CHAPTER VI

CONSTITUTION OF MAGNETS AND MAGNETIC FIELDS

So far we have confined our attention to the space surrounding magnetised bodies-that is, to the lines of force themselves. We have seen how the presence of these and their general character may be recognised from certain qualitative properties, and we have shown how to measure the quantities which determine their disposition and relations, and how to construct them graphically from numerical data. We must now attempt to obtain some insight into the constitution of the magnet itself; and we shall find that there are certain peculiarities of structure which must be assumed for all bodies through which magnetic lines of force are passing.

A.-The magnetisation

93. Magnetism as a molecular property.-Experiment 41. Dip the whole length of a well-magnetised steel knittingneedle in iron filings. Considerable tufts of filings will adhere to the ends, while at the middle, in the indifferent region, there are no filings. Now break the needle at the middle and repeat the experiment with the two halves. In each case filings will adhere to the two ends, even to those which previously constituted the indifferent region. If each half of the needle is broken up into shorter pieces, each of these will be found to be a complete magnet, with two magnetic ends and an intermediate non-magnetic region.

Since the same result is obtained, however far we continue the subdivision, we are led to the conclusion that

even the smallest particles of which a magnet is composed are themselves magnets. The smallest portions into which a body can be resolved by physical means are called molecules. Thus we conceive of a magnet as built up of socalled molecular-magnets,' magnetic properties being attributed to the molecules themselves. It is an essential feature of the magnetic condition that even the smallest particles of a magnet possess polar properties.

94. Chains of molecular magnets. In accordance with the last experiment, the contrariety of properties of north. and south poles, observed in the case of all magnets, must be supposed to extend to the molecules of which a magnet is built up; the north pole of a molecule being a source of lines of force, and the south pole a sink. But the molecules of a magnet cannot have the directions of their magnetic axes distributed in a purely random way. In the neighbourhood of the indifferent zone, for example, the flux of force proceeding from a positive pole must be taken in by a neighbouring negative pole, belonging to an adjacent molecule, or something of this general character must take place; the axes of the little molecular magnets being set more in the direction of the axis of the nonmagnetised body than in any other. Towards the ends of the magnet, the general set of the molecular axes is along lines which intersect the bounding surface, molecular north poles being outermost at one end and south poles at the other. Lines of force originate at the former end, and terminate at the latter. The simplest conceivable arrangement of the molecular magnets is one in which they form chains, whose separate members lie all in the same direction, and have unlike poles in contact. Then throughout nearly the whole length of the chain, the flux of force will pass from one molecule to the next, only the first and the last of the series having a free pole, that is, one in contact with the surrounding region, into which it sends forth lines of force, or from which it receives them

Any ordered arrangement of the magnetic elements of a body is called magnetisation.

95. Model of a bar magnet composed of molecular magnets. The following models will serve to illustrate the structure of a magnet.

1. A number of small equal rectangular blocks are painted red at one end (north-seeking end) and blue at the other (south-seeking end). These are to represent the molecular magnets; they are arranged end to end in chains, and the chains are arranged to fill an approximately rectangular figure, representing the bar magnet. In the middle of the system, the separate constituents of the magnet are to be set with their axes parallel, each one being directly joined to its neighbours before and behind. In the neighbourhood of the ends the directions of the axes are disposed more irregularly, but still so that at one end it is chiefly north poles that point outwards, and at the other, south poles.

2. Into a rectangular board stick several parallel rows of needles with their points directed vertically upwards. From a piece of steel spring cut pieces as many as there are needles, and of length somewhat less than the distance between consecutive needles. At the middle of each piece make an indentation with a centre-punch; this will cause the two halves to bend round somewhat, so that when the piece of spring is mounted with the indentation supported upon a needle-point, it will not fall off, its centre of gravity being below the point of support. Now magnetise the pieces of spring and mount them upon the needle-points; they arrange themselves in chains and groups which are more or less stable (EWING). At one end of the system all the poles directed outwards are north-seeking, at the other, south-seeking. Now approach to this model of a bar magnet a declination needle in either of the two principal positions mentioned in § 38, and the same effects will be observed as in the case of an actual bar magnet.

96. Uniform magnetisation.-Generally speaking the places of emergence and immergence of lines of force are not confined to the ends of a magnet (compare, for example, fig. 4, p. 17); so that even in the interior the chains of

molecules cannot be regularly arranged, and it is only quite near the middle that the general direction of the molecular magnetic axes is along the axis of the bar. This may be regarded as due to a certain demagnetising influence of the ends,' which brings about a loosening of the combinations of molecular magnets. In bar magnets, then, especially those with free ends, the magnetisation is more or less irregular.

But we may so order the disposition of the lines of force in the interior, that every volume-element of the magnet is in precisely the same magnetic condition; the magnetisation being then called uniform. In the case of very long thin bar magnets, for example, the demagnetising influence of the ends is small; the general direction of the molecular magnetic axes being parallel to the axis of the bar throughout most of its length, and the lines of force appearing almost exclusively at the ends.

To form a model of a bar thus uniformly magnetised we may arrange end to end the little blocks described in § 95, so as to form straight chains of equal length, placed side by side.

The more molecular chains there are ending at the terminal faces of a uniformly magnetised bar, the more lines of force emerge into the surrounding field. Since we suppose every element of the bar to be in the same magnetic condition, the strength of pole m is proportional to the crosssection w, and the same is true for every uniform longitudinal strip of the bar. Again, for any portion of the length of the magnet, the magnetic moment (§ 67) is greater the greater the length, for the ends of the molecular chains, which alone act as poles, are then further apart. A uniformly magnetised bar, as well as any smaller bar cut from it, has therefore a magnetic moment proportional to its cross-section w, and to its length 7, that is, proportional to its volume v.

97. The toroid or anchor-ring. The completely uniform magnetisation of a bar is prevented by the disturbing effect of the ends. Here the lines of force begin to diverge

from one another, as do also the chains of molecular magnets. To obtain an approach to uniform magnetisation in a mass of iron or steel, we must make it in the form of a ring, or some such endless shape. We may then magnetise it so that no lines of force leave or enter it, the direction of magnetisation being everywhere tangential to the surface. When the ring is circular in form and of circular cross-section it is called an anchor ring or toroid (French tore a ring). Since such a toroid neither emits nor absorbs lines of force, it is without external magnetic influence. In its interior also it may be shown that the magnetic force vanishes.

By the method of divided touch' (§ 19), we may produce a very fair approach to uniform magnetisation in such a ring. A more effective method of magnetisation will be described later on.

98. The divided toroid.-Even when the toroid is not quite complete, but is divided by a gap, we may assume the magnetisation to be uniform, provided that the breach of continuity is not too considerable. In that case the lines of force issuing from one face of the gap pass directly over to the other face, comparatively few of them spreading out into the surrounding region.

A nearly closed magnetised toroid, divided only by a narrow air-gap, we shall call a 'divided toroid.'

These two examples of approximately uniform magnetisation, the closed and the divided toroid, have important technical applications. Since they have no assignable poles, their properties cannot be deduced from the ordinary action at a distance theory.

99. Magnetic moment per unit volume; intensity of magnetisation. For a uniformly magnetised body, or for any part of it, the magnetic moment divided by the volume has a perfectly determinate value, which depends upon the degree to which the body is magnetised. For the quotient in question depends on the number and strength of molecular magnets per unit volume, and the closeness with which their axes agree with one another in direction.