Galvanometers

The galvanometer already described, as used in the last section, was supposed to consist of a single turn of wire, bent into the form of a circle, with a small magnet hanging at the centre. If, however, we have two turns of wire round the magnet, and the same current circulates through the two, the force on the magnet is doubled, for each circle producing the same effect, the effect of the two is double that of one; and if the wire have n turns, the force will be n times that due to a wire with one turn. Thus the force which is produced by a current of strength i, at the centre of a coil of radius r, having n turns of wire, is 2nπi/r.

But we cannot have n circles each of the same radius, having the same centre; either the radii of the different circles are different, or they have different centres, or both these variations from the theoretical form may occur. In galvanometers ordinarily in use, a groove whose section is usually rectangular is cut on the edge of a disc of wood or brass, and the wire wound in the groove.

The wire is covered with silk or other insulating material, and the breadth of the groove parallel to the axis of the disc is such that an exact number of whole turns of the wire lie evenly side by side in it.

The centre of the magnet is placed in the axis of the disc symmetrically with reference to the planes which bound the groove. Several layers of wire are wound on, one above the other, in the groove. We shall call the thickness of a coil, measured from the bottom of the groove outwards along a radius, its depth.

Let us suppose that there are n turns in the galvanometer coil. The mean radius of the coil is one n^th of the radius of a circle, whose circumference is the sum of the circumferences of all the actual circles formed by the wire; and if the circles are evenly distributed, so that there are the same number of turns in each layer, we can find the mean radius by taking the mean between the radius of the groove in which the wire is Wound and the external radius of the last layer. Let this mean radius be r; and suppose, moreover, that the dimensions of the groove are so small that we can neglect, the squares of the ratios of the depth or breadth of the groove to the mean radius r, then it can be shown⁽¹⁾ that the magnetic force, due to a current i in the actual coil, is n times that due to the same current in a single circular wire of radius r, so that it is equal to 2nπi/r.

And if the magnet be also small compared with r, and the plane of the coils coincide with the meridian, the relation between the current i and the deflection φ is given by

Unless, however, the breadth and depth of the coil be small compared with its radius, there is no such simple connection as the above between the dimensions of the coil and the strength of the magnetic field produced at its centre. The strength of field can be calculated from the dimensions, but the calculation is complicated, and the measure-merits on which it depends are difficult to make with accuracy.

(1)	Maxwell, Electricity and Magnetism, vol ii. §711