K12 Electromagnetism and magnetism

Interaction between a magnet and a conductor through which flows a current

The thermal and chemical effects of an electric current occur in the track of the current. Consider next actions of currents away from it. Just as electricity at rest has its electric field, so does the moving one; the environment of a conductor carrying a current exercises apparent distant action: Especially on nearby magnetic needles. A magnetic needle has at every point on Earth's surface a definite direction (in a definite magnetic meridian) and, if you force it to turn elsewhere and then release it, it will always return to its initial direction. Apparently a force (Earth's magnetism) keeps the needle within the magnetic meridian; it requires work, to deflect it from it. Work of this kind can be performed by an electric current: It diverts the magnetic needle (first discovered by Oerstedt 1820) and thereby performs what only a magnet can do - in other words: Flowing electricity exerts magnetic forces. For the direction in which the current turns the needle you have the rule: Imagine you swim in the conductor, with the current, with your head forwards, the face turned to the needle; then the North pole of the deflected needle will be turned towards your left hand (swimming rule of Ampère). If you make an adjustment for Earth's magnetism by bringing into the neighbourhood of the needle a magnet, directed in a definite manner, it will obey unimpeded the diverting force of the current. If you carry the needle around the conductor, it will always place itself perpendicularly to it, the North pole ahead, as described by the swimming rule. Fig. 533 displays this for a conductor, perpendicular to the plane of the drawing.

Thus, the North pole of the needle (arrow head) experiences a force to circulate the conductor; so does the South pole, but in the opposite direction to that of the North pole. If the conductor is very flexible, say a longer narrow strip of tinsel, hanging beside a vertical magnetic rod, the strip will wind itself around the magnet, when the current is closed, the ends of the strip in opposite directions corresponding to the opposite poles. Thus, every pole acts by itself on the conductor through which flows a current and not only, because is is connected to the opposite pole. Corresponding to the law of the equality of action and reaction, the magnet must also act on the current. The pole tends to make the conductor circulate around it just as the conductor has done with it: In the set-up of Fig. 534 b, the magnet is fixed and the conductor can move (Faraday). If you close the current, the conductor describes about the pole of the magnet the mantle of a cone. In the arrangement of Fig. 534 a, where M is the magnet and S and the mercury form the circuit, the North pole circulates - in the direction corresponding to the swim rule about S.

Interaction between conductors with flowing current

A full understanding of the interaction between a magnet and electric currents is only reached when we examine the mutual interaction of two currents (Ampère 1820). Electric currents attract or repel (electro-dynamically) each other depending on their relative directions (Fig. 535); parallel currents of equal direction attract, anti-parallel currents repel each other. The frame, referred to as Ampère's frame (Fig. 537), demonstrates this well: The frame BC can rotate in the bearings a and c has current flow, as is indicated by the arrows. A second frame MN, also with current flowing through it, is placed parallel to it nearby and fixed. If you rotate the movable frame so that B and M approach each other, you observe repulsion, between C and N attraction.

Fig. 538 demonstrates that currents in the same direction attract each other: A very thin, elastic, vertically hanging screw spring, through which flows current and the lower end of which - with a weight extending the spring - dips freely movable into mercury. The spring and the mercury form a circuit. In all the windings of the spring the direction of the current is the same, whence they attract each other, the spring shortens. pulls in spite of the weight its movable end upwards out of the mercury and breaks the circuit. Now the spiral spring follows the pull of the weight, dips again into the mercury and thus the cycle repeats itself.

Active conductors, which cross one another (Fig. 536), attract each other, if both move towards the intersection or move away from it. If one moves there, the other moves away, they repel each other.

The electro-dynamometer for the measurement of current intensities depends on the interaction of current carrying conductors (Fig. 539). V is a fixed frame with wire wound around it, W a similar frame which can rotate in the bearings B. Both frames form the circuit 2VBWC1. The frame W stands without current, acted upon by a torsion spring F. at right angle to the frame V. When current flows through it, it tends to rotate so that the conductors through which flows current in the same direction lie next to each other. This rotation twists the spring F more or less. A position of rest is reached, when the tension of the spring is in equilibrium with the electro-dynamic action between the frames. The pointer z, linked to W, indicates the current intensity on an empirically calibrated scale. The direction of the pointer's movement remains the same at a change in the direction of the current, whence these instruments are suitable for employment with alternating currents (Siemens).

A movable active conductor can also move along a fixed active conductor (Fig. 540). The parts of the conductor to the right of m must repel the conductor ab, those to the left of m attract it, whence it must move along cd towards c. Hence the movable bow b (Fig. 541) rotates, that is, it pushes itself along the fixed conductor, which surrounds the mercury vessel.

Solenoid. Electromagnet Thus, the surroundings of an electric current act like those of a magnet. This becomes especially clear when the conductor forms a solenoid (Greek: swlhn = pipe), a screwed wire, the windings of which support each other's action (Fig. 542). A solenoid, the axis of the windings of which can rotate about a vertical axis (Fig. 543), locates itself like a magnet needle, the plane of the windings at right angle to the magnetic meridian. Its axis corresponds to that of a magnet needle, the South pole B lying to the side, seen from which the current flows clockwise around the axis. - Two solenoids interact like two magnets, equally named ends repel, differently named ends attract each other - this is easily understood, because, if two solenoids lie with the equally (differently) named ends A and A' together (Fig. 543), then parts of the conductors lie side by side, in which the currents are directed opposite (in the same direction), that is, repel (attract) each other. A solenoid behaves with respect to a magnet like a magnet with respect to another magnet; the North pole of the magnet attracts the South pole of the solenoid and repels the North pole of the solenoid. Ampère concluded from this that the magnet and the solenoid are similar. According to his hypothesis, the magnetic field of magnetized bodies, should be generated by currents inside molecules - Ampère's molecular currents. Their existence can be proved by experiments (Einstein, Haas 1915), which let one understand that a not magnetic iron rod, around which you feed a solenoid current (Fig. 544), becomes a ,magnet - an electro-magnet; the solenoid current makes them parallel and directs them in the same direction, whence they generate the external magnetic field.

The electric magnet is employed in innumerable appliances, which are switched on from an arbitrarily distant location (through a circuit), and can perform mechanical work. For example, you have among them the regulation of clocks by a standard clock in an astronomical observatory, operation of a warning sound system along a railways track or activation of an electric telegraph writer. In each case, activation of a magnet performs the work: Here the activated mechanism adjusts a clock, there a hammer hits periodically a bell, there a typewriter is turned on and operated.

Until 1900, the most used telegraph apparatus was that of Samuel Finley Breese Morse 1791-1872 1844 (Fig. 545). E is the electromagnet. As long and as often as it is activated, it attracts the anchor A and presses by the angled lever CID the strip of paper hp against the roller c, covered with ink. Depending on the duration of its activation, it draws points or dashes, which form the Morse alphabet; for example, - = a, -··· = b, etc. Its place was taken gradually by the telegraph type writer of David Edward Hughes 1831-1900. Submarine telegraphy employs the very sensitive galvanometer of W.Thomson, in which a fine glass tube is deflected to the right or left, the ink is sprayed on the paper strip (Fig. 546); more recently, also a typewriter is being used.

Magnetism

Electro-magnets are artificial magnets. There exist also natural ones - magnetite, an iron ore with the known magnetic properties of attracting iron and steel; however, only the fact of their mere existence is of interest here. Their magnetic effects disappear in comparison with the forces of artificial magnets. since artificial magnets can be very strong; an electro-magnet which can lift an adult human being has only moderate dimensions. Pieces of iron, attracted by a magnet, become themselves magnetic, if they are in contact with it, and even more so, if you move several times a magnet over their surface in the same direction: They themselves become artificial magnets.

A bar magnet is most strongly magnetic at its ends, less so towards its centre and not at all at the centre. This is demonstrated, for example, by its appearance, when it is covered with iron dust. The longer it is compared with its cross-section, that is, the more it approaches the form of a needle, the more seems the maximum of its ability to attract iron concentrated at two points - its poles - (in the case of bar magnets, at a distance of about 1/12 of its length). The line, on which the poles lie, is called the axis of the magnet. It you support a needle formed magnet (Fig. 548), so that its axis can turn freely in the horizontal plane, it comes to rest in a certain direction. If you force it out of this position and release it, it will resume its initial direction. If you bring it into this direction, but in such a manner that the initially forward end is at its back, it will rotate by 180º and resume its initial position. This direction is approximately North-South. This is the reason why you call the pole which seeks North, the North pole, the other the South pole. The turning force, which returns the needle to its initial position, arises from the action of Earth's magnetism. You can confirm the fact that only turning forces are active by letting a magnet swim on water in a vessel(Fig. 549); it will be turned into the magnetic meridian, but not be attracted to the edge of the vessel. Due to its direction seeking property, magnets serve as compass - needles which are supported on a pin and are able to rotate in the horizontal plane. (Fig. 548).

For use in ships, the circular subdivision of the circle is fixed to the magnetic needle; the ship moves around it and the compass container has a mark corresponding to the ship's keel. In order to remove the effect of the ship's oscillations, the compass is in Cardan suspension. In the compass used on land for direction finding, the needle moves in a circular container, the rim of which has a scale.

Fundamental law of the force of interaction between two magnets

North- and South poles of magnets are related to each other in some sense as positive and negative electricity. If you place two magnet needles side by side, equally named poles repel (North pole the North pole, South pole the South pole), but the North pole attracts the South pole, etc.). Just recall what was said earlier about the interaction between equally and unequally named electricities; imagine the electricity replaced by magnetism and North magnetism replaced by positive, South magnetism by negative electricity. You will the immediately understand the fundamental law (Coulomb): K = m₁·m₂/r². This law states: Two poles with magnetic quantities m₁ and m₂ interact with a force K, which is directly proportional to the amounts of magnetism and inversely proportional to the square of the distance between them - repulsion or attraction depending on the signs of their magnetism. The unit of amounts of magnetism will be found as follows: Let there be given two equally strong poles 1 cm apart from each other; if they interact with the force 1, that is, 1 dyn, we ascribe to both of them unit magnetism (unit pole). At any location, the magnetic force is measured in terms of the number of force units (dyn) by which they act on a unit pole placed there. If m is the amount of magnetism at each of the poles of a bar magnet, l the distance between the poles, then its magnetic moment is m·l; it corresponds to the moment of a couple.

Naturally, in order to confirm Coulomb's law, you cannot create two single poles just as you cannot create two single, electrically charged bodies. However, you can attain almost the same objective with two very long bar magnets (Coulomb). Their magnetism is concentrated at their extreme ends, the remaining length being next to indifferent. For example, you can let the South poles of two magnets approach each other and investigate their interaction without, due to their lengths, the North poles disturbing the experiment.

Magnetic lines of force

The fundamental law of the force acting between two magnet poles has exactly the same form as the corresponding law for electric charges. By considerations, analogous to the ones just referred to, we arrive also here at the magnetic potential, the level surface of the magnetic potential and above all at the magnetic lines of force (Faraday). All the lines of force characterize the magnetic field - our next topic.

If you place a small magnetic pole as testing body somewhere in a field, a certain force acts on it: Its direction is visualized by the direction, its magnitude by the density of the lines of force at any location in the field. Lines of force are only products of our imagination, nevertheless you can display them. Let NS be a bar magnet; place a small magnet needle near it in the plane of Fig. 550a. The poles of the magnet and of the magnet needle interact and the needle positions itself in the direction of the resultant force, which acts on it; this direction is that of the line of force at that location. If the entire field is occupied by magnet needles, we get a complete view of the lines of force, (We disregard here the interaction of the magnetic needles on each other!)

In order to display the lines of force, you use iron dust; under the influence of the magnet, they themselves become magnetic and arrange themselves just like the magnet needles. For example, place a sheet of paper on top of the magnet, cover it with iron dust and tap the paper softly.

You must take into consideration that such lines of force enter space in all directions (Fig. 550b), that is, that Fig. 550a only tells us about their layout in the plane of the drawing.

Magnetic field strength, measured by the density of the lines of force

Fig. 550a shows that close to the magnet, that is, where the force is greatest, the lines of force are closest together; further away, where the force is weaker, they are wider apart. The density of the lines of force at a location in the field can serve as a measure for the local force; we understand by density the number of lines of force, which pass through a 1 cm² cross-section, perpendicularly to the direction of the lines of force. (Do not view these lines of force as real objects! The force around a pole of a magnet is always uniformly - more strictly: continuously - distributed and by no means concentrated on lines. Only the clarity, associated with the image of lines of force, justifies us to imagine the continuous field of force replaced by the unsteady field of lines.)

We can express field strength at a given location with the aid of the number of lines of force: Around a unit pole, at a distance of 1 cm, you have everywhere the force 1 dyn. The spherical surface of radius 1 cm about the unit pole has the area 4p·1²=4p cm². If we now subdivide the lines of force, radiating from the unit pole, into 4p bundles (Faraday's induction tubes), then every cm² at a distance of 1 cm is hit by one bundle of lines of force. In order to simplify the picture, imagine every individual bundle replaced by a line of force running along its centre*. At a distance of 1 cm from the unit pole, there then passes exactly one line of force through an area of 1 cm², perpendicular to its direction. Hence 4p·m lines radiate from a pole of strength m. At a distance of 1 cm from this pole pass then m lines through 1 cm² in agreement with Coulomb's law, according to which there acts at this place a force of m dyn. If we now imagine at the distance of 2 cm another spherical surface around the pole, it has the area 4p·2² cm². Through every cm² of this surface now pass of the 4p·m lines only 4p·m/4p·2² = m/4 lines, that is, the density of lines at the distance of 2 cm has sunk to 1/4 or, more general, at the distance r to 1/r². However, according to Coulomb's law, the force has decreased in the same ratio.

* By 4p = 12.56 lines of force, you must, of course, understand 1256 lines per 100 cm².

We can now make the following statement: If from a pole of strength m radiate 4p m lines of force, then everywhere in the field the force is numerically equal to the number of lines of force, which pass there through 1 cm² at right angle to the lines of force. The density of the lines of force thus becomes a measure of field strength. The unit of field strength is called 1 Gauß. The statement "a field of 100 Gauß" then says that at this location pass at right angle through 1 cm² 100 lines of force or that a force of 100 dyn acts on the unit pole.

If the strength of a pole m = 1000 units of magnetism and r = 10 cm, then the number of lines of force radiating from this pole is n = 4p·m = 4·3.14·1000 = 12560, whence the density of lines of force B at the distance 10 cm is

B = n/4p·r² = 12560/1256 = 10,

that is, 10 lines meet 1 cm² at that location in the field. Just so is there the force according to Coulomb's law:

m₁·m₂/r² = 1000·1/10² = 10 dyn.

Hence the field has at 10 cm distance the strength of 10 Gauß.

All these consideration only refer to the field of a point-like pole. However, it can be extended to magnets of arbitrary shape and arbitrary fields. In particular, if the lines of force are parallel and at equal distances, the field is said to be homogenous. For example, you can consider Earth's field to be homogeneous within the spaces of practical measurements. The horizontal component of Earth's magnetic field, which has an important role in many measurements, in Central Europe, is 0.2 Gauß (in Berlin 0.18). By means of electro-magnets Kapitza 1894-1984 1927 achieved fields of about 320,000 Gauß (in a space of 2 cm³).

Terrestrial magnetism. Its elements (declination, inclination, horizontal intensity)

A magnetic needle does not point exactly to North; it deviates by a few degrees - the declination angle, from the geographical meridian, at some locations to the West (in 1935 in Berlin by about 9º), at other locations to the East. The plane through Earth's centre and the direction of the needle is called the magnetic meridian. The point on Earth's surface, to which magnet needles point with their North pole, lies in the arctic part of North America (69º 18' N, 95º 27' W), the corresponding one on the southern hemisphere in the South Sea to the South of Australia (72º 25' S, 154º E). These two points are called Earth's magnetic poles.

If you hang a magnet needle in the magnetic meridian and let it turn about a horizontal axis through its centre of gravity, its magnetic axis ab forms with the horizon an acute angle (Fig. 551); on the Northern hemisphere, the North pole, on the Southern hemisphere the South pole points downwards. The acute angle between the downwards inclined part a of the magnetic axis and the horizontal plane is called the angle of inclination. It was about 66º in Berlin in 1935. Like the declination, it changes with the time. Near the magnetic poles of Earth, the needle is vertical: The inclination is 90º.

The angles of declination and inclination at a location on Earth's surface yield the direction of the local force of Earth's magnetism. In this direction, the magnetism attracts the one pole with the same strength as it repels the other pole. The strength with which it acts there on the magnet with unit moment is called total intensity (T). If you decompose T into three mutually perpendicular components - one vertically downwards, the other two in the horizontal plane South-North and West-East - the first determines the vertical intensity, the other two together the horizontal intensity H. Declination, inclination and horizontal intensity are referred to as the elements of Earth's magnetism.

Earth's magnetism in Central Europe for 1910, 0. (German Seewarte)

Horizontal intensity in Gauß

Mean annual change: + 0.00014 - 0.00034 CGS

Western declination

Mean annual change: -0.07º

Northern inclination

Mean annual change: - 0.02 - 0.05º

If you link on a chart two neigbouring points, at which one of these elements has the same magnitude, for example, the horizontal intensity is 0.2 Gauß, you obtain certain curves (iso-magnetic lines) which cover Earth's entire surface. The most important ones are: Lines of equal declination (isogones), of equal inclination (isoclines), of equal total intensity (isodynamens) and of equal horizontal intensity (horizontal isodynamen) (Fig. 552).

The numerical values of the terrestrial magnetic elements, obtained for thousands of locations, yield the conclusion that Earth can be considered to be a magnet, the axis of which is inclined to the axis of rotation by 12º. There also exists a magnetic equator along which the inclination vanishes. The regions of Western and Eastern declination are separated by the isogones of 0º - agones; there were in 1935 two of them. The numerical values of the terrestrial magnetic elements are not constant, but oscillate in time steadily (secularly, annually, even daily): At exceptional occasions, they change abruptly - like a storm (magnetic thunderstorm) - coinciding with such events on the Sun; Earth currents and polar lights are linked to Earth's magnetism. The study of the elements of terrestrial magnetism is mainly linked to the names of Humboldt, Gauß , von Neumayer and L.A. Bauer. The first proposed the setting up of magnetic observatories, the second looked after the accuracy of terrestrial magnetic measurements, the third made terrestrial magnetism an indispensable part of scientific expeditions; the fourth measured magnetism in the service of the Carnegie Institute for 20 years on a ship without iron parts on the oceans, filled gaps in many magnetic charts and showed that many previous measurements were at fault.

Absolute (Earth magnetic) measure of current intensity

You can measure the Earth magnetic field in absolute units (c, g, s), whence the field due to a current can also be measured by a comparison with the terrestrial magnetic field. In this way, it must be possible to obtain an absolute unit of current strength (apart from the technical units, defined with the silver Volta meter.)

An instrument for absolute current measurements is shown in Fig. 553; it is a circular conductor in a vertical plane, which surrounds a very short, in the horizontal plane rotatable magnet needle. The vertical axis of rotation of the needle coincides with the vertical diameter of the circle and the plane of its rotation with the horizontal plane through the circle's centre. You place the circular plane of the conductor at the magnetic meridian. As long as no current flows through the circuit, the needle locates itself on the horizontal diameter of the circle. However, if in addition to Earth's field a current is applied, the needle turns in the direction of the resultant force, due to the simultaneous action of the terrestrial field and the circuit. Earth's field only acts with its horizontal component H. It acts on the unit pole with H dyn, hence on each of the poles of the needle with the magnetic quantity m with m·H dyn. After the needle NS has turned by the angle a out of the magnetic meridian into the position N'S', the lever arm (Fig. 554), at which it acts, is p, that is, l/2·sina (setting the distance of the pole = l; in the position N"S", this arm would be = l/2), whence the turning moment at the needle due to Earth is mH·lsina. The expression ml is the magnetic moment of the needle.

We now turn to the magnetic force of the current. We compute it on the basis of the law of Biot and Félix Savart 1791-1841, established by means of many experiments, which yields the force exerted by a short, current carrying conductor - a circuit element - on a magnet pole at an arbitrary distance from it. Let l denote a short piece of a conductor (Fig. 555), i the local current intensity, m a magnet pole with amount m of magnetism at the distance L from l, and j the angle between the directions of l and L. The force, exerted by l on m is then proportional to sinj · i· m·l/L². If L is perpendicular to l, that is, sin j = 1, the force is proportional to i· m·l/L². It wants to take m (Fig. 533) along a circle about l, that is, it acts perpendicularly to the direction L. The lower Fig. 555 displays l perpendicular to the plane of the drawing, the arrow indicates the direction in which the current acts on the pole. We are here only interested in the action of a circular current on a pole at the centre of the circle. Let r be the radius of the circle, i the current intensity, m the amount of magnetism of the pole. The force exerted by the current on the pole is proportional to i·m·2p r/r², since l = 2p r and L = r, that is, it is proportional to i·m·2p /r. If the pole is a unit pole - we recall that we wanted to measure by the action on it the field strength - than the strength at the centre is proportional to 2p · i/r. In other words, the field intensity increases in the same ratio in which the current intensity i increases and in which r is reduced, that is, the smaller is the circle carrying the current around the pole.

This relationship led Weber to define the absolute unit of current intensity. Imagine a circle of radius 1 cm, on it an arc of 1 cm length and at the centre of the circle a unit pole. Weber calls unit current that current, which is so strong that the piece of the conductor exercises on the pole the unit force or - if you take the entire circle into consideration - which, when it flows around the unit pole at the centre of a circle with a radius of 1 cm, exerts on the pole the force 2p dyn (equal to the weight of about 6.4 mg). This current is the absolute unit of current intensity, measured electro-magnetically (it was measured previously electro-statically). If we conduct an absolute unit of current through a silver Volta meter, it precipitates each second 11.18 mg silver. Industry does not employ the absolute unit, but its tenth part, You call 1/10 of the absolute unit of current intensity 1 Ampere.

This definition of current intensity fixes the hitherto indefinite proportionality factor in the law of Biot-Savart. A current of i absolute units of current intensity now exerts on each pole of magnetism m of a magnet needle at the centre of a circular current with radius r the force m·2pi/r dyn (Fig. 556). The distance of this force from the axis of rotation of the needle is q = cosa ·l/2, whence the turning moment, exerted by the magnetic force of the current on the needle is l·cosa ·2p i·m/r or, since we have set ml = M, cosa·2p i·M/r. Since the needle in the position N'S' acted upon by the two forces (current, Earth's magnetism) is at rest, the turning moments of the two forces are equal, that is, M·2p i/r·cosa = =MH·sina, whence i = H ·r/2p ·tana. In order to express i in absolute units, you must know the horizontal component H of the terrestrial magnetism*. If you change the current intensity, the angle a changes, which the magnet needle forms with the magnetic plane of the meridian, while everything else remains unchanged. Denoting the new current intensity by i₁ and the new angle by a₁, then i₁=H·r/2p ·tana₁, whence i/i₁ = tana/tana₁, that is, the current intensities are interrelated like the tangents of the deflection angles of the needle. The constant H ·r/2p is called the reduction factor of the instrument, shown in Fig. 553.

*In Central Europe, it is about 0.2 units of the magnetic field strength, that is, Earth's magnetic field attacks the unit pole there with a force of about 0.2 dyn.

Galvanometer

There are many instruments, which act similarly to that in Fig. 553. An instrument for the accurate measurement of currents is called a galvanometer; if it is only for an indication of the existence of a current, it is called a galvanoscope. In order to raise the sensitivity of an instrument as much as it is possible, you employ instead of a single wire loop a narrow spool with many loops, when already a weak current generates a strong field (multiplicator). Moreover, you replace the needle, rotating on a point, by a small magnet, suspended by a thin thread, the exact angle of rotation of which is determined by a special procedure. The sensitivity is also raised by weakening Earth's magnetic force, which tends to turn the needle back into the magnetic meridian. You achieve this objective by means of a magnet, which you install near the instrument so that its lines of force neutralize largely those of Earth's field. You can also achieve this by providing the instrument an astatic** pair of needles instead of a simple needle; this is a pair of two rigidly connected needles, which are as equal as possible, which lie parallel over each other and have their poles in opposite directions Fig. (557) The directing force, exercised by Earth's field on such a pair, is small, because it attempts to turn the two magnets in opposite directions. If the two magnets were exactly alike, Earth's field would not exert a directing force. In reality, strengths of magnets always differ a little, so that a certain, although very weak adjustments occurs by Earth's field. There would be no sense in installing an astatic needle pair in a spool, since this could only act very weakly on such a weak needle. In fact, you may only place the one magnet of the pair into the spool (Fig. 558). The current field can then act on the total pole strength of the one magnet, while Earth's field acts only on the difference of the pole strengths of the two magnets .** stasis = stand

All instruments of this kind are sensitive to scattered magnetic fields such like thoseoriginating from power-lines, electric trains, etc., whence you construct galvanometers according to quite a different principle by suspending in the field of a very strong permanent magnet a rotatable spool. Fig. 559 shows the moving coil galvanometer for mirror reading of d'Arsonvale. N and S are the poles of a strong horseshoe magnet and C an iron cylinder in between them, through which the lines of force pass from N to S. The ring formed gap between the poles and the iron cylinder serves for insertion of the movable coil, which consists of a frame with wire around it in several windings. The current enters through the suspension wire A and leaves through the fine coiled spring wire M. If no current flows through the coil, it aligns, due to the force of the suspension, with the plane of the magnet. Passage of current generates in it a field, the lines of force of which are perpendicular to the plane of the windings. The interaction between this field and the horseshoe magnet causes rotation of the coil. The measurement of the angle of rotation is discussed later on. Since the spool is always located in a strong magnetic field, the readings are not appreciably disturbed either by Earth's field nor any external fields of unknown origin,

The same principle is employed in the current- and tension-meter of Weston, which is widely used for technical and scientific purposes (Fig. 560). Between the poles N and S of a fixed, strong, permanent magnet turns the solenoid P. A spiral spring F gives it a certain position relative to the lines of force of the field. If current passes through the coil, it turns until the diverting force of the magnet field balances the torsion of the spring. If the current is switched off, P returns to its old position. The coil is linked to a pointer, which moves over a scale, which is calibrated in Volt or Ampere, depending on whether it is used for measurements of tension or current. For practical reasons, the coil of the ampere meter is given a small, but that of the Volt meter a very large resistance.

Magnetism. a general property of matter. Paramagnetism. Diamagnetism, Permeability

Hitherto, we have only studied the forces in the neighbourhood of a magnet - its field; next, we will look at the magnet itself. Does the ability to be magnetised only belong to iron or also to other substances? Following Faraday 1846, substances can be divided into two classes, as the following experiment demonstrates: In Fig. 561, N and S are the poles of a strong magnet, the dashed segments its lines of force. Two equally shaped, small rods P out of chrome and D out of bismuth are suspended symmetrically between the poles and then released. Then the chrome bar P aligns with the lines of force (axially), the bismuth bar D perpendicularly to them (equatorially). Faraday calls substances which behave like P paramagnetic, the other - most of them - diamagnetic. For example, paramagnetic substances are iron, nickel, cobalt, chrome, palladium, platinum, osmium and many watery solution of metal salts, diamagnetic ones are bismuth, mercury, phosphor, sulphur, water, alcohol and many gases.

The lines of force demonstrate the difference between para- and dia-magnetic substances. Fig. 562 shows a magnetic field which is initially uniform, that is, its lines are parallel and equidistant. If you place a diamagnetic substance P into this field, the lines of force move closer together at the location, now filled by the paramagnetic body. If you place a diamagnetic substance D there, the lines move further apart. So we can say that the lines of force are deflected from their tracks on entering the chrome and the bismuth; they prefer, on the one hand, the path through the chrome to that through the air (Fig. 562 left), on the other hand, the path through the air to that through bismuth (Fig. 562 right). It seems as if, on the one hand, chrome lets lines of force pass more readily than air, on the other hand, air more readily than bismuth. Following Kelvin, this behaviour of substances is called their permeability (m)*. It measures how many more line of force pass through the space filled with a given substance than through a vacuum. We define: Paramagnetic substances are more permeable, diamagnetic ones less permeable than vacuum. Hence, whether a body will place itself axially or equatorially depends not only on its substance, but also on the magnetic conditions of its neighbourhood. No material is very strongly diamagnetic, bismuth most of all. Even the permeability of air relates to that of bismuth like 1:0.999,82.

* The magnetic counterpiece to the dielectric constant. Both have in vacuum the value 1. There is no electric analogue to diamagnetism. There do not exist dielectrics, the dielectric constant of which is < 1.

You write m = 1 + 4pk, a pure number, the unit of which belongs to air (more strictly, vacuum). The quantity k is the susceptibility; it measures the dependence of the magnetization (magnetic moment), m that of the magnetic induction on the strength of the field. Only the permeability of the ferro-magnetic materials depends on the field strength - and very strongly. The larger is the permeability of a kind of iron, the more useful it is for electro-technical purposes; it lies for ordinary substances between 2000 and 5000, it rises for special ones to 20000. The several thousand times larger permeability of iron is employed to protect sensitive equipment from the effects of magnetic fields (magnetic shielding). You surround them by iron covers, which conduct the lines of force through them and thus keep them away from the apparatus as, for example, the armoured galvanometer of Du Bois 1863-1918 and Heinrich Rubens 1865-1922, the extremely light magnetic system is enclosed within several iron shields. The formulae for permeability and susceptibility are:

Molecular theory of magnetism

The preceding considerations have shown that ferro-magntism is just a special case. During an exploration of the mechanism. which appears to us as magnetism, we should be able to start from any material. We will start from the steel magnet, since is displays most strongly the characteristic phenomena, which concern us here; for the sake of clarity, consider a bar magnet (Fig. 448) and recall that every magnet has two poles. However often you break the magnet, each fraction is again a magnet. At the fracture, each has a pole, equally strong but with the opposite sign of the pole at the fracture of the neighbouring piece. It we fit the pieces again together in the order they were fractured, the restored magnet has the same properties as before. This suggests that also the smallest parts of the magnet, the molecules, are magnets (magnetic dipoles), whence also inside a magnet rules a force directed from pole to pole (internal field). If we compare the molecular magnets with compass needles, which, lined up pole to pole, the lines of force (Fig. 550a) appear as closed lines: In passing from one pole to the next, they run partly outside, partly inside the magnet.

Experience tells us: Contact with a magnet makes non-magnetic iron magnetic - mere contact, only weak, mutual sliding of touching pieces, much more strongly. Even just an approach to a magnet (the field of a magnet) makes iron magnetic; indeed, it generates a magnetic pole in its vicinity, a pole of opposite sign. The theory of Wilhelm Eduard Weber explains this as follows: Also non-magnetic iron consists of molecular magnets, but their axes are in all directions, whence the totality of the molecular magnets, that is, the piece of iron, is without polarity. An external magnetic effect directs the molecular magnets like magnet needles, all North poles in one direction, all South poles in the opposite direction, whence the piece of iron receives North- and South magnetism. If the magnetic effect is again removed, this induced magnetic state of the iron does not vanish completely. The magnetism which remains is called remanent, and the ability of the iron to hold on to it the coercive force. - James Alfred Ewing 1855-1935 has shown with the aid of many, closely spaced small magnet needles, that the most essential peculiarities of magnetism can be explained in this manner.

Molecular magnets were interpreted by Ampère 1820 as electro-magnets; he imagined every iron molecule to be a centre of an electric circuit. But where is the electromotoric force which maintains this current enduringly? And why does not there develop enduringly Joule's Heat in the circuit? We do not know about currents which lack a circuit's characteristic - electric resistance. This question has also not been resolved by the atomic theory of Bohr, which also leads to molecular circuits. However, molecular circuits are present in ferro-magnetic substances and have even been displayed experimentally by Samuel Jackson Barnett 1873-1956 1915, Einstein and Haas 1915 on the basis of considerations linked to the theory of tops.

As the temperature rises, magnetizability decreases steadily and vanishes almost completely at a certain temperature (transition temperature) named Curie point after its discoverer Curie - for iron at about 765ºC, for nickel at about 360ºC. This is in agreement with the theory of molecular magnets: The external magnetic field tends to arrange the magnetic axes of the molecules uniformly, but the heat tends towards their ideal disorder, approaches its goal at rising temperature and eventually overcomes the effect of the field. Hence there are beyond the transition temperature also ferro-magnetic substances which are only strongly para-magnetic. At the Curie point, the specific heat of a substance changes discontinuously.

Magneton

The electron structure of atoms, following Lenard, Rutherford and Bohr, allows to explain that all substances of any kind of atom react to an external magnetic field: The reaction arises from the action of the field on the electrons, circulating the nucleus, since the motion of the electrons represents an Ampère molecular current, the magnetic action of which is equivalent to that of a bar magnet. To start with, the inevitable action of the magnetic field on the trajectories of the electrons is to deform them. However, the manner, in which the atom as a whole reacts to the field, depends on whether the electron paths in the atom are such that the resulting magnetic moments balance each other or combine into a total moment. If they balance, the atom is not magnetic and reacts to the external field dia-magnetically unless the external field cancels the mutual compensation and the atom obtains thereby an induced magnetic moment. If they combine into a total moment, the atom is para-magnetic and reacts correspondingly.

We have spoken here all the time about the magnetic properties of matter in general without referring to ferro-magnetism. It forms really only a special case and, indeed, probably in Crystal Physics and not in Atomic Physics. Present day research (in 1935!) attempts to understand magnetic properties as an atomic elementary process. This is the direction of Bohr's atomic theory, which identifies the circulating electrons with Ampère's molecular currents and in the process - this is most important! - leads to an atomic unit of magnetic moment, so to say, an elementary quantum of magnetic moment, the Magneton (a term due to Pierre Ernest Weiss 1865-1940 who, without starting like Bohr from theoretical considerations, was guided there earlier empirically). According to Bohr, the smallest atomic magnetic moment (Bohr's magneton) is generated by an electron, which circulates on a one quantum orbit about a positive nucleus; it is computed at m = 9.21·10^-21, or related to the mole m·N (where N is Loschmidt's Number 6.06·10²³), M = 5548 Gauß·cm. Weiss' magneton is about one fifth of this and contradicts Quantum Theory.

Direction-quantumization

One of the most important predictions of the Quantum theory (Sommerfeld and Debye) concerns the behaviour of atomic magnets in a magnet field: What direction will the vector of the magnetic moment have relative to the direction of the lines of force. In a field, the axes of the magneton will not have an arbitrary direction, not all possible angles to the lines of force - that is, the directions will not be distributed arbitrarily - but they will form with them only certain angles, which depend on the moment of the magneton, but not on the strength of the field. If the atom has a moment of one magneton - the simplest case! - it must align according to the direction- quantumization theory so that the axis of the moment coincides with the direction of the external field. Two possibilities correspond to this mechanically unique specification of the direction with respect to the magnetic direction of the atom: The atom, conceived as an elementary magnet, can align in such a way that its magnetic direction, - the direction - is in the magnetic direction of the external field or is opposite to it (parallel and anti-parallel adjustment of the moment axis with respect to the external field). In 1935, the direction-quantumization theory could not be linked to the ferro-magnetic problem. Otto Stern 1888-1969 and Walter Gerlach have demonstrated visually with silver atoms spatial quantumization of directions and thereby proved the atomic theory of the magnetic moment by discovering as elementary quantum of the magnetic moment Bohr's magneton. According to the theory, the normal silver atom can align itself to the lines of force parallel or anti-parallel; in a non-homogenous field, all atoms split therefore into two parts - Stern and Gerlach have confirmed this experimentally for rays from silver atoms.

Ferro-magnetism. Magnetic hysteresis. Remanence and coercive forces

Iron, nickel and cobalt (and Heusler's alloys, for example, 55% copper, 30% manganese, 15% aluminium, which owe their ferro-magnetic character to the manganese) differ from all other para-magnetic bodies in that they themselves become real magnets under the influence of magnetic forces, that is, permanent magnets. However, their magnetism decreases gradually, for example, as the temperature rises or during certain mechanical treatments, but it never disappears totally. They form the ferro-magnetic group of metals (Fig. 564). Nickel and cobalt, viewed as magnets, are practically unimportant; the importance of iron is much greater in electro-technics.

Ferro-magnetism is decisively characterized by the hysteresis of Warburg 1881. A non-magnetic bar of iron (magnetic iron must be demagnetized initially in a solenoid), placed in a magnetic field, becomes magnetic at a certain level. If you remove it from the field, it retains some of it. If you then place it into a field of different intensity, apart from the strength of this field, its magnetization depends also on the amount of its earlier magnetization (magnetic prehistory of iron).

In order to generate the field, you employ a solenoid, push the bar to be investigated into it, magnetize it by turning on the current and gradually strengthening it, then revert the direction of the current and demagnetize it again. (The field is more or less uniform, its strength H can be computed from the dimensions of the solenoid and the current intensity.) The curve 0A (Fig. 565) shows the growth of the intensity of the pole of the iron bar with that of the field. Abscissa is the field intensity H acting on the bar, ordinate the corresponding intensity of the pole B of the bar. Prior to switching on the current - for H = 0 (starting point) - the bar has the pole strength B = 0. As you strengthen the current in the solenoid, the field intensity H grows and more so the pole strength B of the bar. When H = 1, the pole strength B has reached the value 3000 (the point x). Approximately at H = 8, the bar is saturated, its pole strength does not grow further, even if you strengthen the field. If we again weaken the field, also the pole strength of the bar drops, but not so that at the former values of the field strength, for example, H = 1, the former value of the pole strength (B = 3000) again returns. There arises a new curve AC: Now, throughout, there correspond larger values of B to the same values of H. Thus, B = 5800 corresponds to H = 1. When H returns to 0, B is still 5000 (the point C); the residual magnetism is that strong and its strength changes with the kind of iron.

Fig. 564 shows: At a given field intensity H, while still being magnetized, the bar has a smaller pole strength (values of B on the branch ascending to A) than while it is being demagnetized. (values of B on the branch descending from A to D. The difference between the two values of B becomes the smaller the closer is the field strength H to the saturation value and vanishes at this value. If you now send current through the solenoid in the opposite direction, whereby you invert the direction of the magnetic field (H = -1, etc.), the pole strength of the magnet decreases more and more; at about H=-2, it vanishes (the point D), that is, the iron is again not magnetic. If you go to larger negative values of H, the iron inverts its poles. Finally, at H = - 8, you reach again saturation, but with interchanged poles (the point A'). If you now weaken the field again, we have the same experiences as in the upper part of the curve. The pole strength does not move along A'D, but returns along the curve A'C'D', which is initially much flatter. At the field strength H = 0, there remains again a very considerable magnetism (the point C'); only the transition to positive field strengths raises it (the point D'). Hence we can say that iron always tends to hold on to the magnetic state which it has obtained.It resists to some extent the change which the change of the field tries to impose on it. The changes of the pole strength always lag behind those of the field strength. This is the reason why this behaviour is called magnetic hysteresis (Greek: usterew = I stay back). Ferro-magnetic substances differ fundamentally from all other substances by their hysteresis. Only iron, cobalt and nickel as well as certain of their alloys display hysteresis.

The distance 0C, that is, the pole strength which the bar has, although the field strength is zero, displays its residual magnetism. The distance 0D, the field strength required to make B = 0, that is, to make it again unmagnetic after it was previously magnetic in the opposite direction, yields the measure for the force with which it holds on to its acquired magnetism (coercive force). Different kinds of iron differ greatly by their residual magnetism and coercive force and therefore, for given technical applications, they must be selected on the basis of their recorded magnetization curves. Soft iron (Swedish charcoal iron) has the largest residual magnetism, but the smallest coercive force. If it is magnetized, it is soon saturated; if the magnetizing force is again removed, it retains much magnetism; however, the smallest demagnetizing force is sufficient to rid it of magnetism. In contrast, steel retains in the same situation only very little magnetism, but holds on to the little amount, which only a very large, oppositely directed magnetizing force can remove. Hence you can readily make steel into a permanent magnet by means of a sufficiently large magnetizing force; on the other hand, soft iron is useless for this purpose.

Thanks to its property of being very quickly magnetized and demagnetized, iron is the soul of electrotechnics. In certain apparatus and machines, the magnetic circular process occurs every second 50 to 60 times, almost according to Fig. 565 . This to and fro magnetization is opposed by iron by magnetic friction, which leads to hysteresis and is overcome by work. However, this work is wasted, is converted into heat and heats up the iron for no purpose. You can compute from the area in the hysteresis loop the wasted energy. For one ton of soft iron, submitted to 100 magnetization cycles each second, this work is 17 - 18 horse powers (James Alfred Ewing 1855-1935).

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