In a medium with permittivity \( \varepsilon \) and permeability \( \mu \), the speed of light \( v \) is given by
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( v=\displaystyle\frac{1}{\sqrt{\mu\varepsilon}} \)
Maxwell’s equations give the speed of an electromagnetic wave in terms of the permittivity and permeability of the medium:
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} \)
In vacuum this becomes \( c = 1/\sqrt{\mu_0\varepsilon_0} \approx 3\times10^{8}\,\mathrm{m\,s^{-1}} \). A medium with larger \( \mu \) or \( \varepsilon \) slows the wave down.
Note: A similar question was also asked in CUET (UG) 2023 on 15-06-2023 (Slot 2).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Summary – “… The speed of light, or of electromagnetic waves in a material medium is given by
\( \displaystyle v = \frac{1}{\sqrt{\mu\,\varepsilon}} \)
where \( \mu \) is the permeability of the medium and \( \varepsilon \) its permittivity.”