Four charges `+q, -1, +q` and `-q` are placed in order on the four consecutive corners of a square of side a. The work done in interchanging the positions of any two neighbouring charges of the opposite sign is

Options

A. `q^2/(4piepsilon_0a)(-4+sqrt2)`
B. `q^2/(4piepsilon_0a)(4+2sqrt2)`
C. `q^2/(4piepsilon_0a)(4-2sqrt2)`
D. `q^2/(4piepsilon_0a)(4+sqrt2)`

Answer

C

Explanation

`W=DeltaU=U_(f)-U_(i)`
`=1/(4piepsilon_0) [((-q^2)/a-q^2/(sqrt2a)+q^2/a+q^2/a-q^2/(sqrt2a)-q^2/a)-((-q^2)/a+q^2/(sqrt2a)-q^2/a-q^2/a+q^2/(sqrt2a)-q^2/a)]` ltbr. `=q^2/(4piepsilon_0a) [4-2sqrt2]`