Question

For the shown system of fixed charges, where should a third charge of $3nC$ be placed, so that the system remains in equilibrium.

Answer 1

We know that the third charge should be placed on the line joining the two charges and near the smaller charge towards left.

Distance of third charge from charge of smaller magnitude is given by
$x=\left[\frac{\sqrt{q_1}}{\sqrt{q_2}-\sqrt{q_1}}\right]L$,
where $q_1$ is magnitude of $4nC$ charge and
$q_2$ magnitude of $-25nC$ charge
$\Rightarrow x=\left[\frac{\sqrt{4}}{\sqrt{25}-\sqrt{4}}\right]\times 1$
$\Rightarrow x=0.67\text{m}$