Question

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.

• A. $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$
• B. $\frac{1}{\sqrt{5}}(\hat{i}+2\hat{j})$
• C. $\frac{1}{\sqrt{5}}(2\hat{i}+\hat{j})$
• D. $\frac{1}{\sqrt{2}}(\hat{j}+\hat{k})$

Answer 1

Answer: (A)

$\hat{ E }=\hat{ k }$
$\vec{ B }=2 \hat{ i }-2 \hat{ j }$
$ \Rightarrow \hat{ B }=\frac{\vec{ 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 }) $
$\hat{ C }=\frac{1}{\sqrt{2}}(\hat{ i }+\hat{ j })$