An electromagnetic wave propagating through vacuum is described by \( \vec{E} = E_{0}\sin(-kx + \omega t)\hat{\jmath} \) V/m and \( \vec{B} = B_{0}\sin(-kx + \omega t)\hat{k} \) T. Then, which of the following is true?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( E_{0}k = B_{0}\omega \)
In an electromagnetic wave in vacuum the amplitudes are related by \( E_0 = cB_0 \), and the wave speed is \( c = \omega/k \) for a wave \( \sin(\omega t - kx) \).
\( \displaystyle \frac{E_0}{B_0} = c = \frac{\omega}{k} \)
\( E_0k = B_0\omega \)
The directions are consistent too: \( \hat{\jmath}\times\hat{k} = \hat{\imath} \), so \( \vec{E}\times\vec{B} \) points along \( +x \), the direction in which \( \sin(-kx + \omega t) \) travels.
Note: A similar question was also asked in CUET (UG) 2026 on 07-06-2026 (Slot 2) and on 20-05-2026 (Slot 2), and in CUET (UG) 2023 on 02-07-2023 (Slot 3) and on 14-06-2023 (Slot 1).
NCERT (2026-27):
Nature of Electromagnetic Waves – “… The speed of propagation of the wave is \( (\omega/k) \).”
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
\( \displaystyle B_0 = \left(\frac{E_0}{c}\right) \qquad (8.10) \)”