Four equal charges `Q` are placed at the four corners of a square of each side is 'a'. Work done in removing a charge `-Q` from its centre to infinity is

Options

A. zero
B. `(2q^(2))/(pi in_(0) a)`
C. `(sqrt(2) q^(2))/(pi in_(0) a)`
D. `(q^(2))/(2 pi in_(0) a)`

Answer

C

Explanation

Potential at the centre `O` of the sqaure due to four equal charges `q` at four courners
`V = (4q)/(4pi in_(0) (a sqrt(2))//2) = (sqrt(2)q)/(pi in_(0) a)`
`W_(0 oo) = -W_(oo 0) = -(-q)V = (sqrt(2)q^(2))/(pi in_(0) a)`