Question

A plane electromagnetic wave of frequency $100MHz$ is travelling in a vacuum along the x-direction. At a particular point in space and time,

$\begin{array}{l}\overrightarrow{B}=2.0\times {10}^{-8}kT\end{array}$ (where$\begin{array}{l}\hat{k}\end{array}$is the unit vector along the z-direction). What is $\begin{array}{l}\overrightarrow{E}\end{array}$ at this point? (speed of light, $c=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$)

• A. $\begin{array}{l}0.6\hat{j}\frac{V}{m}\end{array}$
• B. $\begin{array}{l}6.0\hat{k}\frac{V}{m}\end{array}$
• C. $\begin{array}{l}6.0\hat{j}\frac{V}{m}\end{array}$
• D. $\begin{array}{l}0.6\hat{k}\frac{V}{m}\end{array}$

Answer 1

The correct option is C

$\begin{array}{l}6.0\hat{j}\frac{V}{m}\end{array}$

Explanation for the correct answer is,

Step 1. Given Data:

$\Rightarrow f=100MHz$

$\Rightarrow \begin{array}{l}\overrightarrow{B}=2.0\times {10}^{-8}kT\end{array}$

$$\begin{gathered} \Rightarrow c=3\times {10}^8\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right. \\ \Rightarrow v=3\times {10}^{8}m/s \end{gathered}$$

Step 2. As we know:

$$\begin{gathered} \begin{array}{l}\overrightarrow{E}=\overrightarrow{B}\times \overrightarrow{V}\end{array} \\ \Rightarrow \begin{array}{l}\overrightarrow{E}=2\times {10}^{-8}k\times 3\times {10}^{8}i\end{array} \\ \begin{array}{l}\Rightarrow \overrightarrow{E}=6(\hat{k}\times \hat{i})\\ \therefore \overrightarrow{E}=\frac{\begin{array}{l}6\hat{j}V\end{array}}{m}\end{array} \end{gathered}$$

Hence, the correct option is (C).