Question

A plane electromagnetic wave of frequency $100\text{MHz}$ is travelling in vacuum along the x- direction. At a particular point in space and time, $\overrightarrow{B}=2.0\times {10}^{-8}\hat{k}\text{T}$ (where, $\hat{k}$ is unit vector along z - direction). What is $\overrightarrow{E}$ at this point?
(speed of light $c=3\times {10}^8\text{m/s}$)

• A. $0.6\hat{j}\text{V/m}$
  
• B. $6.0\hat{k}\text{V/m}$
  
• C. $6.0\hat{j}\text{V/m}$
  
• D. $0.6\hat{k}\text{V/m}$
  

Answer 1

The correct option is C $6.0\hat{j}\text{V/m}$


Given, $\overrightarrow{v}=3\times {10}^8\hat{i}\text{m/s}$ and $\overrightarrow{B}=2.0\times {10}^{-8}\hat{k}\text{T}$

We know that, $E=Bc$
$E=(2\times {10}^{-8})\times (3\times {10}^8)$
$E=6\text{V/m}$

And direction of propagation of wave is parallel to $\overrightarrow{E}\times \overrightarrow{B}$.
So, $\hat{i}=\hat{j}\times \hat{k}$
$\overrightarrow{E}=6\hat{j}\text{V/m}$