Question

A plane electromagnetic wave of frequency 35 MHz travels in free space along the X-direction. At a particular point (in space and time), \( \vec{E} = 9.6 \hat{j} \, \text{V/m} \). The value of the magnetic field at this point is:

• A. \( 3.2 \times 10^{-8} \hat{k} \, \text{T} \)
• B. \( 3.2 \times 10^{-8} \hat{i} \, \text{T} \)
• C. \( 9.6 \hat{j} \, \text{T} \)
• D. \( 9.6 \times 10^{-8} \hat{k} \, \text{T} \)

Answer 1

The Correct Option is A

For an electromagnetic wave, the electric field \( \vec{E} \) and magnetic field \( \vec{B} \) are related by the speed of light \( c \):  
\(\frac{E}{B} = c\)
where \( c = 3 \times 10^8 \, \text{m/s} \).

Step 1: Calculate the magnetic field \( B \):  
Given \( E = 9.6 \, \text{V/m} \),  
\(B = \frac{E}{c} = \frac{9.6}{3 \times 10^8} = 3.2 \times 10^{-8} \, \text{T}\)

Step 2: Determine the direction of \( \vec{B} \):  
Since the wave travels along the X-direction and \( \vec{E} \) is along \( \hat{j} \), the magnetic field \( \vec{B} \) must be perpendicular to both the direction of propagation and \( \vec{E} \). By the right-hand rule:  
\(\vec{B} \, \text{points along} \, \hat{k}.\)

Thus, the magnetic field at this point is \( 3.2 \times 10^{-8} \hat{k} \, \text{T}. \)

The Correct Answer is: \( 3.2 \times 10^{-8} \hat{k} \, \text{T}. \)