To keep these movements in mind numerous rules have been suggested, of which the following will be found convenient:
Corkscrew Rule.—If the direction of travel of a right handed corkscrew represent the direction of the current in a straight conductor, the direction of rotation of the corkscrew will represent the direction of the magnetic lines of force.
Ques. What is the effect of a current flowing in a loop of wire?
Ans. If, in figs. 116 and 117, the current flow in the direction indicated by the arrow, the lines for magnetic force are found to surround the loop as shown; all the lines leave on one side of the loop and return on the other; accordingly, a north pole is formed on one side, and a south pole on the other.
Solenoids.—A solenoid consists of a spiral of conducting wire wound cylindrically so that, when an electric current passes through it, its turns are nearly equivalent to a succession of parallel circular circuits, and it acquires magnetic properties similar to those of a bar magnet.
Ques. What is the character of the lines of force of a solenoid in which a current is flowing?
Ans. The lines of force must be thought of as closed loops linked with the current. The conductor conveying the current passes through all the loops of force, and these are, so to speak, threaded or slung on the current-line of flow, as in fig. 116.
Ques. What is the distribution of the lines of force?
Ans. The lines of force form continuous closed curves running through the interior of the coil; they issue from one end and enter into the other end of the coil, as shown in fig. 117.
Ques. What are the properties of a solenoid?
Ans. A solenoid has north and south poles, and in fact possesses all the properties of an ordinary permanent magnet, with the important difference that the magnetism is entirely under control.
Since a solenoid carrying a current attracts and repels by its extremities the poles of a magnet, two such solenoids will attract and repel each other.
Ques. How does the magnetic strength of a solenoid vary?
Ans. It is proportional to the strength of the electric current passing through it.
Ques. On what, besides the current strength, does the magnetizing power of a solenoid depend?
Ans. The magnetic effect or the magnetizing power is proportional to the number of turns of wire composing the coil.
Ques. How may the magnetizing power of a solenoid be increased?
Ans. By inserting in the solenoid an iron core or round bar of soft iron.
Ques. Describe the action of an iron core.
Ans. At first, the presence of an iron core greatly increases the strength of the field; after a time, however, as the strength of the current flowing in the exciting coils is increased, the conductibility of the iron for the lines of force appears to decrease, until a point is eventually reached when the presence of the iron core appears to have no effect in increasing the strength of the field.
Permeability.—Permeability is a measure of the ease with which magnetism passes through any substance. It is defined as: the ratio between the number of lines of force per unit area passing through a magnetizable substance, and the magnetizing force which produces them.
In other words, it is the ratio of flux density to magnetizing force. Permeability is a measure of the ease with which magnetism passes through any substance. The permeability of good soft wrought iron is sometimes 3000 times that of air, varying with the quality of the iron.
Ques. What is the effect of increasing the magnetization?
Ans. The magnetic permeability decreases as the magnetization increases.
Ques. What is magnetic saturation?
Ans. The state of a magnet which has reached the highest degree of magnetization.
A magnet, just after being magnetized, will appear to have a higher degree of magnetism than it is able to retain permanently; that is, it will appear to be super-saturated, since it will support a greater weight immediately after being magnetized than it will after its armature has been once removed.
For all practical purposes, magnetic saturation may be defined as: That point of magnetization where a very large increase in the magnetizing force does not produce any perceptible increase in the magnetization.
From tests it has been shown that permeability increases with the flux density up to a certain point and then decreases, indicating that the iron is approaching a state of saturation.
Magnetomotive Force.—This is a force similar to electromotive force, that is, magnetic pressure. When a coil passes around a core several times, its magnetizing power, or magnetomotive force, (m.m.f.) is proportional both to the strength of the current and to the number of turns in the coil. The product of the current passing through the coil multiplied by the number of turns composing the coil is called the ampere turns.
It is known by experiment that one ampere turn produces 1.2566 units of magnetic pressure, hence:
that is,
The unit of magnetic pressure is the gilbert (named after William Gilbert, the English physicist) and is equal to
Reluctance.—The magnetic pressure (magnetomotive force) acting in a magnetic circuit encounters a certain opposition to the production of a magnetic field, just as electromotive force in an electric circuit encounters opposition to the production of a current. In the magnetic circuit this opposition is called the reluctance; it is simply magnetic resistance and may be defined as: the resistance offered to the magnetic flux by the substance magnetized, being the ratio of the magnetomotive force to the magnetic flux.
The unit of reluctance or magnetic resistance is the oersted (named after Hans Christian Oersted, the Danish physicist) and is defined as: the reluctance offered by a cubic centimetre of vacuum.
Analogy Between Electric and Magnetic Circuits.—The total number of magnetic lines of force, or magnetic flux, produced in any magnetic circuit will depend on the magnetic pressure (m.m.f.) acting on the circuit and the total reluctance of the circuit, just as the current in the electrical circuit depends upon the electrical pressure and the resistance of the circuit.
To make this plain, Ohm’s law states that
expressed in units
The resistance, as already explained, depends on the materials of which the circuit is composed, and their geometrical shape and size.
Similarly, in the magnetic circuit, the total number of magnetic lines produced by a given magnetizing solenoid depends on the magnetic pressure, the material composing the circuit, and its shape and size.
That is,
expressed in units, the equation becomes:
The gilbert is the unit of magnetomotive force, equivalent to the magnetomotive force of .7958 ampere turn.
It should be noted that in the electric circuit resistance causes heat to be generated and therefore energy to be wasted, but in the magnetic circuit reluctance does not involve any similar waste of energy.
Ques. Upon what does the reluctance of a magnetic circuit depend?
Ans. The reluctance is directly proportional to the length of the circuit, and inversely proportional to its cross sectional area.
The reluctance of a magnetic circuit is calculated according to the following equation:
Hysteresis.—The term hysteresis has been given by Ewing to the subject of lag of magnetic effects behind their causes. Hysteresis means to “lag behind,” hence its application to denote the lagging of magnetism, in a magnetic metal, behind the magnetizing flux which produces it.
Ques. What is the cause of hysteresis?
Ans. It is due to the friction between the molecules of iron or other magnetic substance which requires an expenditure of energy to change their positions.
Ques. When do the molecules change their positions?
Ans. Both in the process of magnetization and demagnetization.
Ques. What becomes of the loss of energy due to hysteresis?
Ans. It is converted into heat in changing the positions of the molecules during magnetization and demagnetization.
Ewing gives the value for the energy in ergs dissipated per cubic centimetre, for a complete cycle of doubly reversed strong magnetization for a number of substances as follows:
| Substance | Energy dissipated (ergs) |
| Very soft annealed iron | 9,300 |
| Less soft annealed iron | 16,300 |
| Hard drawn steel wire | 60,000 |
| Annealed steel wire | 70,000 |
| Same steel glass hard | 76,000 |
| Piano steel wire annealed | 94,000 |
| Piano steel wire normal temper | 116,000 |
| Piano steel wire glass hard | 117,000 |
Approximately 28 foot pounds of energy are converted into heat in making a double reversal of strong magnetization in a cubic foot of iron.
Residual Magnetism.—When a mass of iron has once been magnetized, it becomes a difficult matter to entirely remove all traces when the magnetizing agent has been removed, and, as a general rule, a small amount of magnetism is permanently retained by the iron. This is known as residual magnetism, and it varies in amount with the quality of the iron.
Well annealed, pure wrought iron, as a rule, possesses very little residual magnetism, while, on the other hand, wrought iron, which contains a large percentage of impurities, or which has been subjected to some hardening process, such as hammering, rolling, stamping, etc., and cast iron, possess a very large amount of residual magnetism.
Residual magnetism in iron is of great importance in the working of the self-exciting dynamo, and is, indeed, the essential principle of this class of machine.
That is, without residual magnetism in the field magnet core, the dynamo when started would not generate any current unless it received an initial excitation from an external source.
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.
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
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 108.
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
The total number of lines cut by the coil of 50 turns is
which will induce a pressure of
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:
but by Ohm’s law
current = electromotive force / resistance or, I = E/R (2)Substituting (1) in (2)
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.
The induction coil has always been a popular piece of apparatus with those interested in electrical science; the experiments which can be performed with its aid are very numerous. It is of considerable importance, especially in its application to such useful purposes as X ray work, wireless telegraphy and ignition for gas engines. The latter has caused manufacturers to give much attention to the development of the induction coil, resulting in many refinements of design and construction.
Induction coils may be divided into two general classes:
The subject of electromagnetic induction has been fully explained in chapter X, but it may be said, with special reference to induction coils, that the operation of the two classes just mentioned is respectively due to:
Self-induction.—This is the property of an electric current by virtue of which it tends to resist any change in its rate of flow. It is sometimes spoken of as electromagnetic inertia and is analogous to the mechanical inertia of matter.
Self-induction is due to the action of the current upon itself during variations in strength. It becomes especially marked in a coil of wire, in which the adjacent turns act inductively upon each other upon the principle of mutual induction arising between two separate adjacent circuits. Self-induction manifests itself by giving “momentum” to the current so that it cannot be instantly stopped when the circuit is broken, the result being a bright spark at the moment of breaking the circuit. On account of this spark a primary induction coil is used in low tension or “make and break” ignition systems.