Answer to Question #93562 in Electricity and Magnetism for GG

Question

The polarisability of a given material is 1.0×10^-40 C^2mN^−1. Determine its dielectric
constant if the number of molecules in 1 m^3 volume of the material is 5.0×10^25.

Answer 1

The dielectric constant can be calculated from Clausius-Mossotti equation, the result will be:

$$\frac{\epsilon_r-1}{\epsilon_r+2}=\frac{N\alpha}{3\epsilon_0}, \space\\$$

$$\epsilon=\frac{1+\frac{2N\alpha}{3\epsilon_0}}{1-\frac{N\alpha}{3\epsilon_0}}=1.0005648.$$

The other way to calculate the constant is through the total dipole moment per unit volume:

$$\epsilon=1+\frac{N\alpha}{\epsilon_0}=1+\frac{1\cdot10^{-40}\cdot5\cdot10^{25}}{8.85\cdot10^{-12}}=1.0005647.$$