Question

A plane electromagnetic wave of frequency 50 MHz travels in free space along the x-direction . At a particular point in space and time, $\overrightarrow{E}$ = 6.3 $\hat{j}$ V $m^{-1}$. At this point $\overrightarrow{B}$ is equal to

• A. $8.33\times {10}^{-8}\hat{k}T$
• B. $18.9\times {10}^{-8}\hat{k}T$
• C. $4.1\times {10}^{-8}\hat{k}T$
• D. $2.1\times {10}^{-8}\hat{k}T$

Answer 1

Answer: (D)

$2.1\times {10}^{-8}\hat{k}T$

Given: The Electric field intensity due to electromagnetic waves is, $E_0=6.3V/m$

To find: The direction and intensity of the magnetic field of Electromagnetic wave.

The magnetic field intensity due to the wave is given by

$B_0=\frac{E_0}{C}$

$\Rightarrow B_0=\frac{6.3}{3\times {10}^8}=2.1\times {10}^{-8}$ Tesla

Since the propagation of the wave is along $\hat{i}$ (X-direction) and the electric field vector is along $\hat{j}$, the magnetic field of the wave should lie perpendicular to both the direction of propagation and direction of electric field.

So, $\overrightarrow{B}$ should be along $\overrightarrow{k}$ such that $\overrightarrow{E}\times \overrightarrow{B}$ should give $\hat{i}$ ( propagation in X-direction).

$\Rightarrow \overrightarrow{B}=B_0\hat{k}$

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