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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 63490.png
    Smaller SI units are mF, μF, nF and pF (1 mF = 10–3 F, 1 μF = 10–6 F, 1 nF = 10–9 F, 1 pF = 1 μF = 10–12 F)
  • Its dimension: 63505.png.
  • 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
63511.png 63517.png
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

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