Question

A sample of HCl gas is placed in an electric field \(3\times 10^{4}\,NC^{-1}\). The dipole moment of each HCl molecule is \(6\times 10^{-30}\,Cm\). The maximum torque that can act on a molecule is

• A. \(2\times 10^{-34}C^{2}Nm^{-1}\)
• B. \(2\times 10^{-34}Nm\)
• C. \(18\times 10^{-26}Nm\)
• D. \(0.5\times 10^{4}C^{2}Nm^{-1}\)

Hint:

Maximum torque on a dipole is \(\tau_{\max}=pE\), when dipole is perpendicular to the field.

Answer 1

The Correct Option is C

Step 1: Recall torque on an electric dipole.
Torque on a dipole in an electric field is:
\[ \tau = pE\sin\theta \]
Step 2: Maximum torque condition.
Maximum torque occurs when \(\sin\theta = 1\), i.e. \(\theta = 90^\circ\).
So:
\[ \tau_{\max} = pE \]
Step 3: Substitute given values.
\[ p = 6\times 10^{-30} \, Cm,\quad E = 3\times 10^{4}\, NC^{-1} \]
\[ \tau_{\max} = 6\times 10^{-30} \times 3\times 10^{4} = 18\times 10^{-26} \, Nm \]
Final Answer:
\[ \boxed{18\times 10^{-26}\,Nm} \]