What is the relative permittivity of a medium of relative permeability 1.0 in which an electromagnetic wave travels at a speed of \( 2\times10^{8}\,\mathrm{m\,s^{-1}} \)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2.25
The speed of an electromagnetic wave in a medium depends on its permittivity and permeability:
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{c}{\sqrt{\mu_r\varepsilon_r}} \;\Rightarrow\; \varepsilon_r = \frac{1}{\mu_r}\left(\frac{c}{v}\right)^{2} \)
\( \displaystyle \varepsilon_r = \frac{1}{1.0}\left(\frac{3\times10^{8}}{2\times10^{8}}\right)^{2} = (1.5)^{2} = 2.25 \)
Note: A similar question was also asked in CUET (UG) 2025 on 29-05-2025 (Slot 2).