Question

An electric dipole is placed at an angle of 30\(^\circ\) with an electric field of intensity \(2 \times 10^5\) N C\(^{-1}\). It experiences a torque equal to 4 Nm. The charge on the dipole if the dipole length is 2 cm.

• A. 8 mC
• B. 4 mC
• C. 8 \(\mu\)C
• D. 2 mC

Hint:

Torque \(\tau = pE\sin\theta\) where \(p = qd\) is the dipole moment. Make sure to use the full length \(d\) (not half-length) and keep units in SI.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Torque on a dipole: \(\tau = pE\sin\theta = qd \cdot E\sin\theta\).
Step 2: Detailed Explanation:
\[ \tau = q \cdot d \cdot E \cdot \sin\theta \] \[ 4 = q \times 2 \times 10^{-2} \times 2 \times 10^5 \times \sin 30^\circ \] \[ 4 = q \times 2 \times 10^{-2} \times 2 \times 10^5 \times 0.5 \] \[ 4 = q \times 2000 \] \[ q = \frac{4}{2000} = 2 \times 10^{-3} \text{ C} = 2 \text{ mC} \]
Step 3: Final Answer:
The charge on the dipole is 2 mC.