A charge q is lying at mid-point of the line joining the two similar charges Q. The system will be in equilibrium, if the value of q is

For the system to be in equilibrium, net force on charge Q should be zero. So, Q and q should be unlike in nature.

$\therefore \frac{k·Qq}{r^2}+\frac{kQ·Q}{(2r{)}^2}=0\text{ or charge, }q=\frac{-Q}{4}$