Find the ratio of electric work done in bringing a charge `q` from `A` to `B(W_(AB))` and that from `B` to `C(W_(BC))` in a sphere of charge `Q` distributed uniformly throughout its volume.

Options

A. `1`
B. `1.5`
C. `0.75`
D. None of these

Answer

A

Explanation

Work done by electric field
`W_(AB) = q(V_(A) - V_(B))`
`= q[(3Q)/(8 pi epsilon_(0)R)-(Q)/(4pi epsilon_(0)R)]`
`= (Qq)/(8pi epsilon_(0)R)`
`W_(BC) = q(V_(B) - V_(C))`
`= q[(Q)/(4 pi epsilon_(0)R)-(Q)/(8pi epsilon_(0)R)]`
`= (Qq)/(8pi epsilon_(0)R)`
`rArr (W_(AB))/(W_(BC)) = 1`