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

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}(\hat{i}+\hat{j})$

Electromanetic wave will propagate perpendicular to the direction of Electric and Magnetic fields
$\hat{C}=\hat{E}\times \hat{B}$
Here unit vector $\hat{C}$ is perpendicular to both $\hat{E}$ and $\hat{B}$
Given, $\overrightarrow{E}=\hat{k},\overrightarrow{B}=2\hat{i}-2\hat{j}$

$\therefore \hat{C}=\hat{E}\times \hat{B}=\frac{1}{\sqrt{2}}\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& 0& 1\\ 1& -1& 0\end{array}\right|=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

$\Rightarrow \hat{C}=\frac{\hat{i}+\hat{j}}{\sqrt{2}}$