An electromagnetic wave of frequency 5GHz , is travelling in a...

Given : Frequency of wave $f = 5GHz$

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

Relative permittivity, ${ϵ}_{r} = 2$ and Relative permeability, ${\mu}_{r} = 2$ Since speed of light in a medium is given by,

$v = \dfrac{1}{\sqrt{\mu} \in} = \dfrac{1}{\sqrt{{\mu}_{r}{\mu}_{0} \cdot {ϵ}_{r}{\in}_{0}}}$

$v = \dfrac{1}{\sqrt{{\mu}_{r}{ϵ}_{f}}}\dfrac{1}{\sqrt{{\mu}_{0}{ϵ}_{0}}} = \dfrac{C}{\sqrt{{\mu}_{r}{ϵ}_{r}}}$

Where $C$ is speed of light is vacuum

$∴ v = \dfrac{3 \times {10}^{8}}{\sqrt{4}} = \dfrac{30 \times {10}^{7}}{2}m{s}^{- 1}$

$= 15 \times {10}^{7}m{s}^{- 1}$

$∴$ Ans. is $15$