Page:Elementary Text-book of Physics (Anthony, 1897).djvu/303

§ 256] It is the quantity of electricity transferred during one second by a current of one ampere (§ 291).

256. Electrical Potential.— The electrical forces have a potential similar to that discussed in §§ 53–57. The unit quantity of positive electricity is taken as the test unit. Since (§ 252, (4)) the potential at every point of a charged conductor is the same, the surface of the conductor is an equipotential surface. The potential of this surface is often called the potential of the conductor. A conductor joined to ground is at the potential of the earth. It will be shown (§ 260) that the potential of the earth is not appreciably modified when a charged conductor is joined to ground.

For these reasons it is usual to take the potential of the earth as the fixed potential or zero from which to reckon the potentials of electrified bodies. The potential of a freely electrified conductor and of the region about it is thus positive when the charge of the conductor is positive, and negative when it is negative. A conductor joined to ground is at zero potential.

The difEerence of potential between two points is equal to the work done in carrying a unit quantity of electricity from one point to the other. We then have the equation $$Q (V' - V) = $$ work. Hence follows the dimensional equation $$[V' - V] = \frac{ML^2T^{-2}}{M^{\frac{1}{2}}L^{\frac{3}{2}}T^{-1}} = M^{\frac{1}{2}}L^{\frac{1}{2}}T^{-1},$$ the dimensions of difference of potential in electrostatic units. If any distribution of a charge exist on a conductor, which is such that the potential at all points in the conductor is not the same, it is unstable, and a rearrangement goes on until the potential becomes everywhere the same. The process of rearrangement is said to consist in a flow of electricity from points of higher to points of lower potential.

On this property of electricity depends the fact that a closed conducting surface completely screens bodies within it from the action of external electrical forces. For, whatever changes in potential occur in the region outside the closed conductor, a redistribution will take place in it such as to make the potential of every