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The force and acting on the system are as follows.

T is tension in string, F is coulomb force and mg is weight.

For equilibrium,

$T\; \cos\; q = mg \;and\; T \sin q = F $

$\therefore \tan \theta= \large\frac{F}{mg}=\frac{1}{4 \pi \in_0 X^2} \frac{q^2}{mg}$

If $\theta$ is small.

$\therefore \tan \theta \sin \theta \approx \large\frac{x}{2l}$

$\therefore \large\frac{x}{2l} = \frac{1}{4 \pi \in_0 x^2} \frac{q^2}{mg}$

$x= \bigg\{ \large\frac{q^2 l}{2 \pi \in _0 mg}\bigg\}^{1/3}$

Hence A is the correct answer.

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