Question:

In a plane electromagnetic wave traveling in free space, the electric field component oscillates sinusoidally at a frequency of 2x1010 Hz and amplitude of 48 Vm-1. Then the amplitude of the oscillating magnetic field is: (Speed of light in free space = 3x108 ms-1)

Updated On: May 1, 2025

  • 1.6 × 10-6 T

  • 1.6 × 10-9 T

  • 1.6 × 10-8 T

  • 1.6 × 10-7 T

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The Correct Option is D

Approach Solution - 1

To determine the amplitude of the oscillating magnetic field in a plane electromagnetic wave, we utilize the relationship between the electric field \( E \) and the magnetic field \( B \) in free space, which is given by:

\( E = cB \) 

 

where:

  • \( E \) is the amplitude of the electric field, given as 48 V/m.
  • \( c \) is the speed of light in free space, \( 3 \times 10^8 \) m/s.
  • \( B \) is the amplitude of the magnetic field, which we need to find.

Rearranging the equation to solve for \( B \), we get:

\( B = \frac{E}{c} \)

 

Substitute the known values:

\( B = \frac{48\, \text{V/m}}{3 \times 10^8\, \text{m/s}} \)

 

Calculate \( B \):

\( B = 1.6 \times 10^{-7} \, \text{T} \)

 

Thus, the amplitude of the oscillating magnetic field is \( 1.6 \times 10^{-7} \, \text{T} \), which matches the provided correct answer.

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Approach Solution -2

Given :
\(C=\frac{E_0}{B_0}\)
\(B_0=\frac{E_0}{C}\)
Then,
\(=\frac{48}{3\times10^8}\)
= 1.6 × 10-7 T
So, the correct option is (D) : 1.6 × 10-7 T

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Concepts Used:

Electromagnetic waves

The waves that are produced when an electric field comes into contact with a magnetic field are known as Electromagnetic Waves or EM waves. The constitution of an oscillating magnetic field and electric fields gives rise to electromagnetic waves.

Types of Electromagnetic Waves:

Electromagnetic waves can be grouped according to the direction of disturbance in them and according to the range of their frequency. Recall that a wave transfers energy from one point to another point in space. That means there are two things going on: the disturbance that defines a wave, and the propagation of wave. In this context the waves are grouped into the following two categories:

  • Longitudinal waves: A wave is called a longitudinal wave when the disturbances in the wave are parallel to the direction of propagation of the wave. For example, sound waves are longitudinal waves because the change of pressure occurs parallel to the direction of wave propagation.
  • Transverse waves: A wave is called a transverse wave when the disturbances in the wave are perpendicular (at right angles) to the direction of propagation of the wave.