Q 12-01-001JEE MainTop questionMedium
Point charges $+4\ \mu\text{C}$ and $+1\ \mu\text{C}$ are $30\ \text{cm}$ apart. At what distance from the $4\ \mu\text{C}$ charge, on the line joining them, is the electric field zero?
Answer: (C) $20\ \text{cm}$
Concept. Between two like charges their fields point in opposite directions, so the null point is where the magnitudes are equal.
Step 1. Equate magnitudes. At distance $x$ from the $4\ \mu$C charge:
$$\frac{k(4)}{x^2} = \frac{k(1)}{(30 - x)^2} \;\Rightarrow\; \frac{2}{x} = \frac{1}{30 - x}$$
Step 2. Solve. $60 - 2x = x \Rightarrow x = 20$ cm.
Answer. $20$ cm (Option C).
Solution by Sreeraj P, M.Sc Physics