An EM wave travelling in vacuum is described by \( \vec{E} = \vec{E}_0\sin(kx - \omega t)\,\hat{j} \) and \( \vec{B} = \vec{B}_0\sin(kx - \omega t)\,\hat{k} \)
Which of the following relation is true?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( E_0k = B_0\omega \)
In vacuum the ratio of the amplitudes of the electric and magnetic fields of an electromagnetic wave equals the speed of light, and the speed of a wave \( \sin(kx - \omega t) \) is \( \omega/k \).
\( \displaystyle \frac{E_0}{B_0} = c = \frac{\omega}{k} \)
Cross-multiplying gives
\( E_0k = B_0\omega \)
Note: A similar question was also asked in CUET (UG) 2026 on 07-06-2026 (Slot 2), on 25-05-2026 (Slot 1) and on 20-05-2026 (Slot 2), and in CUET (UG) 2023 on 02-07-2023 (Slot 3).
NCERT (2026-27):
Nature of Electromagnetic Waves – “… The speed of propagation of the wave is (ω/k). Using Eqs. [8.7(a) and (b)] for Ex and By and Maxwell’s equations, one finds that
\( \displaystyle \omega = ck, \quad \text{where, } c = 1/\sqrt{\mu_0\varepsilon_0} \qquad [8.9(a)] \)
… 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
\( \displaystyle B_0 = (E_0/c) \qquad (8.10) \)”