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In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by $\hat{ k }$ and $2 \hat{ i }-2 \hat{ j },$ respectively What is the unit vector along direction of propagation of the wave.
$\frac{1}{\sqrt{2}}(\hat{ i }+\hat{j})$
$\frac{1}{\sqrt{5}}(\hat{ i }+2 \hat{ j })$
$\frac{1}{\sqrt{5}}(2 \hat{ i }+\hat{ j })$
$\frac{1}{\sqrt{2}}(\hat{j}+\hat{k})$
Solution
$\hat{ E }=\hat{ k }$
$\overrightarrow{ B }=2 \hat{ i }-2 \hat{ j } \Rightarrow \hat{ B }=\frac{\overrightarrow{ B }}{| B |}=\frac{2 \hat{ i }-2 \hat{ j }}{2 \sqrt{2}}$
$\Rightarrow \hat{ B }=\frac{1}{\sqrt{2}}(\hat{ i }-\hat{j})$
Direction of wave propagation $=\hat{ C }=\hat{ E } \times \hat{ B }$
$\hat{ C }=\hat{ k } \times\left[\frac{1}{\sqrt{2}}(\hat{ i }-\hat{ j })\right]$
$\hat{ C }=\frac{1}{\sqrt{2}}(\hat{ k } \times \hat{ i }-\hat{ k } \times \hat{ j })$
$\hat{ C }=\frac{1}{\sqrt{2}}(\hat{ i }+\hat{ j })$
