Magnetic Measurements - field, magnet, needle, ratio, moment, angles and susceptibility

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MAGNETIC MEASUREMENTS One of the simplest pieces of apparatus used for magnetic measurements is the magnetometer (q.v.), which consists of a small magnetic needle (single or composite) pivoted, or suspended usually in such a way that the torsional control of the suspension is small. There are many forms of the instrument suitable for different purposes. In the simple pivoted type of instrument, the needle usually has attached to it at right angles a long pointer whose ends move over a circular scale marked in degrees. In the suspended magnet type (a typical example is represented in fig. 4), a mirror is attached to the needle, and the deflection measured by means of a lamp and scale. Essentially magnetometers measure a magnetic field by comparison with a standard field, e.g., that of the earth, or a field artificially produced.

Let H be the standard field (say the earth's horizontal field) and F the field which it is desired to measure, arranged to be at right angles to H. Normally the needle lies in the direction of H, and, when the field F is applied, it will be deflected through an angle 0 (see fig. 5), where By observing 0, F may be determined if H is known.

Magnetic Moment.

One of the most accurate methods for determining the moment, M, of a bar magnet is that of C. F. Gauss, which also gives the value of H, the earth's horizontal field. The magnet is first suspended horizontally in the earth's field, and caused to vibrate in small arcs. If the torsional con trol of the suspension is small, the time of oscillation is given by where K is the moment of inertia of the magnet. A correction may be applied for the torsional control, which is equivalent to an increase in H. The product MH can thus be determined accurately, provided the field is uniform and not sufficiently strong to cause an alteration in the moment of the magnet.

The ratio M/H is then found by a magnetometric method.

Susceptibility: Dia-, Para- and Ferro-magnetics.—The ratio of the intensity of magnetization to the magnetic field (the field inside the specimen) is known as the susceptibility, and is usually denoted by K ; and the ratio of the induction to the field is termed the permeability, The susceptibility is a measure of the magnetic moment per unit volume in unit field. It is sometimes more convenient to deal with

the specific susceptibility, x, a measure of the moment per unit mass, and defined by There are two main classes of magnetic substances, dia- and paramagnetics (in some cases, under different conditions, a single substance may exhibit both dia- and paramagnetic properties). For diamagnetics, the susceptibility is negative. The magnetiza tion induced is in the opposite direction to that of the field. The permeability, µ , correspondingly, is less than one, so that the induction B is less than in the surrounding medium. For dia magnetics, The magnet is placed so that the field it produces at the mag netometer needle is at right angles to the magnetic meridian. Let m be the pole strength and 2/ the distance between the poles of the magnet (for a cylindrical magnet whose length is from Jo to 3o times its diameter, this is approximately f, of the length). Let d be the distance from the centre of the magnet to the magnetometer needle, 0 the deflection of the needle : (I) In the end-on position (the A position of Gauss, see fig. 6) the magnet is placed so that its axis is in a line which is perpen dicular to the magnetic meridian and which passes through the centre of suspension of the needle.

Then, for the field due to the magnet, (2) In the broadside-on position (B position of Gauss) the magnet is placed at right angles to the magnetic meridian so that the direction of the undeflected suspended needle bisects it at right angles (fig. 7), and From the values of M/H and MH, M and H may be found separately.

It will be noticed that the ratio of the magnetic field due to the magnet in the two positions for the same value of d is equal to 2. It may be shown that if the force between two poles varies as the inverse nth power of the distance between them, the ratio would be equal to ?I. An accurate and fairly direct confirmation of the in verse square law may be obtained by magnetometric experiments with magnets in the various positions.