First slide

Electromagnetic waves and its nature

Question

In a plane electromagnetic wave, the directions of electric filed 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.

Easy

A

$\frac{1}{\sqrt{5}} (2 \hat{i} + \hat{j})$
B

$\frac{1}{\sqrt{2}} (\hat{j} + \hat{k})$
C

$\frac{1}{\sqrt{2}} (\hat{i} + \hat{j})$
D

$\frac{1}{\sqrt{5}} (\hat{i} + 2 \hat{j})$

Solution

$\begin{array}{l} \hat{P} = \hat{E} \times \hat{B} \\ W h e r e \hat{P} = U n i t v e c t o r a l o n g p r o p a g a t i o n d i r e c t i o n \\ \Rightarrow \hat{P} = \hat{K} \times (\frac{2 \hat{i} - 2 \hat{j}}{2 \sqrt{2}}) \\ \Rightarrow \hat{P} = \frac{1}{\sqrt{2}} (\hat{j} + \hat{i}) \end{array}$

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