Question

Three point charges $Q_1$, $Q_2$and $Q_3$ in that order are placed equally spaced along a straight line. $Q_2$and $Q_3$ are equal in magnitude but opposite in sign. If the net force on $Q_3$ is zero, the value of $Q_1$ is :

• A. $Q_1=\left|Q_3\right|$
• B. $Q_1=\sqrt{2}\left|Q_3\right|$
• C. $Q_1=2\left|Q_3\right|$
• D. $Q_1=4\left|Q_3\right|$

Answer 1

The correct option is D $Q_1=4\left|Q_3\right|$

$Q_{2}and{Q}_3$ are equal is magnitude but opposite in sign.
$\therefore Q_{2}and{Q}_3$ experience attractive force due to each other. Now $Q_1$ must have sign of $Q_3$ to repel it so that Net force on $Q_3$ is zero
$\Rightarrow \frac{-k{Q}_2{Q}_3}{r^2}=\frac{k\left(Q_1\right)Q_3}{(2r{)}^2}$

$\Rightarrow Q_1=-4Q_2$

$\Rightarrow Q_1=4\mid Q_3\mid$

as $\mid Q_2\mid =\mid Q_3\mid$