Consider a uniformly charged spherical shell of radius R having charge Q charge Q can be through to be made up of number of point charges `q_(1),q_(2),q_(3). . . ` etc. the electrostatic energy of the charged shell is sum of interaction energies of all possible pairs of charges.
`U=sum(q_(i)q_(j))/(4piepsilon_(0)r_(ij))`
Where `r_(ij)` is distance between `q_(i)` and `q_(j)`. for continuous charg on the shell, the summation has to be carried through intergration.
(a). Calculate the electrostatic energy of the shell. We can term this energy as self energy of the shell.
(b). Calculate the work done in assembling a spherical shell of uniform charge Q and radius R by bringing charges in small installments from infinity and putting them of the shell. Do you ding the answers in (a) and (b) to be same?

Answer

(a). `(Q^(2))/(8 pi in_(0)R)`
(b). Same as in (a)