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 $=\hat{C}=\hat{E}\times \hat{B}$
$\hat{C}=\hat{k}\times \left[\frac{1}{\sqrt{2}}(\hat{i}-\hat{j})\right]$
$\hat{C}=\frac{1}{\sqrt{2}}(\hat{k}\times \hat{i}-\hat{k}\times \hat{j})$
$\hat{C}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$