Q 12-01-158JEE MainJEE Main 2025 (2 Apr, Shift 1)Easy
A point charge $+q$ is placed at the origin. A second point charge $+9q$ is placed at $(d, 0, 0)$ in the Cartesian coordinate system. The point in between them where the electric field vanishes is:
Answer: (B) $(d/4,\ 0,\ 0)$
Let the field vanish at $x$ between the charges. The two fields are opposite there, so their magnitudes must be equal:
$$\frac{kq}{x^2} = \frac{k(9q)}{(d-x)^2} \Rightarrow \frac{d-x}{x} = 3 \Rightarrow x = \frac d4$$
The point is $(d/4,\ 0,\ 0)$, closer to the smaller charge as expected.
Solution by Sreeraj P, M.Sc Physics