# An electromagnetic wave of frequency

Question:

An electromagnetic wave of frequency $3 \mathrm{GHz}$ enters a dielectric medium of relative electric permittivity $2.25$ from vacuum. The wavelength of this wave in that medium wil be_______ $\times 10^{-2} \mathrm{~cm}$

Solution:

$(667)$

$\mathrm{f}=3 \mathrm{GHz}, \varepsilon_{\mathrm{r}}=2.25$

$\mathrm{V}=\lambda \mathrm{f} \Rightarrow \lambda=\frac{\mathrm{v}}{\mathrm{f}}$

$\mathrm{C}=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$

$\mathrm{V}=\frac{1}{\sqrt{\mu_{0} \mu_{\mathrm{r}} \varepsilon_{0} \varepsilon_{\mathrm{r}}}} \Rightarrow \lambda=\frac{\mathrm{C}}{\mathrm{f} \cdot \sqrt{\mu_{0} \varepsilon_{0}} \cdot \sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}} \cdot \mathrm{f}}$

$\Rightarrow \lambda=\frac{3 \times 10^{8}}{\mathrm{f} \cdot \sqrt{\mu_{\mathrm{r}} \cdot \sqrt{\varepsilon_{\mathrm{r}}}}} \Rightarrow \lambda=\frac{1}{3 \times 10^{9} \times \sqrt{1} \times \sqrt{2.25}}$

$\Rightarrow \lambda=667 \times 10^{-2} \mathrm{~cm}$