# An electromagnetic wave is represented by the electric

Question:

An electromagnetic wave is represented by the electric field $\vec{E}=E_{0} \hat{n} \sin [\omega t+(6 y-8 z)]$. Taking unit vectors in $x$,

$y$ and $z$ directions to be $\hat{i}, \hat{j}, \hat{k}$, the direction of propogation

$\hat{s}$ is:

1. (1) $\hat{s}=\frac{3 \hat{i}-4 \hat{j}}{5}$

2. (2) $\hat{s}=\frac{-4 \hat{k}+3 \hat{j}}{5}$

3. (3) $\hat{s}=\left(\frac{-3 \hat{j}+4 \hat{k}}{5}\right)$

4. (4) $\hat{s}=\frac{3 \hat{j}-3 \hat{k}}{5}$

Correct Option: , 3

Solution:

(3) $\hat{S}=\frac{6 \hat{j}+8 \hat{k}}{\sqrt{6^{2}+8^{2}}}=\frac{-3 \hat{j}+4 \hat{k}}{5}$