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:
Answer & explanation
Correct answer: option 2
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.$
$\text{Sign: } q>0\ (\text{force is to the right, same direction as } \vec E).$