Question

A plane electromagnetic wave of frequency 20 MHz travels through a space along $ z $-direction. If the electric field vector at a certain point in space is 6 V/m, then what is the magnetic field vector at that point?

• A. \( 2 \times 10^{-5} \, \text{T} \)
• B. \( 3 \times 10^{-5} \, \text{T} \)
• C. \( 2 \, \text{T} \)
• D. \( \frac{1}{2} \, \text{T} \)

Hint:

For electromagnetic waves, the electric field and magnetic field are related by \( E = cB \). This relationship helps in calculating the magnetic field if the electric field is known.

Answer 1

The Correct Option is A

For an electromagnetic wave, the electric field \( E \) and the magnetic field \( B \) are related by the equation: \[ E = cB \] where:
- \( E \) is the electric field,
- \( B \) is the magnetic field,
- \( c \) is the speed of light in a vacuum, \( c = 3 \times 10^8 \, \text{m/s} \). We are given:
- \( E = 6 \, \text{V/m} \),
- \( \nu = 20 \, \text{MHz} = 20 \times 10^6 \, \text{Hz} \),
- \( c = 3 \times 10^8 \, \text{m/s} \). Using the relationship \( E = cB \), we can solve for \( B \): \[ B = \frac{E}{c} = \frac{6}{3 \times 10^8} = 2 \times 10^{-5} \, \text{T} \]
Thus, the magnetic field vector at that point is: \[ \text{(A) } 2 \times 10^{-5} \, \text{T} \]