The speed of an electromagnetic wave in a material medium is given by (Symbols have their usual meaning)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (μ ε)−1/2
Maxwell’s equations give the speed of an electromagnetic wave in terms of the permeability and permittivity of the medium it travels through.
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = (\mu\varepsilon)^{-1/2} \)
In a material medium \( \mu \) and \( \varepsilon \) are those of the medium; in vacuum they become \( \mu_0 \) and \( \varepsilon_0 \).
Why the other options are incorrect
Option (2) (μ0 ε0)−1 — Incorrect. This has the wrong power; \( 1/(\mu_0\varepsilon_0) \) equals \( c^{2} \), not a speed.
Option (3) (μ ε)−1 — Incorrect. This also has the wrong power; \( 1/(\mu\varepsilon) \) is the square of the speed.
Option (4) (μ0 ε0)−1/2 — Incorrect. \( (\mu_0\varepsilon_0)^{-1/2} \) is the speed c in vacuum, not in a material medium.
Note: A similar question was also asked in CUET (UG) 2025 on 20-05-2025 (Slot 2), and in CUET (UG) 2023 on 13-06-2023 (Slot 2).
NCERT (2026-27):
Summary – “… The speed \( c \) of electromagnetic wave in vacuum is related to \( \mu_0 \) and \( \varepsilon_0 \) (the free space permeability and permittivity constants) as follows: \( c = 1/\sqrt{\mu_0\,\varepsilon_0} \). … 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.”