In a plane electromagnetic wave, the electric field varies as \( E_z = 90\sin(500x + 20 \times 10^{10}t)\,\mathrm{V/m} \). The expression of its magnetic field variation is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3 \times 10^{-7}\sin(500x + 20 \times 10^{10}t)\,\mathrm{T} \)
In an electromagnetic wave the amplitudes of the electric and magnetic fields are related by \( E_0 = c\,B_0 \). The magnetic field varies in the same phase as the electric field, so only its amplitude has to be found; the sine term is the same in all four options.
\( \displaystyle B_0 = \frac{E_0}{c} = \frac{90\,\mathrm{V\,m^{-1}}}{3\times10^{8}\,\mathrm{m\,s^{-1}}} = 3\times10^{-7}\,\mathrm{T} \)
So \( B = 3\times10^{-7}\sin(500x + 20\times10^{10}t)\,\mathrm{T} \).