Galvanometer Constant

The strength at the centre of a coil of the magnetic field produced by a unit current flowing in it, is called the galvanometer constant of the coil.

Hence, if a current i be flowing in a coil of which the galvanometer constant is G, the strength of the field at the centre of the coil is Gi, and the lines of force are at right angles to the coil.

Let us suppose that a coil, of which the galvanometer constant is G, is placed in the magnetic meridian, with a magnet at its centre, and that the dimensions of the magnet are so small that, throughout the space it occupies, we may treat the magnetic field as uniform; then, if the magnet be deflected from the magnetic meridian, through an angle φ by a current i, the moment of the force on it due to the coil is GiMcosφ, M being the magnetic moment of the magnet, while the moment of the force, due to the earth, is HMsinφ; and since these must be equal, the magnet being in equilibrium, we have

In using a tangent galvanometer it is not necessary that the earth's directing force alone should be that which retains the magnet in its position of equilibrium when no current passes round the coil. All that is necessary is that the field of force in which the magnet hangs should be uniform, and that the lines of force should be parallel to the coils. This may be approximately realised by a suitable distribution of permanent magnets.

If the coil of wire can be turned round a vertical axis through its centre, parallel to the plane of the circles, the instrument can be used as a sine galvanometer. For this purpose place the coils so that the axis of the magnet lies in their plane before the current is allowed to pass. When the current is flowing, turn the coils in the same direction as the magnet has been turned until the axis of the magnet again comes into the plane of the coils, and observe the angle ^ through which they have been turned. Then we can show, as in chap, xviii, that

To obtain these formulae, we have supposed that the dimensions of the magnet are small compared with those of the coil. If this be not the case, the moment of the force produced by the magnetic action of the coil when used as a tangent galvanometer is not MGcosφ, as above, but involves other terms depending on the dimensions of, and distribution of magnetism in, the magnet.

In order to measure the deflexions, two methods are commonly in use. In the first arrangement there is attached to the magnet, which is very small, a long pointer of glass, aluminium, or some other light material. This pointer is rigidly connected with the magnet, either parallel to or at right angles to its axis, and the two, the magnet and pointer, turn on a sharp-pointed pivot, being supported by it at their centre, or are suspended by a fine fibre free from torsion. A circle, with its rim divided to degrees, or in good instruments to fractions of a degree, is fixed in a horizontal plane so that the axis of rotation of the magnet passes through its centre, and the position of the magnet is determined by reading the division of this circle with which the end of the pointer coincides. In some cases the end of the pointer moves just above the scale, in others the pointer is in the same plane as the scale, the central portion of the disc on which the graduations are marked being cut away to leave space for it, and the graduations carried to the extreme inner edge of the disc. With the first arrangement it is best to have a piece of flat mirror with its plane parallel to the scale, beneath the pointer, and, when reading, to place the eye so that the pointer covers its own image formed by reflexion in the mirror. The circle is usually graduated, so that when the pointer reads zero, the axis of the magnet is parallel to the plane of the coils if no current is flowing.

In order to eliminate the effects of any small error in the setting, we must proceed in the following manner: Set the galvanometer so that the pointer reads zero, pass the current through it, and let θ be the deflexion observed. Reverse the direction of the current so that the needle may be deflected in the other direction; let the deflexion be θ'. If the adjustments were perfect - the current remaining the same - we should have θ and θ' equal; in any case, the mean, (θ+θ')/2, will give a value for the deflection corrected for the error of setting.

To obtain a correct result, however, the position of both ends of the pointer on the scale must be read. Unless the pointer is in all positions a diameter of the circle, that is, unless the axis of rotation exactly coincides with the axis of the circle, the values of the deflexions obtained from the readings at the two ends will differ. If, however, we read the deflexions θ, θ₁, say, of the two ends respectively, the mean (θ+θ₁), will give a value of the deflexion corrected for errors of centering.⁽¹⁾ Thus, to take a reading with a galvanometer of this kind, we have to observe four values of the deflexions, viz. two, right and left of the zero respectively, for each end of the needle. This method of reading should be adopted whether the instrument be used as a tangent or a sine galvanometer.

The second method of measuring the deflexion has been explained at full length in the account of the last experiment (p. 391). A mirror is attached to the magnet, and the motions of the magnet observed by the reflexion by it of a spot of light on to the scale. The following modification of this method is sometimes useful.⁽²⁾ A scale is fixed facing the mirror, (which should in this case be plane) and parallel to it. A virtual image of this scale is formed by reflexion in the mirror, and this image is viewed by a telescope which is pointed towards the mirror from above or below the scale. The telescope has cross-wires, and the measurements are made by observing the division of the scale, which appears to coincide with the vertical cross-wire, first without, and then with a current flowing in the coiL For details of the method of observation see §23.

In the best tangent galvanometers⁽³⁾ there are two coils, of the same size and containing the same number of turns, placed with their planes parallel and their centres on the same axis. The distance between the centres of the coils is equal to the radius of either, and the magnet is placed with its centre on the axis midway between the two coils. It has been shown⁽⁴⁾ that with this arrangement the field of force near the point at which the magnet hangs is more nearly uniform than at the centre of a single coil. It has also been proved that in this case, if G be the galvanometer constant, n the number of turns in the two coils, r the mean radius, and ζ the depth of the groove filled by the wire, then

Various other forms of galvanometers have been devised for special purposes. Among them we may refer to those which are adapted to the measurement of the large currents required for the electric light. An account of Sir William Thomson's graded galvanometers arranged for this purpose will be found in 'Nature,' vol. xxvi p. 506, while the latest forms of the instruments designed by Professors Ayrton and Perry are described in the 'Philosophical Magazine' for April 1884.

(1)	See Godfray's Astronomy, §93
(2)	See §23, p. 146.
(3)	Helmholtz's arrangement, Maxwell, Electricity and Magnetism, vol. ii. §715.
(4)	Maxwell, Electricity and Magnetism, vol. ii. §713.