Question

A sample of HCl gas is placed in
a uniform electric field of magnitude
3 x 104 NC-. The dipole moment of each
HCl molecule is 3.4 x 10-30 Cm. Calculate
the maximum torque experienced by
each HCl molecule.
Solution​

Answer 1

Given :

• Electric field ( E ) = 3 x 10⁴ N / C
• Dipole moment ( p ) = 3.4 x 10-³⁰ Cm

To find :

• Maximum torque experienced by the molecule (τ)

Solution :

The torque acting upon a dipole placed in an electric field is a cross product of dipole moment and electric field .

$\leadsto \tau = - p E \sin \theta$

Also ,

$\leadsto \overrightarrow{\tau }= \overrightarrow{p} \times \overrightarrow{ E}$

$\leadsto | \overrightarrow{\tau }|= |\overrightarrow{p} \times \overrightarrow{ E} |$

Hence ,

$\leadsto \tau = p E \sin \theta$

The torque produced is maximum when θ = 90 ,

$\leadsto \tau = p E \sin 90$

$\leadsto \tau = p E$

$\leadsto \tau = 3.4 \times 10^{-30} \times 3 \times 10^4$

$\leadsto \tau = 10.2 \times 10^{-26} \:N/m$

Hence ,

The maximum torque produced by the HCl molecule is 10.2 x 10-²⁶ N/ m .