Nature of Electromagnetic Waves

It follows from Maxwell’s equations that the electric field and magnetic field in an electromagnetic wave are perpendicular to each other and also perpendicular to the direction of propagation.

This can be understood from the discussion of displacement current in a capacitor. Inside the plates of a capacitor, the electric field is perpendicular to the plates, and the magnetic field produced due to displacement current is along the perimeter of a circle parallel to the capacitor plates, showing that the electric and magnetic fields are mutually perpendicular.

A typical plane electromagnetic wave may propagate along the z-direction. In such a case, the electric field E_x​ is along the x-axis and the magnetic field B_y​ is along the y-axis, while both vary sinusoidally with the z-coordinate at a given time.

Thus, the electric field, the magnetic field, and the direction of propagation are all mutually perpendicular.

Mathematical Representation

The electric and magnetic fields of the plane electromagnetic wave are written as:

Here, k is related to wavelength λ by:

The quantity ω is the angular frequency. The magnitude of the wave vector is k, and its direction gives the direction of propagation of the wave.

Using Maxwell’s equations for the above electric and magnetic fields, one obtains:

where

This standard wave relation may also be written in terms of frequency ν and wavelength λ as:

From Maxwell’s equations, the magnitudes of the electric field and magnetic field in an electromagnetic wave are related by:

• Electromagnetic waves are self-sustaining oscillations of electric and magnetic fields in free space or vacuum.
• No material medium is involved in these oscillations.
• They differ from the other waves studied earlier in that they can propagate without a material medium.

When a material medium is present, the electric and magnetic fields inside the medium are described using the permittivity ε and magnetic permeability μ of the medium. These replace ε₀​ and μ₀​ in Maxwell’s equations.

In such a medium, the velocity of light becomes:

Therefore, the velocity of light depends on the electric and magnetic properties of the medium.

The velocity of electromagnetic waves in free space or vacuum is a fundamental constant. Experiments with electromagnetic waves of different wavelengths show that this velocity remains the same, independent of wavelength, to within a few metres per second out of a value of 3 × 10⁸ m/s.

The constancy and accurately known value of this velocity are so important that it is used to define a standard of length.

Technological Importance

Electromagnetic waves are technologically important because they can carry energy from one place to another. shaalaa

• Radio and TV signals from broadcasting stations carry energy. shaalaa
• Light carries energy from the Sun to the Earth, making life possible on Earth.

A plane electromagnetic wave of frequency 25 MHz travels in free space along the x-direction. At a particular point in space and time, \[\vec E\] = 6 . 3\[\hat j\]​ V/m. The magnetic field at that point is found using:

Substituting values:

Since the electric field is along the y-direction and the wave propagates along the x-axis, the magnetic field must be perpendicular to both. Using vector algebra, \[\vec E\] × \[\vec B\]  must point along the x-direction, so the magnetic field is along the z-direction.

Thus,

The magnetic field in a plane electromagnetic wave is given by:

(a) Wavelength and Frequency

Comparing with the standard form, the wavelength is:

The frequency is:

(b) Electric Field Expression

Using E₀ = B₀c:

The electric field component is perpendicular to both the direction of propagation and the magnetic field. Therefore, the electric field along the z-axis is:

• Electric and magnetic fields in an electromagnetic wave are perpendicular to each other.
• Both fields are perpendicular to the direction of propagation.
• Electromagnetic waves are self-sustaining oscillations in a vacuum.
• No material medium is required for their propagation.
• In a vacuum, their speed is 3 × 10⁸ m/s.
• In a material medium, velocity is \[\frac {1}{\sqrt {με}}\].
• Radio, TV signals, and light are important examples of energy transfer by electromagnetic waves.