# Capacitance of a conductor

Charge given to a conductor increases its potential, i.e.,

*Q*∝

*V*⇒

*Q = CV*

where

*C*is a proportionality constant, called capacity or capacitance of conductor. Hence, capacitance is the ability of conductor to hold the charge.- Its SI unit is
^{–3}F, 1 μF = 10^{–6}F, 1 nF = 10^{–9}F, 1 pF = 1 μF = 10^{–12}F) - Its dimension: .
- Capacity of a body is independent of charge given to the body or its potential raised and depends on shape and size only.

# Capacity of an isolated spherical conductor

When charge

*Q*is given to a spherical conductor of radius*R*, then potential at the surface of sphere is (Fig. 1).**Fig. 1**

⇒

If Earth is assumed to be a conducting sphere having radius

*R*= 6400 km. Its theoretical capacitance*C*= 711 μF. But for all practical purposes capacitance of Earth is taken infinity and its potential*V*= 0.# Energy of a charged conductor

Electrostatic potential energy of a conductor carrying charge

*Q*, capacitance*C*, and potential*V*is given by