Question

A plane electromagnetic wave of frequency $25 \,MHz$ 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 $B=\frac{E}{c}=\frac{(6.3\, V / m )}{\left(3 \times 10^{8} \,m / s \right)}=2.1 \times 10^{-8} T$
$\vec{E}$ 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, $\vec{B}=2.1 \times 10^{-8} \hat{k} \,T$