Question

A plane electromagnetic wave of frequency $25\text{GHz}$ is propagating in vacuum along the $z-$direction. At a particular point in space and time, the magnetic field is given by $\overrightarrow{B}=5\times {10}^{-8}\hat{j}\text{T}.$ The corresponding electric field $\overrightarrow{E}$ is $\text{(speed of light c}=3\times {10}^8{\text{ms}}^{-1})$

• A. $1.66\times {10}^{-16}\hat{i}\text{V/m}$
• B. $-1.66\times {10}^{-16}\hat{i}\text{V/m}$
• C. $-15\hat{i}\text{V/m}$
• D. $15\hat{i}\text{V/m}$

Answer 1

The correct option is D $15\hat{i}\text{V/m}$

Amplitude of electric field $\left(E\right)$ and magnetic field $\left(B\right)$ of an electromagnetic wave are related by the relation

$\Rightarrow E=Bc$

We know that, direction of propagation is along $\overrightarrow{E}\times \overrightarrow{B}$
Given that direction of propagation is along $z$ axis and $\overrightarrow{B}$ is directed along $y$ axis.
Hence $\overrightarrow{E}$ is directed along $x$ axis.

$\Rightarrow E=5\times {10}^{-8}\times 3\times {10}^8=15\text{N/C}$

$\Rightarrow \overrightarrow{E}=15\hat{i}\text{V/m}$