An electromagnetic wave travels in a medium at a speed of \( 2 \times 10^{8}\,\mathrm{m/s} \). If the relative permeability \( (\mu_r) \) of the medium is 1.0, then the relative permittivity \( (\varepsilon_r) \) of the medium is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2.25
The speed of an electromagnetic wave in a medium is set by its permeability and permittivity; for a non-magnetic medium the refractive index is \( n = c/v \).
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{c}{\sqrt{\mu_r\,\varepsilon_r}} \)
\( \displaystyle \varepsilon_r = \frac{1}{\mu_r}\left(\frac{c}{v}\right)^{2} \)
\( c = 3\times10^{8}\,\mathrm{m/s} \)
\( v = 2\times10^{8}\,\mathrm{m/s} \)
\( \mu_r = 1.0 \)
\( \displaystyle \varepsilon_r = \frac{1}{1.0}\left(\frac{3\times10^{8}}{2\times10^{8}}\right)^{2} = (1.5)^{2} = 2.25 \)
Note: A similar question was also asked in CUET (UG) 2023 on 24-05-2023 (Slot 3).