# Capacitance of a Spherical Conductor (or) Capacitor

## Capacitance of a Spherical Conductor (or) Capacitor

Capacitor is a device that stores electrostatic field energy. Capacitors provide temporary storage of energy in circuits and can be made to release the energy when required. The property of a capacitor that characterizes its ability to store energy is called its capacitance. When energy is stored in a capacitor, an electric field exists within the capacitor.

As we have already known that a single conductor can also act as a capacitor, here we will find the capacitance of a single isolated sphere. For this, let a charge q be given to a spherical conductor of radius R and then potential on it is $$V=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{q}{R}$$.

The other conductor is supposed to be at infinity, whose potential will be taken as zero. So, the potential difference between the sphere and the conductor at infinity becomes, V – 0 = V.

Then capacitance is $$C=\frac{q}{V}=4\pi {{\varepsilon }_{0}}R$$.

Thus, the capacitance of a spherical conductor is $$C=4\pi {{\varepsilon }_{0}}R$$.

For example, the earth is a spherical conductor of radius $$R=6.4\times {{10}^{6}}m$$. The capacitance of the earth is:

$$C=4\pi {{\varepsilon }_{0}}R=\left( \frac{1}{9\times {{10}^{9}}} \right)\times \left( 6.4\times {{10}^{6}} \right)=711\times {{10}^{-6}}F=711\mu F$$.

Therefore, we can say that Farad is a big unit. Thus, nobody in the universe can have a capacitance of 1F.