In the above problem , the value of `Q` for which charges will remain stationary is

Options

A. `q sqrt(3)`
B. `(q)/(sqrt(3))`
C. `-(q)/(sqrt(3))`
D. `-q sqrt(3)`

Answer

3

Explanation

If net force on each `q` is zero , for this
`sqrt(3) vec(F) + vec(F)_(3) = 0`
`sqrt(3) .(1)/(4 pi in_(0)) (q^(2))/(L^(2)) + (1)/(4 pi in_(0)) (Qq)/((L//sqrt(3))^(2)) = 0`
`sqrt(3) q + 3 Q = 0`
`Q = -(q)/(sqrt(3))`