If the ratio of relative permeability and relative permittivity of a uniform medium is $1: 4$. The r

Question

If the ratio of relative permeability and relative permittivity of a uniform medium is $1: 4$. The ratio of the magnitudes of electric field intensity $(E)$ to the magnetic field intensity ( $H$ ) of an EM wave propagating in that medium is $$ 	ext { (Given that } \sqrt{\frac{\mu_0}{\varepsilon_0}}=120 \pi 	ext { ) } $$

Professor PC Thomas Classes · Answer

(c) : Given, $\frac{\mu_r}{\varepsilon_r}=\frac{1}{4}$ From $c=\frac{1}{\sqrt{\mu \varepsilon}}$ and $c=\frac{E}{B}$ $\frac{1}{\sqrt{\mu \varepsilon}}=\frac{E}{B}$ ...(i) and $B=\mu \mathrm{H}$ Putting (ii) in equation (i), we get $ \begin{aligned} & \frac{E}{\mu H}=\frac{1}{\sqrt{\mu \varepsilon}} \ & 	herefore \quad \frac{E}{H}=\frac{\mu}{\sqrt{\mu \varepsilon}}=\sqrt{\frac{\mu}{\varepsilon}}=\sqrt{\frac{\mu_o \mu_r}{\varepsilon_o \varepsilon_r}} \ & \quad=\sqrt{\frac{\mu_0}{\varepsilon}} \sqrt{\frac{\mu_r}{\varepsilon_r}}=120 \pi 	imes \sqrt{\frac{1}{4}}=\frac{120 \pi}{2}=60 \pi \ & 	herefore \quad E: H=60 \pi: 1 \end{aligned} $