Choose the incorrect statements from the following:
(A) The energy density of an electric field in electromagnetic waves is \( (\varepsilon_0 E^{2}/2) \)
(B) The total energy of electromagnetic waves falling on a surface is \( 6.0 \times 10^{5}\,\mathrm{J} \) and the momentum delivered to the surface, if absorbed fully, is \( 2 \times 10^{3}\,\mathrm{kg\,m/s} \)
(C) The speed of the electromagnetic waves is \( E_0/B_0 \)
(D) The energy density of magnetic field in electromagnetic waves is \( (B^{2}/\mu) \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
An electromagnetic wave carries energy in both its fields, and when it is fully absorbed it delivers momentum \( p = U/c \).
(A) The energy density of an electric field in electromagnetic waves is \( (\varepsilon_0 E^{2}/2) \) — Correct statement. The electric energy density is \( u_E = \frac{1}{2}\varepsilon_0 E^{2} \).
(B) The total energy of electromagnetic waves falling on a surface is \( 6.0 \times 10^{5}\,\mathrm{J} \) and the momentum delivered to the surface, if absorbed fully, is \( 2 \times 10^{3}\,\mathrm{kg\,m/s} \) — Incorrect statement. The momentum is \( U/c \), as worked out below; it is \( 2\times10^{-3} \), not \( 2\times10^{3}\,\mathrm{kg\,m/s} \).
\( \displaystyle p = \frac{U}{c} = \frac{6.0\times10^{5}\,\mathrm{J}}{3\times10^{8}\,\mathrm{m\,s^{-1}}} = 2\times10^{-3}\,\mathrm{kg\,m\,s^{-1}} \)
(C) The speed of the electromagnetic waves is \( E_0/B_0 \) — Correct statement. The field amplitudes are related by \( E_0 = c\,B_0 \), so \( c = E_0/B_0 \).
(D) The energy density of magnetic field in electromagnetic waves is \( (B^{2}/\mu) \) — Incorrect statement. The magnetic energy density is \( u_B = B^{2}/2\mu_0 \); the factor \( \frac{1}{2} \) is missing.
Note: Statement (C) of this question is from the latest textbook (2026-27). Statements (A), (B) and (D), on the energy density and the momentum of an electromagnetic wave, are printed only in the pre-rationalised textbook (2022-23). They were removed from the latest book, and they also appear to be out of the CUET 2026 syllabus.
NCERT (2026-27):
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
\( \displaystyle B_0 = \frac{E_0}{c} \qquad (8.10) \)”
NCERT (Pre-rationalised edition, 2022-23):
Nature of Electromagnetic Waves – “… We have seen in chapter 2 that in a region of free space with electric field E, there is an energy density (ε0E2/2). Similarly, as seen in Chapter 6, associated with a magnetic field B is a magnetic energy density (B2/2μ0). … If the total energy transferred to a surface in time t is U, it can be shown that the magnitude of the total momentum delivered to this surface (for complete absorption) is,
\( \displaystyle p = \frac{U}{c} \qquad (8.12) \)”