The speed of electromagnetic waves in a material medium is given by (Symbols have their usual meanings)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( v = (\mu\epsilon)^{-0.5} \)
From Maxwell's equations the speed of an electromagnetic wave in a medium of permeability \( \mu \) and permittivity \( \epsilon \) is
\( \displaystyle v = \frac{1}{\sqrt{\mu\epsilon}} = (\mu\epsilon)^{-0.5} \)
In vacuum \( \mu = \mu_0 \) and \( \epsilon = \epsilon_0 \), which gives \( c = (\mu_0\epsilon_0)^{-0.5} \).
Why the other options are incorrect
Option (1) \( v = (\mu\epsilon)^{0.5} \) — Incorrect. The exponent has the wrong sign; the speed is \( 1/\sqrt{\mu\epsilon} \).
Option (2) \( v = (\mu_0\epsilon_0)^{-0.5} \) — Incorrect. This is the speed of light in vacuum, \( c \), not the speed in a material medium.
Option (4) \( v = (\mu_0\epsilon_0)^{0.5} \) — Incorrect. The exponent has the wrong sign, and it uses the vacuum constants instead of those of the medium.
Note: A similar question was also asked in CUET (UG) 2026 on 18-05-2026 (Slot 2), and in CUET (UG) 2023 on 13-06-2023 (Slot 2).
NCERT (2026-27):
Summary – “… The speed of light, or of electromagnetic waves in a material medium is given by
\( \displaystyle v = \frac{1}{\sqrt{\mu\,\epsilon}} \)
where μ is the permeability of the medium and ε its permittivity.”