Q. A charge $q$ is placed at the centre of the line joining two equal point charges each equal to$\mathcal{Q}$. The system of three charges will be in equilibrium if $q$is equal to
A) $+ \mathcal{Q}/4$
B) $- \mathcal{Q}/2$
C) $+ \mathcal{Q}/2$
D) $- \mathcal{Q}/4$
Explanation
(d) For equilibrium of system of charges,
force produced between $q$ and $\mathcal{Q +}$ force produced between $\mathcal{Q}$ and $\mathcal{Q} = 0$
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$\frac{1}{4\pi\varepsilon_{0}}\frac{q\mathcal{Q}}{(r/2)^{2}} + \frac{1}{4\pi\varepsilon_{0}}\frac{\mathcal{QQ}}{r^{2}} = 0$
$\Rightarrow \frac{4q\mathcal{Q}}{r^{2}} + \frac{\mathcal{QQ}}{(r/2)^{2}} = 0 \Longrightarrow q = - \frac{\mathcal{Q}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.