A point charge Q is placed at the origin . Find the electrostatic energy stored outside the sphere of radius R centred at the origin.

Explanation

To find the potential energy, we assume that the charge is brought from `infty` and given to the shell .During this process work will be done against the electron field of charge already present on the shell.
Let at a certain instant, the charge on the shell is q. the potential at its surface is `V = ( q)/(4 pi epsilon_(0)R)`
The work done in bringing a charge dp from infinity to the surface of the shell is `d W = ( V-0)` dq ( infinity at zero potential )
`implies dW = ( q)/( 4pi epsilon_(0)R) dq`
`implies W = int _(0)^(Q) ( qdq)/(4 pi epsilon_(0)R)`
`implies U = ( Q^(2))/( 8 pi epsilon_(0)R)`