Question

A plane $\text{EM}$ wave of frequency $25\text{MHz}$ travels in free space in $x$-direction. At a particular point in space and time $\overrightarrow{E}=6.3{\text{Vm}}^{-1}\hat{j}$ then $B$ at that point is-

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

Answer 1

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

Given,

$f=25\text{MHz}=25\times {10}^6\text{Hz};\overrightarrow{E}=6.3{\text{Vm}}^{-1}\hat{j}{E}_0=6.3{\text{Vm}}^{-1}$

As we know, $\left(\frac{E_0}{B_0}\right)=c$

$\therefore B_0=\left(\frac{E_0}{c}\right)=\left[\frac{6.3}{3\times {10}^8}\right]=2.1\times {10}^{-8}\text{T}$

$\because \overrightarrow{E}$ is along $y$-direction and wave is travelling along $x$-direction, hence $\overrightarrow{B}$ has to be perpendicular to both $x$ and $y$ axes.

$\Rightarrow \overrightarrow{E}\times \overrightarrow{B}$ should be along $x$ direction.

$\therefore \overrightarrow{B}$ should be along $z$-direction.

Hence, $\overrightarrow{B}=B_0\hat{k}$

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

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.