Two point charges q and -3q are placed at a distance l apart on the x-axis. At what coordinate on the x-axis (measured from charge q) is the net elec…

Let $q$ be at $x = 0$ and $-3q$ at $x = l$. The net electric field can be zero only in the region where the individual fields oppose each other. Since the charges are of opposite signs, this must lie outside the interval, closer to the smaller magnitude charge ($q$), i.e., to the left of $q$. Let the distance be $x$. Then $\frac{kq}{x^2} = \frac{k(3q)}{(x+l)^2} \implies (x+l)^2 = 3x^2 \implies x+l = \sqrt{3}x \implies x(\sqrt{3}-1) = l \implies x = \frac{l}{\sqrt{3}-1}$ to the left of $q$.