# 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:

(15)

Given : $\mathrm{f}=5 \mathrm{GHz}$

$\varepsilon_{\mathrm{r}}=2$

$\mu_{\mathrm{r}}=2$

velocity of wave $\Rightarrow v=\frac{c}{n} \ldots(1)$

where, $\mathrm{n}=\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}$ and $\mathrm{c}=$ speed of light $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ $n=\sqrt{2 \times 2}=2$

put the value of $\mathbf{n}$ in we get

$\Rightarrow v=\frac{3 \times 10^{8}}{2}=15 \times 10^{7} \mathrm{~m} / \mathrm{s}$

$\Rightarrow X \times 10^{7}=15 \times 10^{7}$

$X=15$