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Consider a spherical shell of radius R ...

Consider a spherical shell of radius R with a total charge `+Q` uniformly spread on its surface (center 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

A

`((Q+q)^2)/(4piepsilon_0a)`

B

Zero

C

`(q^2)/(4piepsilon_0a)`

D

`(Qq)/(4piepsilon_0a)`

Text Solution

Verified by Experts

The correct Answer is:
C
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)`
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