2.11 CAPACITORS AND CAPACITANCE

A capacitor is a system of two conductors separated by an insulator (Fig. . ). The conductors have charges, say Q1 and Q2, and potentials V1 and V2.

Usually, in practice, the two conductors have charges Q and – Q, with potential difference V = V1 – V2 between them. We shall consider only this kind of charge configuration of the capacitor. (Even a single conductor can be used as a capacitor by assuming the other at infinity.) The conductors may be so charged by connecting them to the two terminals of a battery. Q is called the charge of the capacitor, though this, in fact, is the charge on one of the conductors – the total charge of the capacitor is zero.

The electric field in the region between the conductors is proportional to the charge Q. That is, if the charge on the capacitor is, say doubled, the electric field will also be doubled at every point. (This follows from the direct proportionality between field and charge implied by Coulomb’s law and the superposition principle.) Now, potential difference V is the work done per unit positive charge in taking a small test charge from the conductor to against the field. Consequently, V is also proportional to Q, and the ratio Q/V is a constant: