Electromagnetic WavesMedium
Question
A plane electromagnetic wave is moving in free space with velocity c $= 3 \times 10^{8}\text{ }m/s$ and its electric field is given as $\overrightarrow{E} = 54sin(kz - \omega t)\widehat{j}V/m$, where $\widehat{j}$ is the unit vector along y-axis. The magnetic field vector $\overrightarrow{B}$ of the wave is :
Options
A.$- 1.8 \times 10^{- 7}sin(kz - \omega t)\widehat{i}T$
B.$1.4 \times 10^{- 7}sin(kz - \omega t)\widehat{k}T$
C.$1.4 \times 10^{- 7}sin(kz - \omega t)\widehat{i}T$
D.$+ 1.8 \times 10^{- 7}sin(kz - \omega t)\widehat{iT}$
Solution
$\widehat{B} = \widehat{C} \times \widehat{E} = \widehat{k} \times \widehat{j} = - \widehat{i}$
$${\therefore\overrightarrow{B} = \frac{54}{3 \times 10^{8}}sin(kz - \omega t)( - \widehat{i}) }{= - 1.8 \times 10^{- 7}sin(kz - \omega t)\widehat{i}}$$
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