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Find the electric work done in bringing ...

Find the electric work done in bringing a charge q from A to B in a sphere of charge Q distributed uniformly throughout its volume.
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Text Solution

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The work done by electric force in bringing charge q from A to B is `W_("ele") = q (V_A - V_B)` where
`V_A = (3Q)/(8 pi epsilon_0 R)`,
`V_B = q/(4 pi epsilon_0 R)`
Hence,
`W_("ele") = q ((3 Q)/(8 pi epsilon_0 R) - q/(4 pi epsilon_0 R)) = (Q q)/(8 pi epsilon _0 R)`.
Alternative methode:
The work done from A to B can also be given by `W_("ele")=q int E dr`,
where
`E=(Qr)/(4pi epsilon_(0)R^(3)), r le R`
or `W=q int_(0)^(R)(Q/(4pi epsilon_(0)R^(3))r)dr=(Qq)/(8pi epsilon_(0)R)`
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