ELECTROMAGNETIC INDUCTION
The word _induction_, introduced by Faraday, has various meanings so far
as it relates to electricity. It signifies, in general, phenomena produced
in bodies by the influence of other bodies, having no necessary material
connection with them.
_A body charged with electricity causes or “induces” charges on
neighboring bodies._ The process in this case is called _electrostatic
induction_.
A magnet induces magnetism in neighboring masses of iron or other magnetic
materials by the process of _magnetic induction_.
Again, a moving magnet induces electric currents in neighboring conductors
by the process of _electromagnetic induction_.
=Faraday’s Discovery.=--All dynamos of whatever form, are based upon the
discovery made by Faraday[11] in 1831, which may be stated as follows:
_Electric currents are generated in conductors by moving them in a
magnetic field, so as to cut magnetic lines of force._
=Ques. What does the expression “cut lines of force” mean?=
Ans. A conductor, forming part of an electric circuit, _cuts lines of
force_ when it moves across a magnetic field in such manner as to _alter_
the number of magnetic lines of force which are embraced by the circuit.
It is important to clearly understand the meaning of this
expression, which will be later explained in more detail.
[Illustration: FIG. 126.--Faraday’s dynamo which embodies his discovery in
1831 of _electromagnetic induction_, the principle upon which all dynamos
work, as well as induction coils, transformers, and other electrical
apparatus.]
=Faraday’s Machine.=--After various experiments, Faraday made his “new
electrical machine” as shown in fig. 126. This piece of apparatus is
preserved and was shown in perfect action by Prof. S. P. Thompson in a
lecture delivered April 11th, 1891, after an interval of sixty years.
It consists of a horse shoe magnet and a copper disc attached to
a shaft and supported so as to turn freely. The magnet is so
placed that its inter-polar lines of force traverse the disc
from side to side. There are two copper brushes, one bears
against the shaft, and the other against the circumference of
the disc. A handle serves to rotate the disc in the magnetic
field.
Now, if the north pole of the magnet be nearest the observer and
the disc be rotated clockwise, the current _induced_ in the
circuit will flow out at the brush which touches the
circumference, and return through the brush at the shaft.
=Faraday’s Principle.=--The principle deduced from Faraday’s experiment
may be stated as follows:
_When a conducting circuit is moved in a magnetic field so as to alter the
number of lines of force passing through it, a current is induced therein,
in a direction at right angles to the direction of the motion, and at
right angles also to the direction of the lines of force, and to the right
of the lines of force, as viewed from the point from which the motion
originated._
Faraday’s principle may be extended as follows to cover all cases of
electromagnetic induction:
_When a conducting circuit is moved in a magnetic field, so as to alter
the number of lines of force passing through it, or when the strength of
the field is varied so as to either increase or decrease the number of
lines of force passing through the circuit, a current is induced therein
which lasts only during the interval of change in the number of lines of
force embraced by the circuit._
=Ques. Explain just what happens when a current is induced by
electromagnetic induction.=
Ans. In order to induce an electromotive force by moving a conductor
across a uniform magnetic field, it is necessary that the conductor, in
its motion, should so cut the magnetic lines as to alter the number of
lines of force that pass through the circuit of which the moving conductor
forms a part.
=Ques. What is the proper name for a “conductor” which moves across the
magnetic field?=
Ans. An _inductor_, because it is that part of the electric circuit in
which induction takes place.
In the case of a dynamo, an inductor may be either a copper wire
or copper bar.
=Ques. How may a conducting circuit be moved across a magnetic field
without having a current induced therein?=
Ans. If a conducting circuit--a wire ring or single coil, for example--be
moved in a uniform magnetic field, as shown in fig. 127, so that only the
same number of lines of force pass through it, no current will be
generated, for since the coil is moved by a motion of translation to
another part of the field, as many lines of force will be left behind as
are gained in advancing from its first to its second position.
[Illustration: FIG. 127.--Electromagnetic induction: In order to induce a
current by electromagnetic induction, a conductor must be so moved through
a magnetic field _that the number of lines of force passing through it
(that is, embraced) are altered_. If a coil be given a simple motion of
translation in a uniform magnetic field as indicated in the figure, no
current will be induced _because the number of lines of force passing
through it are not changed_, that is, during the movement as many lines
are lost as are gained.]
=Ques. Describe another movement by which no current will be induced.=
Ans. If the coil be merely rotated on itself around a central axis, that
is, like a fly wheel rotating around a shaft, the number of lines of force
passing through the coil will not be altered, hence no current will be
generated.
=Ques. State the essential condition for current induction in a uniform
field.=
Ans. The coil in which a current is to be induced, must be tilted in its
motion across the uniform field, or rotated around any axis in its plane
as in fig. 128, _so as to alter the number of lines of force which pass
through it_.
[Illustration: FIG. 128.--Electromagnetic induction: If a coil be given a
motion of rotation from any point within its own plane so that it passes
through a uniform magnetic field, a current will be induced in the coil
_because the number of lines of force passing through it is altered_.]
=Ques. In what direction will the current flow in the coil, fig. 128?=
Ans. The current induced in the coil will flow around it in a clockwise
direction (as observed by looking along the magnetic field in the
direction in which the magnetic lines run) if the effect of the movement
be to diminish the number of lines of force that pass through the coil.
The current will flow in the opposite direction, (counter-clockwise) if
the movement be such as to increase the number of intercepted lines of
force.
=Ques. If the magnetic field be not uniform, as in fig. 129, what will be
the result?=
Ans. The effect of moving the coil by a simple motion of translation from
a dense region of the field to one less dense, or vice versa, will be to
induce a current because in either case, the number of lines of force
passing through the coil is altered.[12]
=Laws of Electromagnetic Induction.=--There are certain laws of
electromagnetic induction which, on account of the importance of the
subject, it is well to carefully consider. The facts presented in the
preceding paragraphs are embodied in the following fundamental laws:
[Illustration: FIG. 129.--Electromagnetic induction: If a coil be given a
simple motion of translation in a non-uniform or variable magnetic field,
a current will be induced in the coil, whether the motion be from the
dense to the less dense region of the field or the reverse, _because the
number of lines of force passing through the coil is altered_.]
1. _To induce a current in a circuit, there must be a relative motion
between the circuit and a magnetic field, of such a kind as to alter the
number of magnetic lines embraced in the circuit._
2. _The electromotive force induced in a circuit is proportional to the
rate of increase or decrease in the number of magnetic lines embraced by
the circuit._
For instance, if _n_ equal the number of magnetic lines embraced
by the circuit at the beginning of the movement, and _n′_ the
number embraced after a very short interval of time t, then
the average induced electromotive force = (n - n′)/t
It would require the cutting of 100,000,000 lines per second to
produce an electromotive force equal to that of one Daniell
cell.
The unit of electromotive force, called the _volt_, is the
electric pressure produced by cutting 100,000,000 lines per
second, usually expressed 10^{8}.
[Illustration: FIG. 130.--Experiment illustrating Lenz’s law which states
that in all cases of electromagnetic induction, _the direction of the
induced current is such as to tend to stop the motion producing it_. In
the experiment, in order to produce the induced current, energy must be
expended in bringing the magnet to the coil and in taking it away, which
is in accordance with the law of conservation of energy.]
3. _By joining in series a number of conductors or coils moving in a
magnetic field, the electromotive forces in the separate parts are added
together._
The reason for this is apparent by considering a coil of wire
having several turns and moving in a magnetic field so as to cut
magnetic lines. During the movement, the lines cut by the first
turn are successively cut by all the other turns of the coil,
hence, the total number of lines cut is equal to the number cut
by a single turn multiplied by the number of turns. The
electromotive forces therefore of the separate turns are added.
EXAMPLE--If a coil of wire of 50 turns cut 100,000 lines in
1/100 of a second, what will be the induced voltage?
The number of lines cut per second per turn of the coil is
100,000 × 100 = 10,000,000.
The total number of lines cut by the coil of 50 turns is
10,000,000 × 50 = 500,000,000.
which will induce a pressure of
500,000,000 ÷ 10^{8} = 5 volts.
[Illustration: FIG. 131.--Experiment illustrating Lenz’s law. If a copper
ring be held in front of an ordinary electromagnet, and the current
circulating through the coil of the magnet be in such a direction as to
magnetize the core as indicated by the letters S N, then as the current
increases in the coil more and more of the lines of force proceeding from
N pass through the ring O O from left to right. While the field is thus
increasing currents will be induced in the copper ring in the direction
indicated by the arrows, such currents tending to set up a field that
would pass through the ring from right to left, and would therefore
_retard_ the growth of the field due to the electromagnet M.]
4. _A decrease in the number of magnetic lines which pass through a
circuit induces a current around the circuit in the positive direction._
The term positive direction is understood to be the direction
along which a free N pole would tend to move.
5. _An increase in the number of magnetic lines which pass through a
circuit induces a current in the negative direction around the circuit._
The reason for the change of direction of the current for
decrease or increase in the number of lines cut, as stated in
the fourth and fifth laws, will be seen by aid of the formula
given under the second law, viz:
electromotive force = (n - n′)/t (1)
but by Ohm’s law
current = electromotive force / resistance or, I = E/R (2)
Substituting (1) in (2)
current = ((n - n′)/t)/R or (n - n′)/(Rt) (3)
[Illustration: FIG. 132.--Fleming’s rule for direction of induced current.
Extend the thumb, forefinger and middle finger of the right hand so that
each will be at right angles to the other two. Place the hand in such
position that the thumb will point in the direction in which the conductor
moves, the forefinger in the direction of the lines of force (N to S),
then will the middle finger point in the direction in which the induced
current flows.]
Now in equation (3) if there be a _decrease_ in the number of
lines cut _n′_ will be less than _n_ hence the current will be
positive (+); again, if the lines _increase_ _n′_ will be greater
than _n_, which will give a minus value, that is, the current
will be negative or in a reverse direction.
6. _The approach and recession of a conductor from a magnet pole will
yield currents alternating in direction._
Since the strength of the field depends on the proximity to the
pole, the approach and recession of a conductor involve an
_increase_ and _decrease_ in the rate of cutting of magnetic
lines, hence a reversal of current.
7. _The more rapid the motion, the higher will be the induced
electromotive force._
In other words, the greater the number of lines cut per unit of
time, the higher will be the voltage.
[Illustration: FIG. 133.--A rule for direction of induced current which,
in some cases, is more conveniently applied than Fleming’s rule: Hold the
thumb, forefinger and remaining fingers of the right hand at right angles
to each other; place the hand in such position that the forefinger points
in the direction of motion of the conductor, the three fingers in the
direction of the lines of force, then will the thumb point in the
direction of the induced current.]
8. _Lenz’s law. The direction of the induced current is always such that
its magnetic field opposes the motion which produces it._
This is illustrated in figs. 130 and 131.
=Rules for Direction of Induced Current.=--There are a number of rules to
quickly determine the direction of an induced current, when the direction
of the lines of force, and motion of the conductor are known. The first
rule here given was devised by Fleming and is very useful. It is sometimes
called the “dynamo rule.”
=Fleming’s Rule.=--_If the forefinger of the right hand be pointed in the
direction of the magnetic lines, and the thumb (at right angles to the
forefinger) be turned in the direction of the motion of the conductor,
then will the middle finger, bent at right angles to both thumb and
forefinger, show the direction of the induced current._
The application of this rule is shown in fig. 132. Here the
right hand is so placed at the north pole of a magnet, that the
forefinger points in the direction of the magnetic lines; the
thumb in the direction of motion of the conductor; the middle
finger pointed at right angles to the thumb and forefinger
indicates the direction of the current induced in the conductor.
[Illustration: FIG. 134.--The palm rule for direction of induced current:
If the palm of the right hand be held against the direction of the lines
of force, the thumb in the direction of the motion, then the fingers will
point in the direction of the induced current.]
=Ampere’s Rule.=--_If a man could swim in a conductor with the current,
then the north seeking_ (+) _pole of a magnetic needle placed directly
ahead of him, will be deflected to the left, while the south seeking_ (-)
_pole will be urged to the right._
For certain particular cases in which a fixed magnet pole acts
on a movable circuit, the following converse to Ampere’s rule
will be found useful: If a man swim in the wire with the
current, and turn so as to look along the direction of the lines
of force of the pole (that is, as the lines of force run, _from_
the pole if it be north seeking, _toward_ the pole if it be
south seeking), then he and the conducting wire with him will be
urged _toward his left_.
=The palm rule.=--_If the palm of the right hand be held facing or against
the lines of force, and the thumb in the direction of the motion, then
will the fingers point in the direction of the induced current._
=Self-induction.=--This term signifies _the property of an electric
current by virtue of which it tends to resist any change of value._
Self-induction is sometimes spoken of as _electromagnetic inertia_, and is
analogous to the mechanical inertia of matter.
It is on account of self-induction of the induced currents in the armature
winding of a dynamo, that sparks appear at the brushes when the latter are
not properly adjusted, hence the importance of clearly understanding the
nature of this peculiar property of the current.
Self-induction is fully explained in the chapter following.