CAPACITANCE

CAPACITANCE (in electrostatics), the charge that must be imparted to a body to bring its potential to a value equal to unity, while all surrounding bodies are assumed to be connected to the ground. A sphere of radius R, located in infinite space and having charge M, acts on external points as if its mass were concentrated at the center. The potential of mass M at distance R, equal to the potential of the sphere V, is given by the formula V = M/R or M = V·R. From this it is evident that the capacitance of a sphere is expressed by the length of its radius R cm. To bring the potential of a sphere to unity, it must be given as many electrostatic C.G.S. units of charge as there are centimeters in its radius. Capacitance in general is a quantity expressed in units of length, and the absolute unit of capacitance is the centimeter. The practical unit of capacitance is called the farad and is equal to 9·10¹¹ electrostatic C.G.S. units. In practice, a capacitance one million times smaller, i.e., 9·10¹¹·10^-6 = 9·10⁵, called the microfarad, is also used.