Electro-Magnetic Unit Quantity

Consider a wire one centimetre in length bent into an arc of a circle one centimetre in radius. Let such a quantity of electricity flow per second across any section of this wire as would produce on a unit magnetic pole placed at its centre, a force of one dyne. This quantity is the electro-magnetic unit of quantity of electricity, and the current produced is the electro-magnetic unit of current.

With this definition understood then, we may say that if a current of strength i traverse a wire of length l bent into an arc of a circle of radius r, the force on a magnetic pole of strength m placed at the centre of the circle will be mil/r² dynes in a direction normal to the circle, and the strength of the magnetic field at the centre is il/r².

The magnetic field will extend throughout the neighbourhood of the wire, and the strength of this field at any point can be calculated. Accordingly, a magnet placed in the neighbourhood of the wire is affected by the current, and disturbed from its normal position of equilibrium.

It is this last action which is made use of in galvanometers. Let the wire of length l be bent into the form of a circle of radius r, then we have

and the strength of the field, at the centre of the circle, is 2πi/r.

Moreover, we may treat the field as uniform for a distance from the centre of the circle, which is small compared with the radius of the circle. If then we have a magnet of moment M, whose dimensions are small compared with the radius of the circle, and if it be placed at the centre of the circle so that its axis makes an angle θ with the lines of force due to the circle, and therefore an angle of 90°-θ with the plane of the circle, the moment of the force on it which arises from the magnetic action of the current is 2πM i sin θ/r.

If, at the same time, φ4 be the angle between the axis of the magnet and the plane of the meridian, the moment of the force due to the horizontal component H of the earth's magnetic force is MHsin φ; if the small magnet be supported so as to be able to turn round a vertical axis, and be in equilibrium under these forces, we must have the equation

or

if then we know the value of H, and can observe the angles φ and θ, and measure the distance r, the above equation gives us the value of i.

Two arrangements occur usually in practice. In the first the plane of the coil is made to coincide with the magnetic meridian; the lines of force due to the coil are then at right angles to those due to the earth, and

Hence

and we have

The instrument is then called a tangent galvanometer. In the second the coil is turned round a vertical axis until the axis of the magnet is in the position of equilibrium in the same plane as the circle; the lines of force due to the coil are then at right angles to the axis of the magnet, so that the effect of the current is a maximum, and θ=90°. In these circumstances, therefore, we have, if ψ be the deflection of the magnet,

The instrument is in this case called a sine-galvanometer.

We shall consider further on, the practical forms given to these instruments. Our object at present is to get clear ideas as to an electric current, and the means adopted to measure its strength.

The current strength given by the above equation will, using C.G.S. units of length, mass, and time, be given in absolute units. Currents, which in these units are represented by even small numbers, are considerably greater than is convenient for many experiments. For this reason, among others, which will be more apparent further on, it is found advisable to take as the practical unit of current, one-tenth of the C.G.S. unit. This practical unit is called an ampere.