The velocity of an electromagnetic wave in a medium with εr = 2 and μr = 18 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.5 x 108 m/s
The speed of an electromagnetic wave in a medium is set by the relative permittivity and permeability:
\( \displaystyle v = \frac{1}{\sqrt{\mu_0\mu_r\,\varepsilon_0\varepsilon_r}} = \frac{c}{\sqrt{\mu_r\varepsilon_r}} \)
\( \displaystyle v = \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{\sqrt{18 \times 2}} = \frac{3\times10^{8}}{6}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle v = 0.5\times10^{8}\,\mathrm{m\,s^{-1}} \)
The medium therefore has a refractive index \( n = \sqrt{\mu_r\varepsilon_r} = 6 \).