Question

A plane electromagnetic wave of frequency $50\text{MHz}$ travels in free space along the positive $x-$direction. At a particular point in space and time, $\overrightarrow{E}=6.3\hat{j}{\text{Vm}}^{-1}$. The corresponding magnetic field $\overrightarrow{B}$, at that point will be:

• A. $2.1\times {10}^{-8}\hat{k}\text{T}$
• B. $6.3\times {10}^{-8}\hat{k}\text{T}$
• C. $18.9\times {10}^{-8}\hat{k}\text{T}$
• D. $18.9\times {10}^{-8}\hat{k}\text{T}$

Answer 1

The correct option is A $2.1\times {10}^{-8}\hat{k}\text{T}$

From electromagnetic theory,

$|\overrightarrow{B}|=\frac{|\overrightarrow{E}|}{c}$

$\Rightarrow |\overrightarrow{B}|=\frac{6.3}{3\times {10}^8}=2.1\times {10}^{-8}\text{T}$

and $\hat{E}\times \hat{B}=\hat{c}$

$\Rightarrow \hat{j}\times \hat{B}=\hat{i}$

$\therefore \hat{B}=\hat{k}$

$\Rightarrow \overrightarrow{B}=2.1\times {10}^{-8}\hat{k}\text{T}$

Hence, option $\left(B\right)$ is correct.