Question

For plane electromagnetic waves propagating in the $z$ direction, which one of the following combination gives the correct possible direction for $\vec{E}$ and $\vec{B}$ field respectively ?

• A. $\left(\hat{i}+2\hat{j}\right)$ and $\left(2\hat{i}-\hat{j}\right)$
• B. $\left(\hat{-2i}-3\hat{j}\right)$ and $\left(3\hat{i}-\hat{2j}\right)$
• C. $\left(\hat{2i}+3\hat{j}\right)$ and $\left(\hat{i}-\hat{2j}\right)$
• D. $\left(\hat{3i}+4\hat{j}\right)$ and $\left(4\hat{i}-\hat{3j}\right)$

Answer 1

Answer: (B)

$\left(\hat{-2i}-3\hat{j}\right)$ and $\left(3\hat{i}-\hat{2j}\right)$

Answer 2

$\vec{E}$ and $\vec{B}$ are mutually perpendicular
$\vec{E} \times \vec{B}=\vec{C}=C \hat{k}$
$\Rightarrow(-2 \hat{i}-3 \hat{j}) \cdot(3 \hat{i}-2 \hat{j})=-6+6=0$
$\Rightarrow(-2 \hat{i}-3 \hat{j}) \times(3 \hat{i}-2 \hat{j})=(6+9) \hat{k}=15 \hat{k}$