For the shown system of fixed charges, a third charge of $3 n C$ is placed at $x cm$ towards left from $4 nC$ charge, so that the system remains in equilibrium. Find the value of $x$ (Round off to the nearest integer value)

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Solution

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
$x = [\frac{\sqrt{q_{1}}}{\sqrt{q_{2}} - \sqrt{q_{1}}}] L$ ,
where $q_{1}$ is magnitude of $4 n C$ charge and
$q_{2}$ magnitude of $- 25 n C$ charge
$\Rightarrow x = [\frac{\sqrt{4}}{\sqrt{25} - \sqrt{4}}] \times 1$
$\Rightarrow x = 0.67 m or 67 cm$

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For the shown system of fixed charges, a third charge of 3 nC is placed at x cm towards left from 4 nC charge, so that the system remains in equilibrium. Find the value of x (Round off to the nearest integer value)

For the shown system of fixed charges, a third charge of $3 n C$ is placed at $x cm$ towards left from $4 nC$ charge, so that the system remains in equilibrium. Find the value of $x$ (Round off to the nearest integer value)