Capacitance of a Sphere

Description:

To find the capacitance of a sphere, a metallic sphere of radius R is taken and charge of charge q is given to it. Due to this charge, the potential of sphere raised to V.  So the capacitance due to charge ‘q’ and potential ‘V will be :

C = q/v -----(1)

We know that, potential of a conducting sphere is :

V = 1/4πε₀ Q/R

Putting the value of potential in equation (1) we get:

C = q * 4πε₀ * R/q

C = 4πε₀ * R

Note − Capacitance of a sphere depends on the radius of the sphere. It does not depend on the area or volume of the sphere.

Capacitance of Earth

We know:

Radius of Earth = 6400000 m

Value of 4πε₀ = 1/9 + 10⁹

C = 1 + 6400000/9 + 10⁹

C = 1 + 64/9 + 10⁹

C = 7.1 * 10^-4

Or, C = 711 * 10^-6

C = 711μf.

Or, C_earth = 710μf