The magnetic field in a plane electromagnetic wave is given \( B_y = 2\times10^{-7}\sin(0.5\times10^{3}x + 1.57\times10^{11}t)\,\mathrm{T} \). The frequency of the wave is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 25.0\,\mathrm{GHz} \)
Compare the wave with the standard form \( B = B_0\sin(kx + \omega t) \). The coefficient of \( t \) is the angular frequency \( \omega \), and the frequency is \( f = \omega/2\pi \).
\( \displaystyle \omega = 1.57\times10^{11}\,\mathrm{rad\,s^{-1}} \)
\( \displaystyle f = \frac{\omega}{2\pi} = \frac{1.57\times10^{11}}{2\times3.14} = 2.5\times10^{10}\,\mathrm{Hz} = 25.0\,\mathrm{GHz} \)
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 – …
