Three charge `q , Q` and `-4q` are placed in a straight line , line of length `L`at points distant `0 ,L//2` and `L` respectively from one end. In order to make the net force on `q` zero, the charge `Q` must be equal to

Options

A. `- q`
B. `- 2 q`
C. `(-q)/(2)`
D. q

Answer

A

Explanation

`(F_("Net"))_(q) = 0`
`rArr k (Q q)/(((l)/(2))^(2))+ k ( 4 q ^(2))/( l^(2)) = 0`
where ` k = (1)/( 4 pi epsilon_(0)) rArr 4 Q q + 4 q^(2) = 0 rArr Q = - q `