CHAPTER X
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.
=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.
=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_.
=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:
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}.
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.
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)
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.
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.
=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.