Page:Elementary Text-book of Physics (Anthony, 1897).djvu/330

316 take place in the tubes of force, in a manner consistent with what we know of their nature. Thus this latter view furnishes a more adequate representation of the discharge than the older and simpler view.

We haye already seen (§ 267) that the energy contained in each unit tube is equal to one half the difEerence of potential between its ends. Since $$Q$$ represents the number of unit tubes which pass between the plates, the energy of the field is $$\tfrac{1}{2}Q (V_{A} - V_{B});$$ after the discharge this energy has entered the conductor.

If an arrangement be effected by which the difference of potential between $$A$$ and $$B$$ is kept constantly equal to $$(V_{A} - V_{B}),$$ the work done by the transfer of $$Q$$ units of charge, and therefore the energy lost by the disappearance of $$Q$$ unit tubes of force, is $$Q (V_{A} - V_{B}).$$ Let $$W$$ represent the energy lost by such a continuous discharge or current in unit time, and $$t$$ the time in which $$Q$$ tubes of force disappear. Then $$Wt = Q(V_{A} - V_{B}),$$ and The ratio $$\frac{Q}{t}$$ is represented by $$I$$ and called the current strength or simply the current in the conductor. It may be variously considered as the rate of transfer of charge between the conductors, or as the rate at which the unit tubes of force are destroyed.

272. Electrostatic Unit of Current.—Let us denote the potentials at the two points 1 and 2 in a circuit by $$V_{1}$$ and $$V_{2},$$ and let $$V_{1}$$ be greater than $$V_{2}:$$ then if, in the time $$t,$$ a quantity of electricity equal to $$Q$$ passes through a conductor joining those points from potential $$V_{1}$$ to potential $$V_{2},$$ the energy expended is $$Q(V_{1} - V_{2}).$$

If the conductor be a single homogeneous metal or some analogous substance, and if no motion of the conductor or of any external magnetic body take place, the energy expended in the conductor is transformed into heat. If we suppose this transformation to go on at a uniform rate, and denote the heat developed in unit time by $$H,$$ we may substitute $$H$$ for $$W$$ in equation (94), and have