Question

An electric dipole is placed at an angle of $30^\circ$ in an electric field of intensity $2 \times 10^5$ N/C. It experiences a torque of $0.03$ Nm. If the dipole length is 2 cm, find the charge on the dipole.

• A. $1.5 \times 10^{-5}$ C
• B. $2.0 \times 10^{-5}$ C
• C. $2.5 \times 10^{-5}$ C
• D. $3.0 \times 10^{-5}$ C

Hint:

Quick Tip:
For dipole problems, use: \[ \tau = pE\sin\theta \quad \text{and} \quad p = qd \]

Answer 1

The Correct Option is A

The torque on an electric dipole is given by: \[ \tau = pE \sin\theta \] % Finding dipole moment Using \[ p = \frac{\tau}{E\sin\theta} \] Substituting the values: \[ p = \frac{0.03}{(2 \times 10^5)\times \sin30^\circ} \] Since, \[ \sin30^\circ = 0.5 \] \[ p = \frac{0.03}{10^5} = 3 \times 10^{-7}\ \text{C m} \] % Relation between dipole moment and charge Now, \[ p = qd \] Given: \[ d = 2\text{ cm} = 0.02\text{ m} \] \[ q = \frac{p}{d} = \frac{3 \times 10^{-7}}{0.02} = 1.5 \times 10^{-5}\text{ C} \] \[ \boxed{1.5 \times 10^{-5}\text{ C}} \]