Question

For a plane electromagnetic wave propagating in $x$-direction, which one of the following combination gives the correct possible directions for electric field (E) and magnetic field (B) respectively?

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

Answer 1

Answer: (B)

$(\vec{E}\times \vec{B})$ gives the direction of propagation
$\vec{E}=-\hat{j}+\hat{k},\vec{B}=-\hat{j}-\hat{k}$
$\vec{E}\times \vec{B}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 0& -1& 1\\ 0& -1& -1\end{array}\right|=2\hat{i}$
Also $\vec{E}\cdot \vec{B}=(-\hat{j}+\hat{k})(-\hat{j}-\hat{k})=0$