Six charge of magnitude `+q` and `-q` are fixed at the cornors of a regular hexagon of edge at the cornors of a regular hexagon of edge length a as shown in the figure .The electrostatic interaction energy of the charged particle is :

Options

A. `(q^(2))/(piepsilon_(0)a)[(sqrt(3))/(8)-(15)/(4)]`
B. `(q^(2))/(piepsilon_(0)a)[(sqrt(3))/(2)-(9)/(4)]`
C. `(q^(2))/(piepsilon_(0)a)[(sqrt(3))/(4)-(15)/(2)]`
D. `(q^(2))/(piepsilon_(0)a)[(sqrt(3))/(2)-(15)/(8)]`

Answer

D

Explanation

Interaction energy of system of charges is =`(1)/(2)[U_(1)+.....+U_(6)]=(1)/(2)[6U_(1)]=3U_(1)`
`=3kq^(2)(-(2)/(a)+(2)/(asqrt(3))-(1)/(2a))==(q^(2))/(piepsilon_(0)a)((sqrt(3))/(2)-(15)/(8))`