Question

A plane electromagnetic wave travels in free space. Electric field is $\left|\overrightarrow{E_{\circ }}\right|=E_{\circ }\hat{i}$ and magnetic field is represented by$\left|\overrightarrow{B_{\circ }}\right|=B_{\circ }\hat{k}$. What is the unit vector along the direction of propagation of electromagnetic waves?

• A. $\hat{j}$
• B. $-\hat{k}$
• C. $-\hat{j}$
• D. $\hat{k}$

Answer 1

The correct option is C

$-\hat{j}$

Step 1: Given data

Electric field, $\overrightarrow{E}=E_{\circ }\hat{i}$

magnetic field,$\overrightarrow{B}=B_{\circ }\hat{k}$

Step 2: Find the unit vector along the direction of propagation of EM wave

The direction of propagation of the EM wave is given by the direction of $\overrightarrow{E}\times \overrightarrow{B}$

The unit vector in the direction of $\overrightarrow{E}\times \overrightarrow{B}=\frac{\overrightarrow{E}\times \overrightarrow{B}}{\left|\overrightarrow{E}\times \overrightarrow{B}\right|}$

$$\begin{gathered} =\frac{E_{\circ }\hat{i}\times B_{\circ }\hat{k}}{\left|E_{\circ }\hat{i}\times B_{\circ }\hat{j}\right|} \\ =\frac{E_{\circ }.B_{\circ }\left(\hat{i}\times \hat{k}\right)}{E_{\circ }.B_{\circ }} \\ =-\hat{j} \end{gathered}$$

Hence, option (C) is correct.