Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A plane electromagnetic wave in vacuum that has a peak electric field of \( 60\,\mathrm{V\,m^{-1}} \) has a peak magnetic field of \( 2\times10^{-7}\,\mathrm{T} \).
Reason (R): In an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both (A) and (R) are true but (R) is NOT the correct explanation of (A).
Assertion (A) A plane electromagnetic wave in vacuum that has a peak electric field of \( 60\,\mathrm{V\,m^{-1}} \) has a peak magnetic field of \( 2\times10^{-7}\,\mathrm{T} \). — True. The peak fields follow \( B_0=E_0/c \):
\( \begin{aligned} B_0 &= \frac{E_0}{c} \\ &= \frac{60\,\mathrm{V\,m^{-1}}}{3\times10^{8}\,\mathrm{m\,s^{-1}}} \\ &= 2\times10^{-7}\,\mathrm{T} \end{aligned} \)
Reason (R) In an electromagnetic wave, the electric and magnetic fields are perpendicular to each other and to the direction of propagation. — True. This follows from Maxwell’s equations and holds for every electromagnetic wave.
Why R does not explain A?
(R) fixes only the directions of \( \vec{E} \) and \( \vec{B} \). From (R) alone, any value of \( B_0 \) would fit a peak electric field of \( 60\,\mathrm{V\,m^{-1}} \).
The value \( 2\times10^{-7}\,\mathrm{T} \) in (A) comes only from the relation of the magnitudes, \( B_0=E_0/c \). So (R) is not the correct explanation of (A).
NCERT (2026-27):
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
\( B_0=(E_0/c) \)\( \qquad (8.10) \)”
Nature of Electromagnetic Waves – “… electric and magnetic fields in an electromagnetic wave are perpendicular to each other, and to the direction of propagation.”