where B_g is the density of the flux within the air-gap expressed in
C.G.S. lines per square centimetre, L is the active length of the
conductor within the field in centimetres, and V is the velocity of
movement in centimetres per second. Further, the direction in which the
E.M.F. has the above maximum value is along the length of the conductor,
its "sense" being determined by the direction of the movement[5] in
relation to the direction of the field.
The second fundamental equation of the dynamo brings to light its
mechanical side, and rests on H.C. Oersted's discovery of the
interaction of a magnetic field and an electric current. If a straight
electric conductor through which a current is passing be so placed in a
magnetic field that its length is not parallel to the direction of the
lines of flux, it is acted on by a force which will move it, if free, in
a definite direction relatively to the magnet; or if the conductor is
fixed and the magnet is free, the latter will itself move in the
opposite direction. Now in the dynamo the active wires are placed so
that their length is at right angles to the field; hence when they are
rotated and an electric current begins to flow under the E.M.F. which
they induce, a mutual force at once arises between the copper conductors
and the magnet, and the direction of this force must by Lenz's law be
opposed to the direction of the movement. Thus as soon as the disk of
fig. 1 is rotated and its circuit is closed, it experiences a mechanical
pull or drag which must be overcome by the force applied to turn the
disk. While the magnet must be firmly held so as to remain stationary,
the armature must be of such mechanical construction that its wires can
be forcibly driven through the magnetic field against the mutual pull.
This law of electrodynamic action may be quantitatively stated in an
_equation of mechanical force_, analogous to the equation (I.) of
electromotive force, which states the law of electromagnetic induction.
If a conductor of length L cm., carrying a current C amperes, is
immersed in a field of uniform density B_g, and the length of the
conductor is at right angles to the direction of the lines, it is acted
on by a force