Question

For the shown system of fixed charges, at what distance from $9\text{nC}$ will electric field due to system of charges be zero.

• A. $2.7$ $\text{m}$ from $9nC$ charge towards left
• B. $0.27$ $\text{m}$ from $9nC$ charge towards left
• C. $0.67$ $\text{m}$ from $9nC$ charge towards left
• D. $1$ $\text{m}$ from $9nC$ charge towards left

Answer 1

The correct option is D $1$ $\text{m}$ from $9nC$ charge towards left

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 $9nC$ charge and
$q_2$ magnitude of $-36nC$ charge
$\Rightarrow x=\left[\frac{\sqrt{9}}{\sqrt{36}-\sqrt{9}}\right]\times 1$
$\Rightarrow x=1\text{m}$