Question

An electric dipole with dipole moment $2 \times 10^{-10}\, C \cdot m$ is aligned at an angle $30^\circ$ with the direction of a uniform electric field of $10^4\, N/C$. The magnitude of the torque acting on the dipole is

• A. \(10^{-6}\, N \cdot m\)
• B. \(10^{-5}\, N \cdot m\)
• C. \(10^{-4}\, N \cdot m\)
• D. \(10^{-3}\, N \cdot m\)

Hint:

Torque depends on dipole moment, electric field, and the sine of the angle between them.

Answer 1

The Correct Option is A

Torque \(\tau\) on an electric dipole is: \[ \tau = p E \sin \theta \] Given: \[ p = 2 \times 10^{-10}\, C \cdot m, \quad E = 10^4\, N/C, \quad \theta = 30^\circ \] Calculate: \[ \tau = 2 \times 10^{-10} \times 10^4 \times \sin 30^\circ = 2 \times 10^{-6} \times \frac{1}{2} = 10^{-6}\, N \cdot m \]