Question

A cube of side 1 cm contains 100 molecules each having an induced dipole moment of \( 0.2 \times 10^{-16} \, \text{C} \cdot \text{m} \) in an external electric field of \( 4 \times 10^4 \, \text{N/C} \). The electric susceptibility of the materials is ___

• A. 50
• B. 5
• C. 0.5
• D. 0.05

Answer 1

The Correct Option is B

The electric susceptibility \( \chi_e \) is defined as:\( \chi_e = \frac{P}{\epsilon_0 E} \) where \( P \) is the polarization of the material, \( \epsilon_0 \) is the permittivity of free space, and \( E \) is the external electric field. The polarization \( P \) is the dipole moment per unit volume.
Since there are 100 molecules and each has a dipole moment of \( 0.2 \times 10^{-16} \text{C} \cdot \text{m} \), the total dipole moment \( P \) is:
\( P = 100 \times 0.2 \times 10^{-16} = 2 \times 10^{-14} \text{C} \cdot \text{m}^{-2} \) 
Now, substituting the values into the formula:\( \chi_e = \frac{2 \times 10^{-14}}{(8.85 \times 10^{-12}) \times (4 \times 10^4)} = 5 \)