A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction. If at a particular point in space and time, \( \vec{E} = (9.3\,\hat{\jmath})\,\mathrm{V\,m^{-1}} \), what is \( \vec{B} \) at this point?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( (3.1\times10^{-8}\,\hat{k})\,\mathrm{T} \)
In a plane electromagnetic wave, \( \vec{E} \) and \( \vec{B} \) are perpendicular to each other and to the direction of travel, the wave travels along \( \vec{E}\times\vec{B} \), and their magnitudes are related by \( E = cB \).
\( \displaystyle B = \frac{E}{c} = \frac{9.3\,\mathrm{V\,m^{-1}}}{3\times10^{8}\,\mathrm{m\,s^{-1}}} = 3.1\times10^{-8}\,\mathrm{T} \)
For the direction, \( \vec{E} \) is along \( \hat{\jmath} \) and \( \vec{E}\times\vec{B} \) must be along \( +\hat{\imath} \):
\( \hat{\jmath}\times\hat{k} = \hat{\imath} \)
So \( \vec{B} \) is along \( \hat{k} \), and \( \vec{B} = (3.1\times10^{-8}\,\hat{k})\,\mathrm{T} \).
Note: A similar question was also asked in CUET (UG) 2023 on 22-05-2023 (Slot 3).
Note: NTA picked this question from an NCERT (2026-27) example and changed the figures. Do not ignore NCERT while practising numericals.
NCERT (2026-27):
Nature of Electromagnetic Waves – …
