A point charge Q is located at the origin. Determine the electrostatic energy stored outside a sphere of radius R that is centred at the origin.

Step-by-step solution

The electric field at a distance r from a point charge Q is given by E = Q 4 ₀ r^2 . The electrostatic energy density in the region is u = 1 2 ₀ E^2 . The total electrostatic energy stored outside a sphere of radius R is obtained by integrating the energy density over the volume from r = R to r = . U = _ R ^ u , dV Substituting u and the volume element dV = 4 r^2 dr : U = _ R ^ 1 2 ₀ ( Q 4 ₀ r^2 )^2 4 r^2 dr U = _ R ^ Q^2 8 ₀ r^2 dr U = Q^2 8 ₀ [ - 1 r ]_ R ^ U = Q^2 8 ₀ R