I have a question in which I need to show that sea water is effectively a "good conductor", when considering the propagation of radio waves of frequency $< 10^9$. We're given that the conductivity of sea water is around $5 Sm^{-1}$ and has a refractive index of around $9$.
It is my understanding that in order to show that the sea water is a "good conductor", you would need to show that: $\sigma>>\omega\epsilon_r\epsilon_0$
$\sigma, \omega, \epsilon_0$ are trivial but I am not sure how you would get a value of $\epsilon_r$.
Edit: I managed to solve the problem using Gilbert's help.
Here's my proof:
As, $${v=\frac{1}{\sqrt{\mu\epsilon}}},$$ $$v=\frac{c}{n},$$ $$\mu_r=1,$$ $$\implies v=\frac{1}{\sqrt{\mu_0\epsilon_r\epsilon_0}}=\frac{c}{n},$$
$$\implies \mu_0\epsilon_r\epsilon_0=\frac{n^2}{c^2},$$
$$\implies \mu_0\epsilon_r\epsilon_0=\frac{n^2}{c^2},$$
$$\implies \epsilon_r=\frac{n^2}{c^2\mu_0\epsilon_0},$$
As $\epsilon_0=\frac{1}{\mu_0c^2}$,
$$\implies \epsilon_r=n^2$$
