A plane electromagnetic wave has wavelength \(\lambda\), frequency \(\nu\) and electric field amplitude \(E_0\). Match List-I with List-II.
| List-I | List-II |
|---|---|
| (A) Magnitude of the wave vector | (I) \(E_0/c\) |
| (B) Angular frequency | (II) \(2\pi/\lambda\) |
| (C) Speed of the wave in a medium of permittivity \(\varepsilon\) and permeability \(\mu\) | (III) \(1/\sqrt{\mu\varepsilon}\) |
| (D) Amplitude of the magnetic field when the wave travels in vacuum | (IV) \(2\pi\nu\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
In a plane electromagnetic wave, the fields vary as \( \sin(kz-\omega t) \). The wave vector \( k \) is linked to the wavelength, and the angular frequency \( \omega \) is linked to the frequency.
(A) Magnitude of the wave vector — This matches (II) \( 2\pi/\lambda \). The phase \( kz \) grows by \( 2\pi \) over one wavelength, so \( k\lambda=2\pi \).
(B) Angular frequency — This matches (IV) \( 2\pi\nu \). The frequency is \( \nu=\omega/2\pi \).
(C) Speed of the wave in a medium of permittivity \( \varepsilon \) and permeability \( \mu \) — This matches (III) \( 1/\sqrt{\mu\varepsilon} \). In a medium, \( \varepsilon \) and \( \mu \) take the place of \( \varepsilon_0 \) and \( \mu_0 \) in \( c=1/\sqrt{\mu_0\varepsilon_0} \).
(D) Amplitude of the magnetic field when the wave travels in vacuum — This matches (I) \( E_0/c \). In vacuum the two field amplitudes are related by \( B_0=E_0/c \).
NCERT (2026-27):
Nature of electromagnetic waves – “Here k is related to the wave length λ of the wave by the usual equation”
\( \displaystyle k=\frac{2\pi}{\lambda} \)\( \qquad (8.8) \)
Nature of electromagnetic waves – “This relation is often written in terms of frequency, ν (=ω/2π) and wavelength, λ (=2π/k) …”
Summary – “The speed of light, or of electromagnetic waves in a material medium is given by”
\( \displaystyle v=\frac{1}{\sqrt{\mu\varepsilon}} \)
Nature of electromagnetic waves – “It is also seen from Maxwell’s equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as”
\( \displaystyle B_0=(E_0/c) \)\( \qquad (8.10) \)