Electrical Engineering ⇒ Topic : Capacitance of an Isolated Sphere

.We can find the capacitance of an isolated spherical conductor by assuming that "missing" plate is earth (zero potential). Suppose an isolated conducting sphere of radius r is placed in a medium of relative permittivity Er as shown in Figure.Let charge +Q be given to this spherical conductor. The charge is spread *uniformly over the surface - of the sphere. Therefore, in order to find the potential at any point on the surface of sphere (or outside the sphere), we can assume that entire charge + Q is concentrated at the centre 0 of the sphere.

Potential at the surface of the sphere, V  =

Capacitance of isolated sphere, C =

The following points may be noted :

The capacitance of an isolated spherical conductor is directly proportional to its radius.Therefore, for a given potential, a large spherical conductor (more r) will hold more charge Q (= CV) than the smaller one.

Unit of ε₀ = C/4nr = F/m. Hence, the SI unit of ε₀  is F/m.