Answer to Question #103176 in Electricity and Magnetism for Ajay

Question

A glass of relative permitivity 4 is kept in an external electric field of magnitude 10^2 Vm^–1
.
Calculate the polarisation vector, molecular/atomic polarisability and the refractive index
of the glass

Answer 1

Polarization vector

$P=\chi \epsilon_0 E$

$\epsilon=1+\chi \to \chi=\epsilon-1=4-1=3$

$P=\chi \epsilon_0 E=3\cdot 8.85\cdot 10^{-12}\cdot 100=26.55\cdot 10^{-10} \frac{F\cdot V}{m^2}$

Molecular/atomic polarisability

$P=N\alpha \epsilon_0 E \to \alpha=\frac{P}{N \epsilon_0 E}=\frac{26.55\cdot 10^{-10}}{6.02\cdot 10^{23}\cdot 8.85\cdot 10^{-12}\cdot 100}=0.5\cdot 10^{-23} m^3$

Refractive index

$n=\sqrt{\epsilon\mu}=\sqrt{4\cdot 0.99}=1.99$