Instead of these
ence is now given
to forms similar
to the overload
in the preceding
paragraph, the switch being thrown open by a compressed spring
when the current falls below a certain minimum.
At first sight it is not clear why an underload switch is needed.
The following is an example of its use. Fig. 193 represents a
storage battery B being charged by current from a generator G
through an underload switch S. It was shown in Par. 245 that
in order to drive a current through the battery, the E. M. F. of
the generator should be about ten per cent greater than that of
the battery. Suppose that by some accident during the charging,
such as the belt slipping, the generator should slow down or
should stop. The moment the E. M. F. of the generator falls
below that of the battery, the battery would at once begin to
discharge back, and the resistance of the generator being very
small, the discharge would amount to a short circuit. However,
before a current can be reversed it must die down and pass through
zero, therefore, before the battery could discharge, the underload
switch would trip and thus protect it.
416. Faraday's Discovery of Induction. In Fig. 194, C is a
hollow cylindrical coil of wire connected in circuit with a galva-
nometer G, and M is a magnet held above the coil. If the magnet
be quickly thrust into the coil, the galvanometer needle will be
deflected indicating a current in (7, but the deflection is only
momentary and if the magnet after insertion be held motionless,
the needle will at once return to its zero position. If, after the
needle has come to rest, the magnet be quickly withdrawn from
the coil, the galvanometer will again indicate a momentary
current but in this case in a direction opposite to that produced by
the insertion of the magnet. The more rapidly the magnet is
inserted or withdrawn, the greater the momentary current as
indicated by the greater deflection of the galvanometer needle.
If the magnet be reversed end for end, the currents will likewise
be reversed. Finally, if the magnet be held motionless and the
ELEMENTS OF ELECTRICITY.
coil be moved, the same results are obtained, that is, the motion
of the magnet and coil need only be relative.
These facts were discovered by Faraday in 1831. Their
importance can hardly be overestimated since they are the basis
of nine-tenths of the present commercial production of electricity.
The currents produced in the coil by these movements are said
to be induced and the phenomenon is called induction.
If there be a break in the circuit of the coil there will be an
induced E. M. F. but no current, and, to avoid repetition, it is
to be borne in mind hereafter that whenever reference is made to
induced E. M. F. there will also be an induced current in the same
direction, provided the circuit be complete.
We have already seen (Par. 403) how a magnet may be pro-
duced by the electric current; the above shows the reverse proc-
ess, the production of an electric current by means of a magnet.
It must, however, be noted that in the production of a magnet by
means of a current there is an expenditure of electrical energy,
while in the production of a current by means of a magnet there
is no loss of magnetism and the magnet suffers no diminution in
strength. More physical energy is required to move the magnet
or the coil relative to each other than is required if a soft iron
bar of equal weight be substituted for the magnet, and this extra
energy is the source of the electrical energy.
417. Faraday's Second Discovery. Since inserting into the
coil an unmagnetized bar of iron or steel, otherwise exactly similar
to the magnet, produces no effect, it follows that the current must
have been produced, not by the movement of the magnet alone
but by the movement of the field surrounding the magnet. Since
this field consists of space traversed by lines of force, we may state
that if lines of force are thrust into or withdrawn from a circuit,
an E. M. F. is induced in the circuit. It is not necessary that the
magnet be actually inserted in the coil provided it be so moved as
to alter the number of lines of force traversing the coil. It follows
logically from the foregoing that induced currents may be pro-
duced by using lines of force produced otherwise than by magnets,
that is, by currents.
In Fig. 195 B represents a battery, P a coil of wire and S a.
second coil near to the first and connected to the galvanometer G.
There is no electrical connection between P and S. With K
closed and a current flowing in P, the galvanometer will indicate
a momentary induced current in S if P be moved nearer to S, and
a momentary current in the opposite direction if P be moved
farther from S. This production of an induced current by vary-
ing the position of a current with reference to a circuit was the
second of Faraday's discoveries in induction. To the coil P he
applied the name primary, and to the coil S, the one in which the
current is induced, the name secondary.
Without varying the position of P and S, a momentary current
is induced in S whenever K is closed, and one in the opposite
direction when K is opened. These are but extreme cases of the
general case above, for to close the key is equivalent to bringing
up a current to P from an infinite distance, and to open the
key is equivalent to removing the current in P to an infinite
In the case of the magnet, induction took place only while the
magnet was moving; so in this case induction takes place only
while the current in the primary is changing, or while the primary
with current flowing is being shifted in position relative to the
418. Inertia of Electro -Magnetic Fields. A physical explana-
tion of induction may be given if the following preliminary con-
ceptions be grasped.
(a) The space embraced by an electric circuit is at any given
time pervaded by n lines of force. If the convention be adopted
that lines in one direction are positive, then those in the opposite
direction must be considered negative and therefore n may have
any value, positive, or negative, or zero.
(b) Positive and negative lines of force neutralize each other, in
other words, a sufficient number of lines of force of one kind may
be introduced into a field of the opposite kind to weaken the field,
or to reduce it to zero, or to reverse it.
ELEMENTS OF ELECTRICITY.
(c) Electro-magnetic fields possess a property which has been
termed electro-magnetic inertia and which is analogous to the
inertia of matter. Inertia is a property of matter by which the
matter resists any change of its state with respect to rest or motion.
Thus, a body at rest resists being put in motion and a body in
motion resists being accelerated, retarded, turned aside, or stop-
ped. This resistance manifests itself only so long as the change
in the state of the body is being made and disappears the instant
the change is accomplished. Electro-magnetic inertia may be
said to be the property by which electro-magnetic fields resist any
change in the number or direction of their lines of force. This
resistance manifests itself as E. M. F. and corresponding current
in the circuit, which current tends to produce lines of force of such
number and kind as to keep the original number constant. Like
the inertia of mass, it reveals itself only while the change in the
number of lines in the field is taking place and vanishes as soon
as the change has taken place.
419. Explanation Applied to Magnet and Coil. To illustrate,
consider the case of the magnet and the hollow coil (Fig. 196).
At the outset, the number of lines in the field of the coil may be
considered zero. If we thrust in the magnet in the direction shown
in the figure, we push in lines of force from above downward.
The current induced in the coil is in such direction as to produce
lines of force upward, that is, tending to neutralize those which
are being inserted and thus keeping the original number in the
field unvaried. Applying the right hand rule (Par. 404), we see
that, looking down into the coil from above, the induced current
will be counter-clockwise.
Had the magnet been reversed and the south pole been inserted
in the coil, the lines of force would have been thrust in in a nega-
tive direction, or pointing upwards, which must be considered as a
decrease in the number in the original field. The induced current
would therefore have been in such direction as to send lines of
force downward, that is, viewed from above, it must have been
Upon withdrawing the magnet in the first case, we decrease the
number of lines embraced by the coil. The induced current is in
such direction as to compensate for this withdrawal by producing
lines running downward, hence, looking at the coil from above,
the current is clockwise.
Similarly, withdrawing the magnet which had been inserted
south end foremost produces a counter-clockwise induced current.
420. Explanation Applied to Two Coils. Consider the case of
the two coils as described in Par. 417. Upon closing the key (Fig.
197) the current flows around P as indicated. This produces in
the coil P lines of force in the direction shown by the large arrow,
and as the two coils are now placed, some of these lines pass
through S thus changing the number of lines in the latter's field.
The current induced in S is in such direction as to produce lines of
force opposed to those coming from P. This current, viewed from
P, is therefore counter-clockwise.
Similarly, when K is opened the effect is to withdraw these
lines of force from S and the current induced in S is in direction to
ELEMENTS OF ELECTRICITY.
produce others to replace those being withdrawn, hence, seen from
P, the current is clockwise.
With the current flowing in P, changes in the position of P with
respect to S vary the number of lines through S and induce cur-
rents in S in accordance with the principles just given.
421. Rule for Direction of Induced E. M. F. A simple rule for
remembering the direction of the induced E. M. F. (and current)
in a coil is the following. Look through the coil in the positive direc-
tion of the lines of force; a decrease in the number enclosed induces a
clockwise E. M. F.; an increase induces a counter-clockwise E. M. F.
422. Right Hand Rule for Direction of Induced E. M. F. There
are certain cases where the beginner may be perplexed as to the
application of the foregoing rule. Thus, the conductor under
consideration may not form a coil but may be a straight piece of
wire, or there may be a coil but its position may be in doubt, only
a portion of it being visible. For example, the coils on the arma-
ture of a dynamo are often interwoven in an intricate manner and
further concealed by a covering of insulating material, yet it may
be necessary to determine the direction of the induced E. M. F.
In such cases the following right hand rule seems to be the sim-
plest. Place the right hand upon the conductor, the thumb point-
ing in the direction of its motion, the palm turned to receive the lines
of force of the field; the extended fingers will indicate the direction of
the induced E. M. F.
In Fig. 198 the conductor AB is moving upward and the direc-
tion of the induced E. M. F. is from A to B.
These two rules are of course perfectly compatible. For ex-
ample, suppose AB (Fig. 199) to be a part of either the coil ABC
or of the coil ABD. If it be ABC, the upward movement will
carry it out of the field, there will be a decrease in the number of
lines embraced and the induced E. M. F. will be clockwise, or from
A to B. If it be ABD, the upward movement will carry it into
the field, there will be an increase in the number of lines embraced
and the induced E. M. F. will be counter-clockwise, or again from
A to B.
If the plane of the coil be moved parallel to the lines of force,
or if the coil be moved parallel to itself in a uniform field, there is
no increase or decrease in the number of lines embraced and con-
sequently no induced E. M. F. This same conclusion may be
328 ELEMENTS OF ELECTRICITY.
derived from Par. 358. To induce E. M. F. there must be an ex-
penditure of energy, but since the number of lines embraced by
the coil is unaltered, there is no such expenditure. From another
point of view it may be considered that in each half of the coil
there is induced an equal E. M. F. but these being in opposite
directions, the resultant E. M. F. is zero.
423. Mechanical Production of Electric Current. Since the
insertion of a magnet into a coil induces a momentary current and
the withdrawal of the magnet induces a momentary current in
the opposite direction, it is possible to construct a machine by
which a reciprocating motion is given to a magnet which alter-
nately enters and recedes from a coil and thus induces an alternat-
ing current in the coil and in its circuit. Such a machine would be
of low efficiency. But we have also seen (Par. 417) that it is not
necessary to actually insert the magnet into the coil provided it
be so moved as to vary the number of lines of force through the
coil. For example, it could be swept across the mouth of the coil.
This is the basis of the construction of modern machines for gen-
erating electric current. A number of coils are fixed radially upon
the outer circumference of a circle which rotates within a larger
circle upon whose inner circumference are attached magnets, or
they may interchange places and the magnets may rotate and the
coils remain fixed. As the coils and the magnets sweep by each
other at high speed, alternating currents are induced in the coils
and are drawn off and utilized. Such machines are called gener-
ators and are explained in detail later on.
424. Cutting Lines of Force. Electro-motive force is induced
by varying the number of lines of force embraced by a circuit. A
line of force is a closed curve. A circuit is also a closed figure.
Therefore, like two links of a chain, in order that a line of force
may be inserted into or withdrawn from a circuit, one or the other
must be cut and it is usually the line of force. Hence, on account
of the conciseness of the expression, it is convenient and custom-
ary to speak of the E. M. F. generated by "cutting lines of force."
It must, however, be remembered that, as was shown in Par. 422,
in speaking thus we mean by the number cut the number by which
the original field embraced by the circuit has been increased or
decreased, for when a circuit is moved parallel to itself across a
uniform field, there are certainly lines cut, but since the original
number embraced is unvaried, there is no E. M. F. induced.
425. Relation Between Rate of Cutting of Lines of Force and
the Resulting E. M. F. In Par. 416 it was shown that the more
rapidly the field embraced by the coil is varied, the greater is the
induced E. M. F. The relation between the induced E. M. F. and
the rate of cutting of lines of force may be deduced as follows.
Let EG and DF, Fig. 200, represent two parallel metal rails con-
nected across DE and embracing between them a uniform field
whose positive direction is upward. Let AB be a wire resting
across these rails. If this wire be slid along towards DE, there
will be induced a current I which will flow around the enclosed
rectangle in the direction ABED. If the movement of the wire
and the resulting flow of current continue for a time dt, the total
quantity of electricity which is moved around the circuit is
Q = I.dt, whence / =Q/dt. If during this time the number of lines
of force embraced by the rectangle be decreased by d N, the work
done (which has resulted in moving these Q units around the cir-
cuit) is (Par. 358) W = I.dN.
Substituting in this the expression for / above, we have
The E. M. F. induced in the circuit being E, if the circuit be cut
at any point there will be a difference of potential E between the
opposite sides of the resulting gap. In Par. 72 it was shown that
the difference of potential between two points is measured by the
work expended in moving a unit quantity of electricity from one
point to the other. Since, from the above, it required an expendi-
ture of Q . d N/dt ergs to move Q units through this difference of
potential, to move one unit requires dN /dt ergs, hence
or the induced E. M. F. varies
directly with the rate of cutting of the lines of force.
330 ELEMENTS OF ELECTRICITY.
Had the coil consisted of n turns, the work done would have been
W=Q.n.dN/dt (Par. 358) and hence
E = n '-dt
or the induced E. M. F. also
varies directly with the number of turns in the coil.
It is a simple matter to confirm experimentally the foregoing
426. Absolute Electro -Magnetic Unit of E. M. F. If a coil
embraces N' lines of force and after an interval t embraces N",
the average E. M. F. generated is
If N f N" be positive, there has been a decrease in the number
of lines embraced and the induced E. M. F. is positive or clockwise.
If it be negative, the induced E. M. F. is negative or counter-clock-
If in the above expression N' N" be unity and t be one
second, E becomes unity, whence the absolute electro-magnetic
unit of E. M. F. is defined as that E. M. F. induced by cutting one
line of force per second.
427. The Practical Unit of E. M. P., the Volt. The absolute
unit of E. M. F. is entirely too small for practical purposes, and
even a unit corresponding to the E. M. F. produced by the cutting
of one million lines per second is extremely small. In deciding
upon a practical unit, the Paris Congress of Electricians in 1881
might have taken the E. M. F. produced by cutting one million,
or ten million, or one hundred million, or even one billion lines of
force per second, but in this selection they were probably guided
by the following considerations. Before the adoption of a unit of
E. M. F,, the need for such a unit had been felt and it was quite the
custom to take as an every-day standard of comparison the E. M.
F. of a Daniell cell, the most constant cell then in general use.
In the older books we frequently find E. M. F. specified in terms
of that of so many Daniell cells. To disturb these conceptions
as little as possible, the practical unit was selected as that one
which most nearly approximated to the E. M. F. of a Daniell
cell. The practical unit of electro-motive force, the volt, is there-
fore defined as the E. M. F. produced by cutting one hundred million
(10 8 ) lines of force per second. The volt is therefore equal to 10 8
absolute units of E. M. F. The average E. M. F. of a Daniell
cell is 1.07 volt (Par. 206).
If in Ohm's law, I = E/R, we substitute for I its value in
absolute units /XlO- 1 , and for E its value #Xl0 8 , we see that
for R we must put R XlO 9 , therefore, the ohm is 10 9 absolute units
428. Eddy Currents. In the preceding paragraphs 'we have
considered currents induced in coils when the flux embraced by
the coils is varied. The phenomenon of induction is still more
general and whatever the shape of a conductor, that is, whether it
be a sphere, or a plate, or an irregular lump, currents are induced
in it whenever there is an increase or decrease in the number of
lines of force penetrating the body.
In 1824 Gambey observed that a compass needle set to oscillat-
ing above a sheet of copper came to rest much more quickly than
when placed above a wooden board. This observation was in-
vestigated by Arago who made the additional discovery that a
disc of copper rotated either above or below a needle produces a
deflection of the needle in the direction of the rotation, and if
rotated rapidly enough would cause the needle also to take up a
motion of rotation. This experiment is noteworthy since the
endeavor to account for the movement of the needle led Faraday
to the discovery of induction as outlined in paragraphs 416 and
The movement of the needle may be explained as follows: NS,
Fig. 201, represents a needle suspended above a copper disc which
latter is caused to rotate in a clockwise direction. Consider at
any one instant a strip AB along the diameter of the disc and
332 ELEMENTS OF ELECTRICITY.
parallel to the needle above. The lines of force from the north end
of the needle radiating in all directions, some of them penetrate
the disc. The strip A B is therefore a conductor moving across a
magnetic field and application to each half of AB of the right
hand rule for direction of induced currents (Par. 422) shows that
a current flows from B to A, returning by the right and left as
shown by the broken lines. But, such a current will, in accord-
ance with Oerstedt's rule (Par. 345), cause the north pole of the
needle to move off in a clockwise direction.
Such induced currents flowing around through the mass of the
conductor and returning upon themselves, are, from analogy with
the circular whirls produced in running streams, called eddy
Reflection will show that if the copper plate in the above experi-
ment be suspended by a thread and the needle be rotated just
below it, the plate will take up a motion of rotation in the same
direction. On account of the feebleness of the needle, it is custom-
ary, in showing this fact experimentally, to employ an electro-
magnet. The principle involved in these experiments is applied
in the induction motor, a machine to be described later.
429. Foucault's Experiments. Foucault arranged a copper disc
to rotate like a circular saw between the poles of an electro-magnet.
When the current was off, the only energy required to rotate the
disc was that to overcome the friction of its bearings, but as soon
as the cores were magnetized, resistance to the turning was experi-
enced. If, in spite of the resistance, the disc was forced to rotate,
it rapidly grew hot. Foucault showed that this heating was due
to the circulation of the eddy currents in the copper. If narrow
radial slits were sawed in the disc, thus interrupting the paths of
these circular currents, the resistance to turning and the accom-
panying heating effect disappeared. On account of these experi-
ments, eddy currents are often spoken of as Foucault's currents,
but the two names are synonymous.
In order to produce an electric current there must be an expendi-
ture of energy. This heating effect therefore represents waste
energy and is of much importance in any electrical apparatus in
which the flux is frequently varied, such as electro-magnets,
transformers and electric generators and motors, especially those
employing alternating currents. To avoid this loss of energy,
and also to avoid excessive heating, the cores of electro-magnets
are sometimes made of bundles of soft-iron wires, and the cores of
transformers and of the field magnets and armatures of electric
machines are laminated, or built up of many thin sheets of soft
iron, the principle being that since the eddy currents flow in closed
curves whose planes are perpendicular to the lines of force of the
core, they may be checked if the cores be split up by planes parallel
to the lines of force.
430. Lenz's Law. If a copper cylinder be suspended by a thread
so as to hang between the poles of an electro-magnet, and if this
thread be twisted and then released, the cylinder by its weight
will cause the thread to untwist and, if the current be turned
off, will rotate rapidly. If now the current be turned on, the
rotation will be instantly checked as if an invisible brake had
The principle involved in this phenomenon was given by Lenz
in the form of a general law to the effect that the currents induced
by moving a conductor in a magnetic field are of such direction that
their reaction tends to stop the movement which produces them.
The following illustration will make this clear. Fig. 202 repre-
sents the same arrangement of two rails and a sliding wire as ex-
plained in Par. 425. If A B be pushed in the direction F, a current
will be induced flowing from A to B (Par. 422). AB is therefore
a conductor carrying a current and placed in a magnetic field.
By Par. 352 it is acted upon by a force in the direction R, that is,