# The electric field of a plane electromagnetic wave is given by $\overrightarrow{E}=E_{0}\left ( \widehat{x}+\widehat{y} \right )\sin (kz- \omega t)$ Its magnetic field will be given by: Option: 1 Option: 2 Option: 3 Option: 4

\begin{aligned} &\overrightarrow{\mathbf{E}} \times \overrightarrow{\mathbf{B}} \text { is along } \overrightarrow{\mathbf{C}}\\ &\hat{\mathbf{E}} \times \hat{\mathbf{B}}=\hat{\mathbf{C}}\\ \end{aligned}

Since the electric field is given in the question is  -

$\overrightarrow{E}=E_{0}\left ( \widehat{x}+\widehat{y} \right )\sin (kz- \omega t)$

So by the  cross product we can say that -
$\Rightarrow \overrightarrow{\mathbf{B}}=\frac{\mathbf{E}_{0}}{\mathbf{C}}(-\hat{\mathbf{x}}+\hat{\mathbf{y}}) \sin (\mathbf{k z}-\omega \mathbf{t})$

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