Question

If two charges $+4e$ and $+e$ are at a distance $x$ apart then at what distance charge $q$ must be placed from $+e$, so that it is in equilibrium?

• A. $\frac{x}{2}$
• B. $\frac{x}{3}$
• C. $\frac{x}{6}$
• D. $\frac{2x}{3}$

Answer 1

The correct option is B $\frac{x}{3}$

For equilibrium of $q$
$|F_1|=|F_2|$
$\frac{1}{4\pi {ϵ}_0}\frac{q{q}_1}{x_1^2}=\frac{1}{4\pi {ϵ}_0}=\frac{q{q}_2}{x_2^2}$
$x_2=\frac{x}{\sqrt{\frac{q_1}{q_2}}+1}=\frac{x}{\sqrt{\frac{4e}{e}}+1}=\frac{x}{3}$.