Capacitance of isolated spherical conductor

Capacitance of isolated spherical conductor”:

consider an isolated spherical conductor of radius R.  Let  +Q charge be given to it then charge is distributed uniformly over its outer surface in this condition the surface of a conductor will be an equipotential surface as a result the electric field lines emerging out from it. we know that the electric field lines are normal to the charged surface.  Thus on producing this electric field lines backward they are appeared to coming from centre. Therefore, these distributed charge on the sphere behaves like a point charge which is concentrated at the centre of a sphere.

 we know that:
The electric potential due to point charge +Q at the distance R is--

 ( V = 1/4π£oK × Q/R )    volt

By the definition:
Electric capacitance,
C = Q/V
( Putting the value of V )

C = Q / ( 1/4π£oK × Q/R )

{ C = 4π£oK × R }  farad

For air/vacuum, K = 1

Hence,  ( C = 4π£oR )  farad ----eqn1

This is the capacitance of a spherical conductor.

we know that the term (4π£o) is a constant.
Hence,  [ C α R ]

In CGS system :
1/4π£o =1
Hence, 4π£o = 1

Putting this value in eqn1
[ C = R ]  stat-farad

It is clear from above relation that in CGS system the capacitance of a spherical conductor is numerically equal to the its radius.