Rankers Physics

Properties of EM Waves: Practice Problem & Solution

When light propagates through a material medium of relative permittivity $\epsilon_r$ and relative permeability $\mu_r$ , the velocity of light, v is given by : (c - velocity of light in vacuum) (2022)
$v = \frac{c}{\sqrt{\epsilon_r \mu_r}}$
$v = c$
$v = \sqrt{\frac{\mu_r}{\epsilon_r}}$
$v = \sqrt{\frac{\epsilon_r}{\mu_r}}$

Solution Explained:

To solve this problem, we apply the core principles of Properties of EM Waves. Understanding the underlying formula is key to arriving at the correct answer below:

The velocity of light in a medium is given by $v = \frac{1}{\sqrt{\mu \epsilon}} = \frac{1}{\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r}}$ . Since the speed of light in vacuum is $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ , we get $v = \frac{c}{\sqrt{\epsilon_r \mu_r}}$ .

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