In the following arrangement

Options

A. `V_(A) = (Q(2 sqrt(2) - 1))/(4 pi in_(0) sqrt(2) R)`
B. `V_(B) = (Q(sqrt(2) - 1))/(4 pi epsilon_(0) R)`
C. `W.D.` in moving a charge `+q` from `B` to `A`
`W_(BA) = (qQ(3sqrt(2) - 3))/(4sqrt(2) pi epsilon_(0) R)`
D. all options are correct

Answer

4

Explanation

`V_(A) = (1)/(4 pi in_(0)) [ (2Q)/(R ) + (-Q)/(sqrt(2) R)] = (Q(2sqrt(2) - 1))/(4 pi in_(0) sqrt(2) R)`
`V_(B) = (1)/(4 pi in_(0)) [ (-Q)/(R ) + (2Q)/(sqrt(2) R)] = (Q)/(4 pi epsilon_(0) R) [sqrt(2) - 1]`
`= (Q)/(4 pi in_(0) sqrt(2) R) [ (2 - sqrt(2)]`
`W_(B rarr A) = q(V_(A) - V_(B)) = (qQ)/(4 sqrt(2) pi in_(0) R) [3 sqrt(2) - 3]`