Answer to Question #87322 in Electricity and Magnetism for Sujoy Mandal

Question

The polarisability of a given material is 1.0×10-⁴0 C²mN-¹. Determine it's dielectric constant if the number of molecules in 1 m³ volume of the material is 5.0×10²⅝.

Answer 1

Definition of polarizability:

$$p=\alpha E, \qquad \alpha=1\cdot 10^{-40} C^2mN^{-1}$$

where p is dipole moment of one molucule and E is electric field.

Polarization per unit volume is $P=N\cdot p = N\alpha E = \varepsilon_0 \frac{N\alpha}{\varepsilon_0} E, \, N=5\cdot 10^{25} m^{-3}$ is number of molecules per unit volume, $\varepsilon_0=8.854\cdot 10^{-12} C^2 m^{-2}N^{-1}$ is  electric constant.

Therefore, the dielectric constant

$$\varepsilon=1+\frac{5\cdot 10^{25} \cdot1\cdot 10^{-40} }{8.854\cdot 10^{-12}}=1.00056$$