Q113 / 120 · VITEEE 2008 · Physics

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

  • A
    $2 \times 10^{-34} \mathrm{C}^{2} \mathrm{Nm}^{-1}$
  • B
    $2 \times 10^{-34} \mathrm{Nm}$
  • Correct answer
    C
    $18 \times 10^{-26} \mathrm{Nm}$
  • D
    $0.5 \times 10^{34} \mathrm{C}^{-2} \mathrm{Nm}^{-1}$

Solution

Here $\begin{array}{l} \mathrm{E}=3 \times 10^{4} \mathrm{NC}^{-1} \\ \mathrm{p}=6 \times 10^{-30} \mathrm{Cm} \\ \Gamma_{\max }=? \end{array}$ We have, torque acting on a dipole $\Gamma=\mathrm{pE} \sin \theta$ The maximum value of $\Gamma$, i.e. $\Gamma_{\max }=\mathrm{pE}$ $\begin{aligned} \therefore \Gamma_{\max } &=\left(3 \times 10^{4} \times 6 \times 10^{-30}\right) \mathrm{Nm} \\ &=18 \times 10^{-26} \mathrm{Nm} \end{aligned}$

Hence, the correct answer is option: 'C'.

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