The electric field of a plane electromagnetic wave

Question:

The electric field of a plane electromagnetic wave propagating along the $x$ direction in vacuum is $\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx}) .$ The magnetic field $\overrightarrow{\mathrm{B}}$, at the moment $\mathrm{t}=0$ is :

  1. $\overrightarrow{\mathrm{B}}=\mathrm{E}_{0} \sqrt{\mu_{0} \in_{0}} \cos (\mathrm{kx}) \hat{\mathrm{j}}$

  2. $\overrightarrow{\mathrm{B}}=\frac{\mathrm{E}_{0}}{\sqrt{\mu_{0} \in_{0}}} \cos (\mathrm{kx}) \hat{\mathrm{k}}$

  3. $\overrightarrow{\mathrm{B}}=\mathrm{E}_{0} \sqrt{\mu_{0} \in_{0}} \cos (\mathrm{kx}) \hat{\mathrm{k}}$

  4. $\overrightarrow{\mathrm{B}}=\frac{\mathrm{E}_{0}}{\sqrt{\mu_{0} \in_{0}}} \cos (\mathrm{kx}) \hat{\mathrm{j}}$


Correct Option: , 3

Solution:

$\Rightarrow \overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \cos (\mathrm{wt}-\mathrm{kx}) \hat{\mathrm{k}}$

Now put $\mathrm{t}=0 .$

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