The capacitance of a system depends only on its shape and on the insulators it contains. In general, the capacitance is quite difficult to calculate, but if the geometry is symmetric, Gauss's law makes it possible to find formulas for C.
Parallel Plates:
The simplest geometry is a pair of parallel plates,
each with area A and separated from each other by a distance d
which is small compared to the width of the plates.
The capacitance of this system is
Cylindrical Capacitor
Another simple geometry is the coaxial cylinder in which an inner
cylindrical conductor of length L and radius a is surrounded by an outer
cylindrical conductor of length L and radius b.
We assume that the length of the cylinder is much greater than its radius.
(The round cable you use to connect a VCR to a TV set is an example
of such a capacitor.)
This system has capacitance
Spherical Capacitor Finally,
a spherical capacitor formed of two concentric spherical
conducting shells, one with large radius b and
the other with small radius a, has
capacitance
If the outer conductor is at infinity, we take the limit
to get the capacitance of an isolated
sphere of radius a:
