual, the reciprocal of the velocity of light. We get this factor
by a quantitative investigation of the case which above is only considered quali
tatively. Cf. in this respect paragraph 2, p. 278.