For charges A,B,C and D are plasced at the four corners of a squre of a side a. The energy required to take the charges C and D to infinity (they are also infinitely separated from each other )is

Options

A. `q^2/(4piepsilon_0a)`
B. `(2q^2)/(piepsilon_0a)`
C. `q^2/(4piepsilon_0a)(sqrt2+1)`
D. `q^2/(4piepsilon_0a)(sqrt2-1)`

Answer

C

Explanation

Energy, required `=/_\U=U_f-U_i`
`=1/(4piepsilon_0)[(q^2/a)-(q^2/a-q/(sqrt2a)-q^2/a-q^2/a-q^1/(sqrt2a)+q^2/a)]`
`q^2=(4piepsilon_0)[sqrt2+1]`