The ratio of the electric field (E) and the magnetic field (B) associated with a plane electromagnetic wave is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \omega k^{-1} \)
In a plane electromagnetic wave the fields vary in the same phase, \( E = E_0\sin(kx - \omega t) \) and \( B = B_0\sin(kx - \omega t) \), and their ratio is the speed of the wave.
\( \displaystyle \frac{E}{B} = \frac{E_0}{B_0} = c = \frac{\omega}{k} = \omega k^{-1} \)
Shortcut: The ratio \( E/B \) has the dimensions of a speed. The only option with those dimensions is \( \omega/k \): \( \omega k \) has the dimensions of \( \mathrm{m^{-1}\,s^{-1}} \), \( k/\omega \) of \( \mathrm{s\,m^{-1}} \), and \( \omega \) of \( \mathrm{s^{-1}} \).
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
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
\( \displaystyle \omega = ck, \text{ where, } c = 1/\sqrt{\mu_0 \varepsilon_0} \qquad [8.9(a)] \)”
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
\( \displaystyle B_0 = (E_0/c) \qquad (8.10) \)”