Question

An electromagnetic wave travels in a medium with the speed of $2\times {10}^8\mathrm{m}/\mathrm{s}$. The relative permeability of the medium is $1$. Find the relative permittivity of the medium.

Answer 1

Step 1: Given data

Speed of light, $\mathrm{c}=3\times {10}^{8}m/s$

Speed of wave in the medium, $v=2\times {10}^{8}m/s$

Relative permeability, ${\mathrm{\mu }}_{\mathrm{r}}=1$

To Find

The relative permittivity of the medium.

Step 2: Calculate relative permittivity(${\epsilon }_r$)

Using the formula:

$$\begin{gathered} {\mathrm{\epsilon }}_{\mathrm{r}}=\frac{{\mathrm{c}}^2}{{\mathrm{v}}^2{\mathrm{\mu }}_{\mathrm{r}}} \\ =\frac{{\left(3\times {10}^8\right)}^2}{{\left(2\times {10}^8\right)}^2\times 1} \\ =2.25 \end{gathered}$$

Hence, relative permittivity is $2.25$.