Find the energy stored in a conducting sphere of radius R 1

Find the energy stored in a conducting sphere of radius R = 15 cm and charge Q = 20 C.

Two methods to solve

-You may consider there two be a second conducting sphere whose radius approaches infinity. In this way, there are two spherical conductors which have a capacitance.

-You may alternatively use the energy density formula (but requires integration over spherical volume)

Solution

Capacitor of a spherical capacitor = C = 4*pi*epsilon/(1/a - 1/b)
for b approacing infinity, C= 4*pi*epsilon*a [ where a is the radius of the sphere]
Energy, E = 0.5*Q^2/C = 0.5*Q^2/4*pi*epsilon*a = 0.5*(20*10^-6)^2 / 4*pi*8.854*10^-12 * 0.15 = 11.9897 J