A spherical shell of radius `R_(1)` with a uniform charge q has a point charge `q_0` at its center. Find the work performed by the electric forces during the shell expansion from radius `R_(1)` to radius `R_(2)`.

Explanation

The electrical potential energy of the system is
U = self potential of shell + interaction energy of shell and point charge
`(q^2)/(8 pi epsilon_0 R) + (q q_0)/(4 pi epsilon_0 R)`
Initial potential energy of system is
`U_i = (q^2)/(8 pi epsilon_0 R_1) + (q q_0)/(4 pi epsilon_0 R_1)`
Final potential energy of system is
`U_f = (q^2)/(8 pi epsilon_0 R_2) + (q q_0)/(4 pi epsilon_0 R_2)`
From work energy theorem,
`W = - Delta U = - (U_f - U_i) = U_i - U_f` ... (i)
On substituting the values of `U_i` and `U_f` in Eq. (i), we get
`W = (q(q_0 +(q )/(2)))/(4 pi epsilon_0) [(1)/R_(1) - (1)/r_(2)]`
.