Question

A plane electromagnetic wave travels in free space along X-direction. If the value of $\overrightarrow{B}$ (in tesla) at a particular point in space and time is $1.2\times {10}^{-8}\hat{k}$, the value of $\overrightarrow{E}$ (in V $m^{-1}$) at that point is,

• A. $1.2\hat{j}$
• B. $3.6\hat{k}$
• C. $1.2\hat{k}$
• D. $3.6\hat{j}$

Answer 1

The correct option is D $3.6\hat{j}$

Given: The magnetic field of the plane electromagnetic wave is $1.2\times {10}^{-8}\hat{k}T$

The direction of propagation of the electromagnetic wave is along X-direction.

The magnitude of $\overrightarrow{E}$ is given by:

$E=B\cdot c=(1.2\times {10}^{-8}T)(3\times {10}^{-8}m{s}^{-1})=3.6V/m$

Since the magnetic field is along $Z-$ direction and the wave propagates along $X-$ direction. Therefore $\overrightarrow{E}$ should be in a direction perpendicular to both $X$ and $Z$ axes.

Using vector algebra should be along X-direction.

Since $(+\hat{j})\times \left(\hat{k}\right)=\hat{i}$

$\overrightarrow{E}$ is along the $Y-$direction.

Thus, $\overrightarrow{E}=3.6\hat{j}V{m}^{-1}$