Magnetism

cal action is a couple tending to turn the little magnet to a position parallel to the lines of force. In Fig. 3, if H is the strength of the field, a force Hm acts on each pole of strength m, and the moment of the couple is Hml cos or M H cose, where м is the moment of the magnet. The strength of field is proportional to M/ď3 at a point distant d centimetres from the centre; but the exact value depends on the direction of d with respect to the magnetic axis, or, in other words, to the value of the angle between the line from centre to the little magnet and the plane perpendicular to the axis.

Magnetometer.-The moments of magnets may be compared by the magnetometer, which is simply a small pivoted or suspended magnet needle with a fong pointer, or a reflecting mirror used with a telescope and scale. This magnetic needle normally lies north and south. If a magnet is placed east or west of this, pointing towards it, the needle will be deflected through an angle 0, whenif H is the mag

2M

=H tan 0,

d3 netic field due to the earth. Thus the deflections caused by different magnets are a measure of their respective moments. Magnets may also be compared by suspending them and causing them to oscillate about the axis of suspension. If the suspension thread is so thin that it exerts no appreciable torsional force, the time of a swing is proportional

to

K

MH'

where K is the mo

ment of inertia, and H is the magnetic field of the earth.

Magnetic Action of a Current.Oersted in 1820 found that there was a magnetic field round any conductor through which an electric current was passing. With a long straight conductor the lines of force form circles with the conductor as centre, and the strength of the field is proportional to the current, and inversely as the distance from the centre of the conductor. If the conductor is bent into a circle, the lines of force pass through the inside of the circle, and return on the outside. Setting up a succession of circles on the same axis, with the current passing in the same direction in each, the lines of force will pass along the tube thus formed, returning outside. Such a succession of circles carrying a current is called a 'solenoid,' and is closely imitated by a coil of wire. It is found that the lines of force form much the same diagram as is shown in Fig. 1, with the addition that they can be identified inside of the tube as well as outside. The

523

only difference is that they bend off in smooth curves instead of abrupt angles. Thus a solenoid will behave in all respects like a magnet, and its strength is proportional to the current and to the number of coils. The direction of the lines of force (i.e. the direction in which a north pole would be driven by them) depends on the direction of the current. In a straight wire, the direction of rotation of a righthanded screw (a cork-screw) gives the direction of the lines of force, if the current passes in the direction in which the screw is travelling. Also in a solenoid the lines of force pass along the direction of travel, if the current passes round in a right-handed rotation. The end at which the lines of force emerge is the north pole of the coil, the other being the south pole. Such a magnet is called an electro-magnet.

The power of an electro-magnet is greatly intensified if the inside of the coil is filled with soft iron, and to a lesser extent if hard steel, nickel, cobalt (metal), or the magnetic oxide of iron is used. The iron is said to be magnetized by the coil, or to show 'induced magnetism,' and the magnetism so induced adds its magnetic effect to that of the coil. It was shown by Beetz that the molecules of iron are themselves magnets by nature, and that the absence of magnetic action by iron in the ordinary state is due to the mutual neutralization of the molecular magnets. But under the influence of an additional magnetic force, such as is due to a coil of wire carrying a current, the little magnets

Magnetism

magnetism in iron and other magnetic materials. The chief phenomena are as follows: when a very weak magnetic force is applied to the iron, the resulting magnetism is feeble, and is proportional to the force. An increase in the force produces a very large increase in the magnetism; but a further increase is

FIG. 4.

less and less effective, until the iron ultimately reaches a condition of magnetic saturation. There are thus three distinct stages, which correspond to three conditions of the molecular magnets. To begin with, the particles are arranged in mutually neutralizing positions (Fig. 4). A feeble force draws them slightly apart (A), as shown in the dotted lines, producing a small magnetic effect. But with a stronger force the attraction of some of the poles is overcome, and the particles swing round to a new position (B), which has a much larger magnetic resultant, but the particles still influence one another to a certain extent. Finally, with a very strong force, the particles are arranged completely parallel to the force (c), and the maximum magnetic effect is produced. The positions of different sets of particles will probably vary, and hence the change is not quite sudden, but shows a gradual alteration. If a curve is drawn, in which ordinates represent the magnetization produced, and abscissæ represent the strength

Cast Steel

Magnetism

This is called 'residual magnetism. In a long piece of hardened steel the magnetism is retained with very little loss for many years, and a moderate amount of jarring affects it but little. But with very soft pure iron the magnetism is completely lost if the iron is jarred. Short, thick pieces lose their magnetism very easily, because the lines of force from the poles endeavor to return through the metal and in so doing tend to reverse the magnetism. Thus, a bar may be regarded as made up of a number of thin bars, all with their north poles together, and each north pole tends to demagnetize the neighboring ones. If the piece is very thin in relation to its length, this effect is much diminished, since there would not be so many component pieces, and therefore magnets are preferably made long and thin if they are required to be perma

nent.

Forms of Magnets.-The straight bar magnet is often used for convenience, but it is not so permanent as the horseshoe form, for in this the two poles are brought near together, and the lines of force pass directly across the narrow air gap, with less tendency to return along the metal. A circular magnet with a narrow space between the poles (Fig. 6) affords a very permanent form. Another form is the tubular magnet (Fig. 7), in which one of the limbs envelops the other, and the air gap becomes a narrow ring round the centre pole.

Keepers. The tendency to selfdemagnetization can be much reduced by bridging the gap with a piece of soft iron, called a keeper. Although a high grade of tool steel makes excellent magnets,

O

FIG. 6.

the addition of tungsten or chromium improves the steel, rendering the magnet more lasting, The metal is hardened by rapid cooling from a red heat; but where great constancy of strength is required, as in some forms of electric measuring instruments, a slight tempering is advisable. The magnets are boiled in oil

524

and magnetized several times in succession.

Magnetization of Magnets.Small magnets, such as compass needles, can be made by stroking the steel with each pole of a bar magnet in turn. But a more uniform magnetization can be obtained by placing the little magnets between the poles of a powerful electro-magnet of horseshoe shape. Very long magnets are put into a coil of wire, and a

FIG. 7.

powerful current is sent round the coil for a second or two. Horseshoe magnets can be dealt with in the same way by using suitably shaped coils. For large magnets it is preferable to build up the magnet out of many thin strips of steel of the shape required, each separately magnetized. By this means the whole of the material becomes equally magnetized throughout.

Hysteresis.-The retention of the magnetic state produces a very important effect when the iron is subjected to a changing magnetic field. Let the magnetic field be produced by an alternating or reversing current. Then the direction of magnetization will be reversed at every reversal of the current, and the change will take place gradually. If a cycle of magnetization is followed through, it will be seen that, owing to the residual magnetism, the iron will remain magnetized when the current has died down to zero, and only reverses by the application of a greater or smaller force. The same effect occurs at the next change, so that the state of the iron always lags behind the state of the magnetic field. The effect is called hysteresis.' In a diagram the magnetization curve is seen to be a closed one (Fig. 8); and as the magnetic field is of the nature of a stress, and the resulting magnetization is a strain, the closed curve indicates work done on the iron, which is converted into heat in the metal. By a rapid alternation of the force the temperature quickly rises, and in machinery, when this occurs, due allowance must be made for an efficient method of cooling. If the values of H, the force, and I, the intensity of magnetization, are expressed in c.G.S. units, then the area enclosed gives the loss of energy per cycle in ergs. The more strongly the

Magnetism

iron is magnetized the greater is the loss, and Mr. Steinmetz has shown that it is approximately proportional to aB1, where B is the magnetic induction. In hard steel the coefficient a is large, whereas in very pure soft iron and in certain mild steels a is small. Fig. 9 shows several curves obtained from different qualities of metal. Very careful annealing is essential for low values of this; and since this effect reduces the efficiency of transformers and dynamos, every care is taken to use the softest Swedish iron in all places where the magnetism is periodically reversed. The value OR (Fig. 8) is called the 'retentiveness, and oc the 'coercive force.' In hard steel the coercive is great; but the retentiveness of soft iron is often greater than that of hard steel, though a very small force is sufficient to destroy it. The explanation of this is easily seen from Ewing's theory. After state 2 a new arrangement of the particles is produced, which is fairly stable, and the particles in consequence keep themselves substantially in the same position, while the force falls to zero. Hence, though there is some falling off of the magnetic state from E to R (Fig. 8), the iron is still fairly strongly magnetized. But as the force increases in the reverse direction, the attractions are gradually weakened, until there is another revolution, and the particles swing round to a reversed condition of 2, with gradually increased alignment up to E'. Then the same phenomena occur in the second half of the cycle. A strong verification of Ewing's theory was afforded by Baily's discovery that the hysteresis in a cylinder rotating in a magnetic field reached a maximum value at an induction of some 16,000, and rapidly diminished for higher values, becoming zero when the iron is saturated. In this condition the molecular magnets are never allowed to form new combinations, since the magnetic field only changes in direction, but not in strength. Therefore each molecule rotates individually as the field changes, and hysteresis is eliminated. This proves that the control of the magnets is due to the magnets themselves, and not to friction or other mechanical cause.

Origin of Magnetism.-It was suggested by Ampère that the magnetism in an atom of i-on could be explained by assuming that an electric current circulates in the atom. The modern view of the electric constitution of matter supports this view, while modifying the idea of a current into a circulation of electrons.

Effect of Temperature.-If iron

Magnetism

is heated it becomes more and more susceptibe to magnetism, but the saturation value becomes less and less. Both effects continue up to a red heat, when it suddenly ceases to be affected by a magnetic force, and it becomes no more magnetic than the nonmagnetic metals. On cooling, it again becomes magnetic; but Dr. J. Hopkinson showed that some alloys of iron remained

non

magnetic on cooling to quite low temperatures, then suddenly regaining their magnetic properties. After heating to a red heat, all residual magnetism disappears, and the iron, after cooling, is completely demagnetized. Longcontinued moderate heating has the effect of increasing the coercive force and the hysteresis loss, a temperature of 100° Centigrade prolonged for many days producing a great increment, which remains after the iron is cooled again. This is allowed for in the calculation of the losses in transformers, since these will be smaller at first and gradually increase as the transformer is used. Heating to a red heat completely removes this new condition.

Magnetic Induction. It has been explained that when a ber of iron is magnetized by a coil the magnetic effects of both are added. It is usually more convenient to consider both effects together, and to reckon the total number of lines of force produced. A magnetic field of

and is denoted by k. Hence, since I kн, then μ=1+ 4 ′′ k. The permeability of air and nonmagnetic substances is taken as unity, or the unit magnetic induction is taken as that produced by unit magnetic force in air. In iron the permeability depends on the quality of the iron, and it is also by no means constant for any one sample. For small and moderate values of B the permeability is high, and as the iron approaches saturation the ratio becomes less and less. In Fig.

strength H produces H lines of force per sq. cm. in air, and it will produce an intensity of magnetization I in the iron. Therefore 41 lines of force per sq. cm. will be due to the iron, and the total number will be 41+ H This is called the per sq. cm. magnetic induction,' and is rep

10,000

5 was shown the relation of B to H, and Fig. 10 shows the relation of μ to B for ordinary soft iron. The maximum value of μ may rise to 4,000 in the softest iron, showing what a vast difference is produced by the presence of iron. Alloys of iron or various kinds of steel are for the most part

7:5

In all cases mechanical strain reduces the permeability and increases the hysteresis, well-annealed metal being the most permeable.

The Magnetic Circuit.-If a line of force is traced out completely, it will be found to return into itself, making a closed path, or into the opposite pole of a magnet, through which it may be considered to pass to the initial pole. This path is called the 'magnetic circuit.' If the lines cf force pass round an iron ring magnetized by a coil of wire, the circuit is very definite, as all of the lines of force are confined to the ring. But with a straight bar magnet or straight coil of wire the path through the air is very varied in length and direction, and the idea of a circuit is difficult to apply. In many magnetic appliances, however, the path is wholly or to a great extent through iron, and this conception affords a very simple means of calculation. If the source of magnetism is a coil of wire, as is usually the case, the total magnetizing influencé is called the 'magneto-motive force'; and this equals the magnetic force through each part of the circuit multiplied by the length of the path. It may be shown that this product = 4πnc, where n is the total number of windings in the coil, and c is the current in C.G.S. units. If the current is expressed in ampères,

4 π

the expression becomes nc, or

1.26 nc.

10

The total Magnetic Flux. number of lines of force passing through a coil and round the magnetic circuit is called the 'magnetic flux.' This is depend

remembered that the value of μ varies with the induction, or the number of lines of force per unit area. It is more usual to decide on a definite value for the induction and total flux, and from this to calculate the M.M.F. required to produce it. If the circuit contains a narrow air gap, a second term must be used; and as the permeability of the iron may be over 1,000, and that of the air is 1, it is obvious that even a narrow air gap greatly increases the reluctance of the circuit. The calculation is complicated by the fact that the path from one side of the gap to the other is not a straight one. The lines of force spring outwards or repel one another, thus increasing the area and decreasing the reluctance; and this decrease is difficult to calculate. In the calculation of dynamos, only those lines of force are useful which pass through the core of the armature, and those which escape the core are called 'leakage lines.' It is therefore convenient to express the ratio of total lines (which all pass through the iron) to the useful lines as a leakage coefficient, which may vary from 1.1 up to 1.4 in usual designs. Then the equation beN1/1 N2/2 A;μ1 A242

comes

4πnc 10

+ + etc.,

526

where N1, N2 are the number of lines through the areas A1, A2, and A will represent the area of the air gap between the pole face and the core, while the leakage lines are ignored in this part of the expression. The leakage ceofficient may be calculated, but is usually well known for any particular design of dynamo.

It is clear that this expression is similar to that used for an electric circuit-viz. E.M.F. = C X R. Current corresponds to magnetic lux, and resistance to reluctance. The calculation in electric circuits is, however, considerably simpler, because the conductivity of the material is constant, whereas the permeability of the iron is variable, and also because in the electric circuit the path is almost always strictly enclosed in insulating materials, whereas there is no magnetic insulator, and the lines of force are free to spread. That they confine themselves with some completeness to a path through iron is only due to the high permeability of the iron as compared with air; and any constriction of the iron path at once causes emergence of some of the lines seeking an alternative path. When the problem is more general -as, for example, a piece of iron placed in any position in a magnetic field-the calculation of the effect is much more complex. The iron acts as if it draws the lines of force to itself; for, as it offers an easier path than the air, the lines will bend round so as to enter and lie in the iron. Thus it distorts the magnetic field, the distortion being greater when the length of iron in the direction of the lines of force is considerable,

FIG. 11.

for it offers an important reduction of reluctance. A short piece of iron, especially a sheet placed perpendicularly to the direction, exerts little influence. Fig. 11 shows the effect of a bar of iron in an otherwise uniform field. It will be seen that near the ends the field is strengthened, while at the sides it is reduced. Hence, where observations of the earth's magnetic force are to be made, it is very important that no iron pipes or beams are near.

Magnetic Screening.-Although no material is non-permeable, and hence no space can be completely protected from magnetism, nevertheless, by surrounding a space by a thick iron shell the lines of

Magnetism

force of (say) the earth are induced to pass round the space through the walls of the shell, and the inside is almost completely screened. A second box inside the first gives an improved effect. The method is used to protect delicate galvanometers from the disturbing influence of external magnetic effects. Since the action is due to the lower reluctance of the iron, it is important to use the softest iron, and to make the walls of considerable thickness.

Tractive Force.-Since the opposite poles of two magnets attract each other, there will be a similar attraction between the cores of two electro-magnets, or between the two parts of the core of a single electro-magnet. This is used in electro-magnetic appliances for producing mechanical movement, which can be controlled by the electric current in the coil, and can thus be operated at a distance. Electric bells and indicators, telegraph sounders, and many other contrivances are examples. Since the lines of force pass from one piece of iron to the next, one end will be a north pole and the other a south pole, and hence attraction will result. Another explanation is afforded by stating that the iron tends to move so as to shorten and improve the magnetic circuit -i.e. to reduce the reluctance. This is usually effected by reducing the air gap between the iron parts. The calculation of the force is rendered difficult by the leakage of the lines of force, which invariably occurs at an air gap. If the air gap is very short compared with its area, the tractive force is approximately equal dynes, when B is the induction, and A is the area of surface in sq. cms. Or it may

to

B2A 8π

B 2

be written (500) A kilograms.

Thus, if the iron is strongly magnetized, so that B has the value 20,000, the pull will be 16 kilograms per sq. cm., or 2 cwt. per sq. in. It will be noticed that a high induction is more important than a large area, and therefore the poles of electro-magnets for lifting purposes are reduced at the ends, in order to concentrate the magnetic effect. The appliance is used for lifting iron plates by employing an electromagnet at the end of the chain of the crane instead of a hook or claws. Fig. 12 shows a form of magnet for lifting

purposes.

Another application is seen in the magnetic clutch, by which the two halves of a line of shafting may be connected, or a pulley on a shaft may be fixed to it or run free. Fig. 13 shows a simple form. A single circular coil is embedded in the face of one

Magnetism

half of the clutch, forming an electromagnet of concentric

form, and the other half acts as a keeper or armature. Current is taken to and from the coil by brushes of wire sliding on brass rings insulated from the shaft, When current is 'on,' the two halves are drawn together, and the one drives the other by fric

FIG. 12.

tion. On stopping the current the clutch is instantly released.

Coil and Plunger Mechanism. -If a bar or plunger of iron is brought near to a coil carrying a current, the bar is sucked into the coil, until it reaches the central symmetrical position. The action may be described in different ways. In Fig. 14 is shown the coil with iron core. Some of the lines of force pass into the near end of the core, and emerge at the farther end, thus magnetizing it. The end near to the coil is in a strong field, and the attraction is great; while the more distant end is in a weak field, and the repulsion is therefore weak. Hence there is a pull into the coil, which continues until the pull on each end is equal, which will occur when the centre of the core is in the centre of the coil. This may be expressed by stating that soft iron moves to the strongest part of the field, which Iwill be the centre of the coil. Or it may be said that the iron moves so as to improve the magnetic circuit, and to decrease the reluctance. As the part inside

FIG. 13.

the coil is the more important on account of its small area through which all the lines of force must pass, these different statements have the same meaning. This action is useful when a longer

527

movement is required than in the foregoing examples. For the keeper arrangement, while affording a powerful pull over a short distance, is ineffective if the keeper is at a distance. With the plunger, a long coil may be used, and the effective distance of action extends proportionally. The calculation of the pull is somewhat complex, and depends upon the shape and size of both coil and plunger. With both of the same length, the maximum pull is obtained when the plunger is about half-way into the coil.

Electric Measuring Instruments.-The movement of small pieces of iron in one of the above described ways is much used in instruments for measuring electric current. A simple plunger may be used, hung on the end of a lever, and the movement of the other end of the lever is indicated on a scale. Or the plunger may be hung from a spring balance, and the extensions of the spring are a measure of the current. In others the iron is drawn away from the axis towards the side of the coil, when in short coils the field is strongest. In others the iron lies across the axis, and is turned parallel to it. Various other forms are in use.

Testing of Magnetic Properties of Iron. The measurements required are the permeability and the hysteresis. The permeability is tested by measuring the induction produced by a measured magnetic force. The latter, de

FIG. 14.

pending on the current, the number of coils, and the length of the magnetic circuit, is easily calculated. The induction may be measured by wrapping a small 'search' coil round the sample of iron, the ends of the coil being connected to a ballistic galvanometer. A sudden increase in the current causes an increase in the number of lines of force which pass through the coil, thus inducing an electro-motive force in the search coil, and a momentary current flows round the coil and galvanometer. The consequent swing of the galvanometer needle measures the increase in the magnetic induction in the iron, and by successive increments of current the iron is magnetized by measured amounts. The actual process and the calculations involved are too lengthy to be entered into here. Instead of a search coil and a ballastic galvanometer, the magnetic state of

Magnetism

the iron may be measured by a magnetometer if the iron is in the form of a long straight wire, since its magnetic moment or the strength of the magnetic pole induced at the end is measured by the deflections of the small magnet. There are many special instruments for the purpose, among which may be mentioned Professor Ewing's permeability bridge, in which a bar under test is compared to a standard iron bar, and both are brought to the same magnetic condition by varying the currents in the respective coils in which they are placed. Thus the values of the magnetic force which each requires are found, and the permeability of the standard being known, that of the sample under test is readily calculated. Other forms depend on the tractive force. If two rods, placed end to end in a magnetizing coil, are pulled apart, the force required to separate them is proportional to B2, as stated above. Hence, by measuring the current in the coil and the mechanical force, the values of B and are ascertained. In all these tests it is essential that the length and area of the magnetic circuit should be known, and therefore the circuit is made entirely of the sample to be tested, or else parts of it are completed by very thick blocks of soft iron, the reluctance of which may be neglected. In the magnetometer method this is obviously impossible, since the return path is through the air. Hence it is essential tha the iron rod should be very long and thin, in order that the return path may be of small influence.

Hysteresis Measurement. — In the ballistic or magnetometer methods, a complete cycle may be carried through, and by plotting and measuring the area of the curve so obtained (Fig. 8), the hysteresis may be measured. Other curves are then obtained for different maximum values of B, and the hysteresis curve (Fig. 9) is thus determined. But the value of the hysteresis is usually required when the iron is to be subjected to an alternating field, and each alternation causes a definite loss of energy. The loss may thus be directly measured if a coil of wire is wound round a simple magnetic circuit composed of the iron to be tested, and an alternating current is passed through the coil. The power absorbed is measured on a wattmeter, and from a knowledge of the speed of alternation and the volume of the iron, the loss per cycle per cubic centimetre is determined. To reduce eddy currents in the iron, it must be in the form of thin plates, and the apparatus is built up by piling narrow strips