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 pa.s.s 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 pa.s.sing 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:

[Ill.u.s.tration: 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 pa.s.sing 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}.

[Ill.u.s.tration: FIG. 130.--Experiment ill.u.s.trating 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.

[Ill.u.s.tration: FIG. 131.--Experiment ill.u.s.trating 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 pa.s.s 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 pa.s.s through the ring from right to left, and would therefore _r.e.t.a.r.d_ the growth of the field due to the electromagnet M.]

4. _A decrease in the number of magnetic lines which pa.s.s 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 pa.s.s 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)

Subst.i.tuting (1) in (2)

current = ((n - n')/t)/R or (n - n')/(Rt) (3)

[Ill.u.s.tration: 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.

[Ill.u.s.tration: 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 ill.u.s.trated 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.

[Ill.u.s.tration: 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 a.n.a.logous 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.