Question

If the torque acting on an electric dipole when placed at an angle \(30^{\circ}\) with the direction of a uniform electric field is \(\tau\), then the torque acting on the same dipole when placed in the same field at an angle \(45^{\circ}\) is

• A. \(2\tau\)
• B. \(\frac{1}{2}\tau\)
• C. \(\frac{1}{\sqrt{2}}\tau\)
• D. \(\sqrt{2}\tau\)
• E. \(\tau\)

Hint:

\(\tau = pE \sin \theta\). Torque is maximum at \(\theta = 90^{\circ}\).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Torque on an electric dipole: \(\tau = pE \sin \theta\).

Step 2: Detailed Explanation:
\(\tau_{30} = pE \sin 30^{\circ} = pE \cdot \frac{1}{2}\)
\(\tau_{45} = pE \sin 45^{\circ} = pE \cdot \frac{1}{\sqrt{2}}\)
\(\frac{\tau_{45}}{\tau_{30}} = \frac{1/\sqrt{2}}{1/2} = \frac{2}{\sqrt{2}} = \sqrt{2} \Rightarrow \tau_{45} = \sqrt{2}\tau\)

Step 3: Final Answer:
Torque = \(\sqrt{2}\tau\).