Question: Q. 6. A plane electromagnetic wave of frequency 25 MHz travels in free space along the $x$-direction. At $a$ particular point in space and time, $E=$
$6.3 \hat{j} \mathrm{~V} / \mathrm{m}$. What is $B$ at this point?
U] [SQP II 2017]
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Solution:
Ans. The magnitude of $B$ is
$$ \begin{aligned} B & =\frac{E}{c} \ & =\frac{6.3 \mathrm{~V} / \mathrm{m}}{3 \times 10^{8} \mathrm{~m} / \mathrm{s}} \ & =2.1 \times 10^{-8} \mathrm{~T} \end{aligned} $$
To find the direction, we note that $E$ is along $y$-direction and the wave propagates along $x$-axis. Therefore, $B$ should be in a direction perpendicular to both $x$ and $y$-axes. Using vector algebra, $E \times B$ should be along $x$-direction.
Since, $(+\hat{j}) \times(+\hat{k})=\hat{i}$ so, $B$ is along $z$-direction and is $2.1 \times 10^{-8} \mathrm{~T}$.
[CBSE Marking Scheme 2017]
