Electromagnetic waves travel in a medium at a speed of \( 1.5\times10^{8}\,\mathrm{m\,s^{-1}} \). The relative permeability of the medium is 0.4. The relative permittivity of the medium will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10
The speed of an electromagnetic wave in a medium of permeability \( \mu \) and permittivity \( \varepsilon \) is \( v = 1/\sqrt{\mu\varepsilon} \), while in vacuum \( c = 1/\sqrt{\mu_0\varepsilon_0} \). With \( \mu = \mu_0\mu_r \) and \( \varepsilon = \varepsilon_0\varepsilon_r \):
\( \displaystyle \frac{c}{v} = \sqrt{\mu_r\varepsilon_r} \Rightarrow \varepsilon_r = \frac{1}{\mu_r}\left(\frac{c}{v}\right)^{2} \)
\( \displaystyle \frac{c}{v} = \frac{3\times10^{8}}{1.5\times10^{8}} = 2 \)
\( \displaystyle \varepsilon_r = \frac{2^{2}}{0.4} = 10 \)