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KCET · Physics · Electrostatics

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 ....\(\mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\).

  1. A \(50\)
  2. B \(5\)
  3. C \(0.5\)
  4. D \(0.05\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(5\)

Step-by-step Solution

Detailed explanation

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,
\(\chi_e=\frac{p}{E} \times n=\frac{0.2 \times 10^{-6} \times 100 \times 10^6}{4}\)
\(=5 \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\)