Three point charges Q₁, Q₂ and Q₃ in that order are placed equally spaced along a straight line. Q₂ and Q₃ are equal in magnitude but opposite in sign. If the net force on Q₃ is zero, the value of Q₁ is :

Given Data: 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.

Formula Used: $F=k\frac{q_1{q}_2}{r^2}$

Detailed Solution:

As given ${\mathrm{Q}}_2$ and ${\mathrm{Q}}_3$ are equal in magnitude but are opposite in sign, they will experience attractive force due to each other.

Now ${\mathrm{Q}}_1$ must repel $Q_3$ so that net force on $Q_3$ is zero.

So, we will have, 

$\frac{-{\mathrm{kQ}}_2{\mathrm{Q}}_3}{{\mathrm{r}}^2}=\frac{\mathrm{k}\left({\mathrm{Q}}_1\right){\mathrm{Q}}_3}{(2\mathrm{r}{)}^2}$

${\mathrm{Q}}_1=-4{\mathrm{Q}}_2$

Thus, ${\mathrm{Q}}_1=4\left|{\mathrm{Q}}_3\right| as \left|Q_2\right|=\left|Q_3\right|$