Magnetism

Magnetic Field and Magnetic Moment.

When a small pivoted compass needle is placed near a magnet, it alines itself in a definite direction, this alinement being due to the forces acting on the needle. A region in which such magnetic effects occur constitutes a magnetic field of force. The ordinary orientation of the compass needle is due to the magnetic field of the earth which may be regarded as uniform (homogeneous) over wide regions. A magnet with its equal and opposite poles therefore experiences no resultant force as a whole in the earth's field (as shown by the old experiment of the floating needle) but a couple is exerted on it whose magnitude is a maximum when the needle is at right angles to the magnetic meridian. The strength of a magnetic field, at a point, or the magnetic intensity or force, is measured by the force which a unit pole will experience at that point, the direction being taken as that in which a north pole is urged. The unit is known as the gauss. If H is the strength of the earth's field, 0 the angle between the magnetic axis of the needle and the direction of H (the magnetic meridian), the couple, G, is given by M is the magnetic moment of the needle, and is equal to the product of pole strength into the distance between the poles; M = ml. The conception of magnetic moment is more useful than that of magnetic pole. Magnetic poles do not occur separately (as do positive and negative charges of electricity), and the simplest magnetic piece of matter of physical significance which can be imagined is a small particle possessing a definite magnetic moment. The conception of magnetic poles, charges of magnetism of one sign, is a violent abstraction, but it is frequently useful for it enables much of the mathematical theory of electrostatics and gravitation to be at once adapted to magnetism.

Any magnet may be regarded as built up of a large number of "magnetic particles" with definite moments and with magnetic axes in definite directions. If a number of equal particles are joined end to end, a "line magnet" will be produced, all the poles except those at the ends neutral izing each other. A bar magnet may be regarded as being made up of a large number of line magnets, not necessarily of equal length, placed side by side. The magnetic moment of any small volume will be equal to the sum of the moments of the elementary particles contained in it. The intensity of magnetization at any point may be defined as the ratio of the magnetic moment of a small volume round the point divided by that volume, the direction of magnetization being that of the magnetic axis of the small volume. In terms of pole, the intensity is the pole strength per unit area. Intensity of magneti zation, denoted by I, has thus magnitude and direction. In a uniformly magnetized body I is everywhere the same.

The field round a magnet may be "explored" very easily with the aid of a small compass needle. The needle will set itself along the tangent to the lines giving the direction of the magnetic The lines of force can therefore be readily mapped out. The strength of the field may be estimated by allowing the needle tc oscillate. The frequency of the oscillations will vary approximately as the square root of the magnetic force at the region. The gen eral character of the field may be shown by the neat method which suggested to Faraday the conception of lines of force. A piece

of cardboard is placed over the magnet, sprinkled evenly with iron filings, and then gently tapped. The filings arrange them selves in a series of curves, such as those shown in fig. i. The slightly elongated filings become magnetized most easily along their length, and when the card is tapped, they tend to orientate in the direction of the field for the same reason as does the compass needle.

When a bar magnet such as has so far been considered is placed in a uniform field, each element of the magnet is subject to a force which will be feeble in the middle of the magnet and strong in the region of the poles. Although the resultant force on the magnet as a whole will be zero, there will be oppositely directed resultant forces on the two halves of the magnet. The poles may be more precisely defined as the two points through which the resultant forces act. A bar magnet has not necessarily equal and opposite poles at each end; it may be magnetized so as to have equal poles at the ends, and an opposite pole in the centre— indeed, any number of so-called "consequent poles" may be pro duced. On the other hand, a ring-shaped specimen may be magnetized in such a way as to have no free poles at all.

Induced Magnetism.

The behaviour of a piece of soft iron in a magnetic field indicates that the iron itself becomes a magnet. It is said to be magnetized by induction. The attraction of iron by the poles of a magnet is due to the non-uniformity of the field, for, owing to the induced poles being equal and opposite, there can be no resultant force if the field is uniform. The iron moves towards regions of stronger magnetic force.

The force inside a magnetized body can only be given a definite meaning if it is imagined that a cavity is scooped out of the body in which the magnetic force could be measured. It may be shown that the force will in general vary with the shape and size of the but that values independent of the precise di mensions may be obtained by specifying the shape in a suitable way. All the dimensions of the cavity are to be imagined large compared with the size of the molecules (say i cm.) and small compared with the distance over which the intensity of magneti zation might vary appreciably (say cm.). The most useful conceptions are arrived at by supposing a cylinder is removed, the axis of the cylinder being in the direction of the magnet ization at the point considered. The force which would be exerted on unit pole within a long thin cylinder (fig. 2, a) is known as the magnetic force, H; that within a cylinder whose length is very small compared with the linear dimensions of the ends as the magnetic induc tion, B (fig. 2, b). In the sec ond case the force is increased by that due to the poles on the end surfaces, whose effect in the first case is negligible, and it may be shown, if I is the intensity of magnetization, that It may further be mentioned here that in a spherical cavity, the force H' is given by These results were first given by Poisson, who developed a general mathematical expression giving the forces due to a magnetic body in terms of an equivalent volume and surface distribution of magnetism.