Consider a spherical shell of radius R wil a total charge +Q uniformly spread on its surface (centre of the shell lies at the origin x =0) Two point charge q and -q are brought, one after the other, from far away and placed at `x = -a//2` and `x = +a//2(a lt R)` respectively. Magnitude of the work done in this process is

Options

A. `((Q+q)^2)/(4piepsilon_0a)`
B. Zero
C. `(q^2)/(4piepsilon_0a)`
D. `(Qq)/(4piepsilon_0a)`

Answer

C

Explanation

Initial PE of system
`U_i = (Q^2)/(8 pi epsilon_0R)` (Self energy of shell)
Final PE of system
`=Q/(8 pi epsilon_0R)+(q(-2))/(4piepsilon_0a)+(kQq)/R+(KQ(-q))/(R)`
`=Q/(8 pi epsilon_0R)+(q^2)/(8 pi epsilon_0a)`
Work done `=U_f -U_i`
`=(-q^2)/(4 pi epsilon_0a)`
Magnitude of work done `=(q^2)/(4 pi epsilon_0a)`