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 ....\(\mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\).
- A \(50\)
- B \(5\)
- C \(0.5\)
- D \(0.05\)
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,
\(\chi_e=\frac{p}{E} \times n=\frac{0.2 \times 10^{-6} \times 100 \times 10^6}{4}\)
\(=5 \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\)
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,
\(\chi_e=\frac{p}{E} \times n=\frac{0.2 \times 10^{-6} \times 100 \times 10^6}{4}\)
\(=5 \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\)
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