Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/161

478.] transmitting an electric current a magnet is acted on by forces depending on the position of the wire and on the strength of the current. The space in which these forces act may therefore be considered as a magnetic field, and we may study it in the same way as we have already studied the field in the neighbourhood of ordinary magnets, by tracing the course of the lines of magnetic force, and measuring the intensity of the force at every point.

477.] Let us begin with the case of an indefinitely long straight wire carrying an electric current. If a man were to place himself in imagination in the position of the wire, so that the current should flow from his head to his feet, then a magnet suspended freely before him would set itself so that the end which points north would, under the action of the current, point to his right hand.

The lines of magnetic force are everywhere at right angles to planes drawn through the wire, and are there fore circles each in a plane perpendicular to the wire, which passes through its centre. The pole of a magnet which points north, if carried round one of these circles from left to right, would experience a force acting always in the direction of its motion. The other pole of the same magnet would experience a force in the opposite direction.

478.] To compare these forces let the wire be supposed vertical, and the current a descending one, and let a magnet be placed on an apparatus which is free to rotate about a vertical axis coinciding with the wire. It is found that under these circumstances the current has no effect in causing the rotation of the apparatus as a whole about itself as an axis. Hence the action of the vertical current on the two poles of the magnet is such that the statical moments of the two forces about the current as an axis are equal and opposite. Let m1 and m2 be the strengths of the two poles, r1 and r2 their distances from the axis of the wire, T1 and T2 the intensities of the magnetic force due to the current at the two poles respectively, then the force on m1 is m1T1, and since it is at right angles to the axis its moment is m1T1r1. Similarly that of the force on the other pole is m2T2r2, and since there is no motion observed,

$ m_1T_1r_1+m_2T_2r_2=0.$