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, \( (mg/E)\tan\theta \)
In equilibrium the three forces on the bob balance: the weight \( mg \) downwards, the electric force \( qE \) and the tension \( T \) along the string. The string makes an angle \( \theta \) with the vertical.
The bob is displaced in the direction of the field \( E \), so the electric force acts along \( E \) and the charge is positive. Resolving along the horizontal and the vertical:
\( T\sin\theta = qE \)
\( T\cos\theta = mg \)
Dividing the first by the second:
\( \displaystyle \tan\theta = \frac{qE}{mg} \;\Rightarrow\; q = \frac{mg}{E}\tan\theta \)