Question

The amplitude of electric field in an electromagnetic wave in free space is \( 1000 \, \text{Vm}^{-1} \). The amplitude of the magnetic field in this electromagnetic wave is:

• A. \( 3.0 \times 10^{-3} \, \text{T} \)
• B. \( 3.33 \times 10^{-8} \, \text{T} \)
• C. \( 3.0 \times 10^{11} \, \text{T} \)
• D. \( 3.33 \times 10^{-6} \, \text{T} \)

Hint:

Use the relation \( E = cB \) in vacuum to find the magnetic field amplitude from the electric field amplitude in electromagnetic waves.

Answer 1

The Correct Option is D

The magnetic field \( B \) in free space is related to the electric field \( E \) in an electromagnetic wave by \( E = cB \), or \( B = \frac{E}{c} \). Given \( E = 1000 \, \text{V/m} \) and \( c = 3 \times 10^8 \, \text{m/s} \), the magnetic field is calculated as: \[ B = \frac{1000}{3 \times 10^8} = \frac{10^3}{3 \times 10^8} = \frac{1}{3} \times 10^{-5} = 0.333 \times 10^{-5} = 3.33 \times 10^{-6} \, \text{T} \] Final answer: \( 3.33 \times 10^{-6} \, \text{T} \)