Correct Answer - A
In Fig, let `OP = y lt lt q`.
Net force on charge `(-q//2)` at `P` due to the two given charges is
`F_(net) = 2 F cos theta`, where `/_APO = /_BPO = theta`
`= (2kq (q//2))/((a^(2) + y^(2))) (y)/(sqrt(a^(2) + y^(2))) = (kq^(2))/((a^(2) + y^(2))^(3//2))`
`F_(net) = (kq^(2) y)/(a^(3))`, where `y lt lt a :. F_("net") prop y`