Electric field in plane electromagnetic wave is given by-
\( E_y = 5 \times 10^{-7}\sin(0.25 \times 10^{3}x + 2.5 \times 10^{11}t) \)
The magnetic field associated with it is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( B_x = 1.66 \times 10^{-15}\sin(0.25 \times 10^{3}x + 2.5 \times 10^{11}t) \)
In an electromagnetic wave the electric and magnetic fields oscillate in phase, and their amplitudes are related by \( E_0 = c\,B_0 \). So the magnetic field has the same sine term as the electric field, and only its amplitude has to be found.
\( E_0 = 5\times10^{-7}\,\mathrm{V\,m^{-1}} \)
\( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \)
\( \displaystyle B_0 = \frac{E_0}{c} = \frac{5\times10^{-7}}{3\times10^{8}} = 1.666\ldots\times10^{-15}\,\mathrm{T} \)
This is the amplitude \( 1.66\times10^{-15}\,\mathrm{T} \) (to three figures, as printed), with the same sine term, which is Option (2).