Page:Elementary Text-book of Physics (Anthony, 1897).djvu/366

352 the force is $$2\pi i.$$ If therefore the force exerted be equal to $$2\pi$$, $$i$$ will be equal to unity. We have thus arrived at another definition of unit current from the point of view of Biot's law. The unit current is defined to be that current which, flowing in a circle of unit radius, will exert upon a unit magnet pole at its centre a force equal to $$2\pi$$ dynes.

297. Ampère's Law for the Mutual Action of Currents.—The mutual action of two currents may also be considered as arising from forces between the elements of the currents. It was from this point of view that the action of currents was first investigated by Ampere. While the results obtained by him were not a unique solution of the problem, and must be regarded only as an artificial representation of the action between currents, they are yet of great interest. Without attempting to deduce Ampère's law, we will briefly consider the experiments upon which his deductions were based.

Ampère's method consists in submitting a movable circuit or part of a circuit carrying a current to the action of a fixed circuit, and in so disposing the parts of the fixed circuit that the forces arising from different parts exactly annul one another, so that the movable circuit does not move when the current in the fixed circuit is made or broken. In the first two of his experiments the movable circuit consists of a wire frame of the form shown in Fig. 86. The current passes into the frame by the points $$a$$ and $$b,$$ upon which the frame is supported. It is evident that the two halves of the frame tend to face in opposite directions in the earth's magnetic field, so that there is no tendency of the frame as a whole to face in any one direction rather than any other. If a long straight wire be placed near to one of the extreme vertical sides of the frame and a current be sent through it, that side will move towards the wire if the currents in it and in the wire be in the same direction, and will move away from the wire if the currents be in opposite directions.