The electric field vector oscillates according to the equation \( \vec{E} = 4\sin[1.8y+(5.4\times10^{6})t]\,\hat{k} \). The equation of magnetic field vector is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \vec{B} = 1.33\times10^{-8}\sin[1.8y+(5.4\times10^{6})t]\,\hat{\imath} \)
In an electromagnetic wave, \( \vec{E} \) and \( \vec{B} \) oscillate in phase, are perpendicular to each other and to the direction of travel, and their amplitudes are related by \( E_0 = cB_0 \).
The phase \( 1.8y + (5.4\times10^{6})t \) depends on \( y \), so the wave travels along the \( y \)-axis. \( \vec{E} \) is along \( z \), so \( \vec{B} \) must be along the \( x \)-axis.
\( \displaystyle B_0 = \frac{E_0}{c} = \frac{4\,\mathrm{V\,m^{-1}}}{3\times10^{8}\,\mathrm{m\,s^{-1}}} = 1.33\times10^{-8}\,\mathrm{T} \)
So \( \vec{B} = 1.33\times10^{-8}\sin[1.8y+(5.4\times10^{6})t]\,\hat{\imath} \).