Question

For the shown system of fixed charges, where should a third charge of $2\text{nC}$ be placed, so that the $2\text{nC}$ charge remains in equilibrium?

• A. $0.11$ $\text{m}$ from $9\text{nC}$ charge towards right
• B. $0.41$ $\text{m}$ from $9\text{nC}$ charge towards right
• C. $0.31$ $\text{m}$ from $9\text{nC}$ charge towards right
• D. $0.21$ $\text{m}$ from $9\text{nC}$ charge towards right

Answer 1

The correct option is D $0.21$ $\text{m}$ from $9\text{nC}$ charge towards right

We know that the third charge should be placed on the line joining the two charges and in between them.

Distance of third charge from smaller charge is given by
$x=\left(\frac{\sqrt{q_1}}{\sqrt{q_2}+\sqrt{q_1}}\right)L$
where $q_1$ is charge of smaller magnitude and $q_2$ is charge of large magnitude.

$\Rightarrow x=\left[\frac{\sqrt{9\times {10}^{-9}}}{\sqrt{16\times {10}^{-9}}+\sqrt{9\times {10}^{-9}}}\right]\times 0.5$

$\Rightarrow x=0.21\text{m}$

$\begin{array}{c}\text{Why this question ?}\\ \text{Both the charge are positive hence}\\ \text{a negative charge should be placed}\\ \text{in between the positive charge to}\\ \text{hold them tightly.}\end{array}$