The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3

Question

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $\mu=2 \mu_0$, is ( $\mu_0=$ permeability of vacuum)

Professor PC Thomas Classes · Answer

The speed of electromagnetic waves in a vacuum is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$. In a medium, the speed is $v = \frac{1}{\sqrt{\mu \epsilon}}$. We are given $\epsilon = k\epsilon_0 = 3\epsilon_0$ and $\mu = 2\mu_0$. The speed in the medium is $v = \frac{1}{\sqrt{2\mu_0 \cdot 3\epsilon_0}} = \frac{1}{\sqrt{6\mu_0 \epsilon_0}} = \frac{c}{\sqrt{6}}$. The ratio of the speed in vacuum to the speed in the medium is $\frac{c}{v} = \frac{c}{c/\sqrt{6}} = \sqrt{6} : 1$.