# An electromagnetic wave of frequency

Question:

An electromagnetic wave of frequency $5 \mathrm{GHz}$, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2 . Its velocity in this medium is ____________ $\times 10^{7} \mathrm{~m} / \mathrm{s}$.

Solution:

Given : Frequency of wave $f=5 \mathrm{GHz}$

$=5 \times 10^{9} \mathrm{~Hz}$

Relative permittivity, $\in_{\mathrm{r}}=2$

and Relative permeability, $\mu_{\mathrm{r}}=2$

Since speed of light in a medium is given by,

$\mathrm{v}=\frac{1}{\sqrt{\mu \in}}=\frac{1}{\sqrt{\mu_{\mathrm{r}} \mu_{0} \cdot \in_{\mathrm{r}} \in_{0}}}$

$\mathrm{v}=\frac{1}{\sqrt{\mu_{\mathrm{r}} \in_{\mathrm{r}}}} \frac{1}{\sqrt{\mu_{0} \in_{0}}}=\frac{\mathrm{C}}{\sqrt{\mu_{\mathrm{r}} \in_{\mathrm{r}}}}$

Where $C$ is speed of light is vacuum.

$\therefore \mathrm{v}=\frac{3 \times 10^{8}}{\sqrt{4}}=\frac{30 \times 10^{7}}{2} \mathrm{~m} / \mathrm{s}$

$=15 \times 10^{7} \mathrm{~m} / \mathrm{s}$

$\therefore$ Ans. is 15