Question

Choose the correct answer from the alternatives given.
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 $\overrightarrow{E}\left(inV{m}^{-1}\right)$ at that point is

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

Answer 1

The correct option is D $3.6\stackrel{\wedge }{j}$

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.

To find: The magnitude and direction of the Electric field at that point.

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

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

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 $\overrightarrow{E}\times \overrightarrow{B}$ should be along $X$-direction.

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

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

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

Option $\left(D\right)$ is correct.