Charges `+q , -q , +q` and `-q` are placed at the corners `A ,B,C` and `D` respectively of a square of side `a`. The potential energy of the system is `1//4 pi epsilon_(0)` times

Options

A. `((q^(2))/(a)) (-4 + sqrt(2))`
B. `((q^(2))/(2a)) (-4 + sqrt(2))`
C. `((4q^(2))/(a))`
D. `-((4 sqrt(2) q^(2))/(a))`

Answer

1

Explanation

Number of pairs `= (n(n - 1))/(2) = ( 4 xx 3)/(2) = 6`
`U = (1)/(4 pi in_(0)) [(q xx -q)/(a) xx 4 + (q.q)/(sqrt(2) a) xx 2]`
`= (1)/(4 pi in_(0)) (q^(2))/(a) [ - 4 + sqrt(2)]`