51. The capacity of a conductor is defined to be the numerical value of the charge on the conductor when its potential is unity, all the other conductors in the field being at zero potential.

Two conductors insulated from each other and placed near together form what is called a condenser; in this case the charge on either conductor may be large, though the difference between their potentials is small.

In many instruments the two conductors are so arranged that their charges are equal in magnitude and opposite in sign; in such cases the magnitude of the charge on either conductor when the potential difference between the conductors is unity is called the capacity of the condenser.

If the difference of potential between two conductors, produced by giving a charge + q to one conductor and - q to the other, is V, then q/V is defined to be the capacity between the conductors.

52. Capacity of a Sphere placed at an infinite distance from other conductors. Let α be the radius of the sphere, V its potential, e its charge, the corresponding charge of opposite sign being at an infinite distance. Then (Art. 17), the potential due to the charge on the sphere at a distance r from the centre is e/r; therefore the potential at the surface of the sphere is e/α.