Question

If the torque on electric dipole placed with $30^\circ$ to electric field is $ \tau $, then what will be the torque if it is placed $45^\circ$ with electric field?

• A. \( \tau \)
• B. \( \tau \sqrt{3} \)
• C. \( \tau \sin 45^\circ \)
• D. \( \tau \cos 45^\circ \)

Hint:

The torque on an electric dipole is proportional to the sine of the angle between the dipole moment and the electric field.

Answer 1

The Correct Option is C

The torque on an electric dipole placed in a uniform electric field is given by: \[ \tau = p E \sin \theta \] where: - \( p \) is the dipole moment, - \( E \) is the electric field strength, - \( \theta \) is the angle between the electric field and the dipole. - When the dipole is placed at \(30^\circ\) to the electric field, the torque is: \[ \tau = p E \sin 30^\circ = p E \times \frac{1}{2} \] - When the dipole is placed at \(45^\circ\) to the electric field, the torque will be: \[ \tau' = p E \sin 45^\circ = p E \times \frac{\sqrt{2}}{2} \]
Thus, the torque at \(45^\circ\) is \( \tau \sin 45^\circ \), so the correct answer is: \[ \tau \sin 45^\circ \]