The general statement of a variable current acting on a neighboring
circuit also applies to the approach or recession of an unvarying
current, and to the cutting of lines of force by a conductor at right
angles thereto. For it is evident that the case of a varying current is
the case of a varying number of lines of force cutting or being cut by
the neighboring conductor. As lines of force always imply a current,
they always imply a direction of such current. The cutting of any lines
of force by a closed conductor always implies a change of position with
reference to all portions of such conductor and to the current and
consequently an induced current or currents in one or the other
direction in the moving conductor.
As the inducing of a current represents energy abstracted from that of
the inducing circuit, the direction of the induced current is determined
by (Lenz's Law) the rule that the new current will increase already
existing resistances or develop new ones to the disturbance of the
inducing field.
In saying that a conductor cutting lines of force at right angles to
itself has a current induced in it, it must be understood that if not at
right angles the right angle component of the direction of the wire acts
in generating the current. The case resolves itself into the number of
lines of force cut at any angle by the moving wire.
The lines of force may be produced by a magnet, permanent or electro.
This introduces no new element. The magnet may be referred, as regards
direction of its lines of force, to its encircling currents, actual or
Ampérian, and the application of the laws just cited will cover all
cases.
Induction, Coefficient of Mutual.
The coefficient of mutual induction of two circuits is the quantity of
magnetic induction passing through either of them per unit current in
the other. (Emtage.) It is also defined as the work which must be done
on either circuit, against the action of unit current in each, to take
it away from its given position to an infinite distance from the other;
and also as the work which would be done by either circuit on the other
in consequence of unit current in each, as the other moves from an
infinite distance to its given position with respect to the other
conductor. It depends on the form, size, and relative position of the
two circuits; and on the magnetic susceptibilities of neighboring
substances.
The ether surrounding two circuits of intensity i' and i" must possess
energy, expressible (Maxwell) as 1/2 L i2 + M i i + 1/2 N i12. It can be
shown that M i i1 in any given position of the two circuits is
numerically equal (1) to the mutual potential energy of the two circuits
(2) to the number of lines of induction, which being due to A, pass from
A through B, or equally being due to B, pass from B through A, and M is
styled the coefficient of mutual induction. (Daniell.)