Question

A plane electromagnetic wave of frequency $25MHz$ travels in free space along the $x$ -direction. At a particular point in space and time, $\vec{E}=6.3\hat{j}V/m.$ At this point $\vec{B}$ is equal to

• A. $8.33\times 10^{-8}\hat{k}T$
• B. $18.9\times 10^{-8}\hat{k}T$
• C. $2.1\times 10^{-8}\hat{k}T$
• D. $2.1\times 10^{-8}\hat{i}T$

Answer 1

Answer: (C)

Here, $\vec{E}=6.3\hat{j}V/m$
The magnitude of $\vec{B}$ is $B=\frac{E}{c}=\frac{(6.3V/m)}{\left(3\times 10^{8}m/s\right)}=2.1\times 10^{-8}T$
$\vec{E}$ is along $y$ -direction and the wave propagates along $x$ -axis. Therefore, $\vec{B}$ should be in a direction perpendicular to both $x$ -and $y$ -axes. Using vector algebra $\vec{E}\times \vec{B}$ should be along $x$ -direction.
Since $(+\hat{j})\times (+\hat{k})=\hat{i},\vec{B}$ is along $z$ -direction.
Thus, $\vec{B}=2.1\times 10^{-8}\hat{k}T$