A pendulum of length 'l' having a bob of mass 'm' carrying charge 'q' is suspended from a stationary rigid support in a region of uniform electric field 'E' as shown in the figure. If the system is in equilibrium, the nature and magnitude of 'q' will be:

Positive, $(\frac{mg}{E})\tan θ$

The correct answer is Option (2) → Positive, $(\frac{mg}{E})\tan θ$

$\text{Correct: Positive, } q=\left(\frac{mg}{E}\right)\tan\theta$

$\text{For equilibrium: horizontal components: } T\sin\theta=qE.$

$\text{Vertical components: } T\cos\theta=mg.$

therefore $ \tan\theta=\frac{qE}{mg}\ \Rightarrow\ q=\frac{mg}{E}\tan\theta.$

$\text{Sign: } q>0\ (\text{force is to the right, same direction as } \vec E).$