The electric field \( E \) associated with a progressive electromagnetic wave is given by \( E = E_0\sin(kx - \omega t) \). If \( B_0 \) is the amplitude of the magnetic field associated with the wave, then
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{E_0}{B_0} = \frac{\omega}{k} \)
In an electromagnetic wave the ratio of the amplitudes of the electric and magnetic fields equals the speed of the wave, \( c \). For the wave \( \sin(kx - \omega t) \), the speed is the ratio of the angular frequency to the wave number.
\( \displaystyle \frac{E_0}{B_0} = c, \qquad c = \frac{\omega}{k} \)
\( \displaystyle \frac{E_0}{B_0} = \frac{\omega}{k} \)
Shortcut: \( E_0/B_0 \) has the dimensions of speed. Only \( \omega/k \) (rad per second divided by rad per metre) is a speed; \( k/\omega \) is its inverse, and the squared forms are speed squared or its inverse.
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 \( (\omega/k) \).”
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
\( \displaystyle B_0 = (E_0/c) \qquad (8.10) \)”