Page:Elementary Text-book of Physics (Anthony, 1897).djvu/386

372 '''310. Determination of the Unit of Resistance.'—If the circuit considered in § 306 move from a point where its potential relative to the magnet pole is $$m\Omega '$$ to one where it is $$m\Omega,$$ provided that the magnetic pole do not pass through the circuit, and that the movement be so carried out that the induced current is constant, the electromotive force of the induced current is $$-\frac{m(\Omega ' - \Omega)}{t}\cdot$$ If the movement take place in unit time, and if $$m(\Omega ' - \Omega)$$ also equal unity, the electromotive force in the circuit is the unit electromotive force.''

The expression $$m(\Omega ' - \Omega)$$ is equivalent to the change in the number of tubes of induction passing through the circuit in the positive direction. More generally, then, if a circuit or part of a circuit so move in a magnetic field that, in unit time, the number of tubes of induction passing through the circuit in the positive direction increase or diminish by unity, at a uniform rate, the electromotive force induced is unit electromotive force.

This definition is consistent with the one given in § 303. For, the energy of a circuit carrying the current $$i,$$ due to the field in which it is placed, equals $$iN,$$ and the change of this energy in unit time is the energy expended in the circuit in that time. But this change in energy is $$i\frac{N' - N}{t},$$ and $$\frac{N' - N}{t}$$ is the electromotive force, so that ie represents the energy expended in unit time.

A simple way in which the problem can be presented is as follows: Suppose two parallel straight conductors at unit distance apart, joined at one end by a fixed cross-piece. Suppose the circuit to be completed by a straight cross-piece of unit length which can slide freely on the two long conductors. Suppose this system placed in a magnetic field of unit intensity, so that the lines of force are everywhere perpendicular to the plane of the conductors. Then, if we suppose the sliding piece to be moved with unit velocity perpendicular to itself along the parallel conductors, the electromotive force set up in the circuit will be the unit electromotive force, and if it move with any other velocity $$v,$$ the electromotive force will be equal to $$v.$$