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FUNDAMENTAL EQUATIONS OF ELECTROMAGNETICS
normally to that force; but even with very powerful electro-
static forces these actions will lie at the limits of observation,
and hence it is hopeless to expect to see a ring-magnet set itself
under the action of the weak forces produced by a second ring-
magnet when the moments of both are diminishing.
But our premises permit of our drawing further inferences
It is known that a knowledge of the mutual electromagnetic
potential of two currents, together with the principle of the
conservation of energy, enables us to predict the existence and
absolute value of the inductive action. Similar conclusions
may be drawn for magnetic circuits (rings of soft iron). A
determinate expenditure of work is necessary to maintain in
such a circuit a magnetic current, which we may suppose to
be alternating. If the amount of this work were the same,
whether the magnet were at rest free from any electrical
influence, or did work in moving through the electric field,
nothing could be simpler than the infinite production of work
from this motion. Hence such an independence is impossible.
The work done must depend on the nature and velocity of the
circuit's motion and on the changes in the electric field; and
thus the magnetic (magnetomotive) force which produces this
uniform current must also depend upon these circumstances.
This may be expressed by saying that a magnetic force,
produced by the motion and the changes in the field, is super-
imposed upon the magnetic forces due to other causes; this
added force we may describe as induced. Its magnitude is
given by the condition that for any displacement whatever of
the circuit the external work done in this displacement must
be compensated by an equal additional amount of work which
in consequence of the displacement must be done in the
circuit. This reasoning is in form the same as that used to
deduce the inductive actions in electric circuits; and since
also the forces between magnetic circuits are of the same form
as those between electric circuits, the final result must in form
be the same in both cases. In the laws of electric induction
we need only interchange the words " electric" and " magnetic"
throughout in order to obtain the inductive actions in
magnetic circuits. Thus we find that a plane magnetic
circuit, e.g., a plane ring of soft iron, whose plane is perpen-
dicular to the lines of force in an electric field, is traversed by