A point charge $Q$ is placed at the center of the line joining two equal point charges $+q$ and $+q$. The value of $Q$ if the system of the charges is equilibrium, is

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Aicharya · Accepted Answer

The forces on charge $Q$ due to the other two charges will be equal and opposite and hence it will be in equilibrium. Force on $+\mathrm{q}$ due to the other two charges should also be equal and opposite. Their magnitudes will be equal if $\begin{aligned} & \frac{1}{4 \pi \varepsilon_0} \cdot \frac{\mathrm{q}^2}{\mathrm{r}^2}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{\mathrm{qQ}}{\left(\frac{\mathrm{r}}{2}ight)^2}=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{4 \mathrm{qQ}}{\mathrm{r}^2} \ & 	herefore \mathrm{q}=4 \mathrm{Q} 	ext { or } \mathrm{Q}=\frac{\mathrm{q}}{4} \end{aligned}$ $\mathrm{Q}$ must be negative, hence $\mathrm{Q}=-\frac{\mathrm{q}}{4}$

A point charge $Q$ is placed at the center of the line joining two equal point charges $+q$ and $+q$. The…

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