Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/198

166 opposite to the primary when the secondary wire is approaching the primary wire, and in the same direction when it is receding from it.

In all cases the direction of the secondary current is such that the mechanical action between the two conductors is opposite to the direction of motion, being a repulsion when the wires are approaching, and an attraction when they are receding. This very important fact was established by Lenz.

4. Induction by the Relative Motion of a Magnet and the Secondary Circuit.

If we substitute for the primary circuit a magnetic shell, whose edge coincides with the circuit, whose strength is numerically equal to that of the current in the circuit, and whose austral face corresponds to the positive face of the circuit, then the phenomena produced by the relative motion of this shell and the secondary circuit are the same as those observed in the case of the primary circuit.

531.] The whole of these phenomena may be summed up in one law. When the number of lines of magnetic induction which pass through the secondary circuit in the positive direction is altered, an electromotive force acts round the circuit, which is measured by the rate of decrease of the magnetic induction through the circuit.

532.] For instance, let the rails of a railway be insulated from the earth, but connected at one terminus through a galvanometer, and let the circuit be completed by the wheels and axle of a railway carriage at a distance $$x$$ from the terminus. Neglecting the height of the axle above the level of the rails, the induction through the secondary circuit is due to the vertical component of the earth's magnetic force, which in northern latitudes is directed downwards. Hence, if $$b$$ is the gauge of the railway, the horizontal area of the circuit is $$bx$$, and the surface-integral of the magnetic induction through it is $$Zbx$$, where $$Z$$ is the vertical component of the magnetic force of the earth. Since $$Z$$ is downwards, the lower face of the circuit is to be reckoned positive, and the positive direction of the circuit itself is north, east, south, west, that is, in the direction of the sun's apparent diurnal course.

Now let the carriage be set in motion, then $$x$$ will vary, and