Question

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

Answer 1

$f=3GHz,\epsilon _{r}=2.25$
$v=\lambda f\Rightarrow \lambda =\frac{v}{f}$
$c=\frac{1}{\sqrt{\mu _{0} \epsilon _{0}}}$
$v=\frac{1}{\sqrt{\mu _{0} \mu _{r} \epsilon _{0} \epsilon _{r}}}\Rightarrow \lambda =\frac{1}{f \cdot \sqrt{\mu _{0} \epsilon _{0}} \cdot \sqrt{\mu _{r} \epsilon _{r}}}$
$\Rightarrow \lambda =\frac{C}{f \cdot \sqrt{\mu _{r}} \cdot \sqrt{\epsilon _{r}}}\Rightarrow \lambda =\frac{3 \times 10^{8}}{3 \times 10^{9} \times \sqrt{1} \times \sqrt{2 . 25}}$
$\Rightarrow \lambda =667\times 10^{- 2}cm$