Q 12-01-141JEE MainJEE Main 2019 (9 Jan, Shift 1)Easy
Three charges $+Q$, $q$, $+Q$ are placed respectively, at distance, $0$, $d/2$ and $d$ from the origin, on the $x$-axis. If the net force experienced by $+Q$, placed at $x = 0$, is zero, then value of $q$ is
Answer: (C) $-Q/4$
Force on the charge at $x = 0$ from $+Q$ at $x = d$ (repulsive) is $\dfrac{kQ^2}{d^2}$ towards $-x$. For zero net force, $q$ must attract it, so $q$ is negative, with
$$\frac{kQ|q|}{(d/2)^2} = \frac{kQ^2}{d^2} \Rightarrow 4|q| = Q \Rightarrow q = -\frac Q4$$
Solution by Sreeraj P, M.Sc Physics