When a conductor is charged its potential increases. It is found out by experimentally that for an isolated conductor (conductor should be of finite dimension, so that potential of infinity can be assumed to be zero) potential of the conductor is proportional to charge given to it.

$q \propto V \Rightarrow q=C V$

$q=$ charge on conductor

$V=$ potential of conductor

and $\mathrm{C}$ is proportionality constant called capacitance of the conductor.

Note :

(1) C does not depends on the q and V.

Let the radius of an isolated spherical conductor is $\mathrm{R}$.

And let there is charge $Q$ on sphere.

$$ \therefore $$ Potential V $=\frac{\mathrm{KQ}}{\mathrm{R}}$

Hence by formula : $Q=C V$

$$ \begin{aligned} & Q=\frac{C K Q}{R} \\\\ & C = 4\pi { \in _0}R \end{aligned} $$

$$ \therefore $$ Capacitance of an isolated spherical conductor

$$C = 4\pi { \in _0}R$$

Note :

(1) If the medium around the conductor is vacuum or air.

$C_{\text {Vacuum }}=4 \pi { \in _0} R$

Where $\mathrm{R}=$ Radius of spherical conductor. (may be solid or hollow.)

(2) If the medium around the conductor is a dielectric of constant $\mathrm{K}$ from surface of sphere to infinity.

$\mathrm{C}_{\text {medium }}=4 \pi { \in _0} \mathrm{KR}$

(3) $\frac{\mathrm{C}_{\text {medium }}}{\mathrm{C}_{\text {air/vaccum }}}=\mathrm{K}=$ dielectric constant.

(4) C depend on the shape and size of the conductor.

(5) C depend on the medium where conductor presents.

(6) C depend on the presence of other charges or conductor.