In a plane electromagnetic wave in vacuum, the amplitude of the electric field is 12 V m-1. At a certain point and instant, the electric field is 6 V m-1. The magnetic field at that point and instant is (Take \(c=3\times10^{8}\ \mathrm{m\,s^{-1}}\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(2\times10^{-8}\ \mathrm{T}\)
In a plane electromagnetic wave, \( E \) and \( B \) vary with the same factor \( \sin(kz-\omega t) \). So the two fields are in phase. When \( E \) is half of \( E_0 \), \( B \) is also half of \( B_0 \). Since \( B_0=E_0/c \), the fields at any point and instant are related by \( B=E/c \).
\( E=6\ \mathrm{V\,m^{-1}} \)
\( \begin{aligned} B &= \frac{E}{c} \\ &= \frac{6}{3\times10^{8}} \\ &= 2\times10^{-8}\ \mathrm{T} \end{aligned} \)
This is half of the amplitude \( B_0 \), just as 6 V m-1 is half of 12 V m-1.
NCERT (2026-27):
Nature of electromagnetic waves – “… The electric and magnetic fields Ex and By are perpendicular to each other, and to the direction z of propagation. We can write Ex and By as follows:”
\( E_x=E_0\sin(kz-\omega t) \qquad B_y=B_0\sin(kz-\omega t) \)\( \qquad [8.7(a), (b)] \)
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”
\( B_0=(E_0/c) \)\( \qquad (8.10) \)