Q129 / 180 · KCET 2024 · Physics

A cube of side 1 cm contains 100 molecules each having an induced dipole moment of $0.2 \times 10^{-6} \mathrm{C}-\mathrm{m}$ in an external electric field of $4 \mathrm{NC}^{-1}$. The electric susceptibility of the materials is ....$\mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$.

  • A
    $50$
  • Correct answer
    B
    $5$
  • C
    $0.5$
  • D
    $0.05$

Solution

Induced dipole moment, $p=0.2 \times 10^{-5} \mathrm{C}$ Number of molecules, $n=100$ molecule $/ \mathrm{cm}^3$ $=100 \times 10^6$ molecule $/ \mathrm{m}^3$ $E=4 \mathrm{~N} / \mathrm{C}$ $\therefore$ Electric susceptibility, $\chi_e=\frac{p}{E} \times n=\frac{0.2 \times 10^{-6} \times 100 \times 10^6}{4}$ $=5 \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$

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

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