Selfcapacitance

Self-capacitance, or the self-capacitance of an isolated conductor, is the capacitance of that conductor with respect to infinity. It is the proportionality between the net charge on the conductor and its electrostatic potential relative to infinity, expressed by Q = C V, where V is the conductor’s potential when all other conductors are at infinity (ground).

For a simple geometry in free space, the self-capacitance can be computed from the object's shape. A perfectly conducting sphere of radius R in vacuum has C = 4π ε0 R. With ε0 ≈ 8.854×10^−12 F/m, this gives C ≈ 1.11×10^−10 F per meter of radius. Thus a sphere with radius 1 cm has about 1.1 pF, and a sphere with radius 1 m has about 111 pF. In general, self-capacitance depends on geometry and surroundings; irregular shapes or nearby objects can alter the charge distribution and the resulting capacitance.

In the presence of nearby conductors, the simple relation Q = C V is extended to a capacitance matrix that relates charges to potentials of all conductors. The energy stored in a charged conductor is U = Q^2 /(2C) = (1/2) C V^2 for a single conductor.

Self-capacitance is a useful concept in high-voltage engineering, nanotechnology, and electronics for estimating the amount of charge needed to reach a given potential. It is distinct from mutual capacitance between two conductors.