Properties of Electromagnetic Waves

If the wave is moving along the x-axis, then usually:

• The electric field \(\vec{E}\) oscillates along the y-axis.
• The magnetic field \(\vec{B}\) oscillates along the z-axis.
• The wave itself travels along the x-axis.

So \(\vec{E}\), \(\vec{B}\), and the direction of propagation form a mutually perpendicular trio.

where \(\vec{k}\) is the direction of wave propagation.

In vacuum, the speed of any electromagnetic wave is:

Maxwell showed that the speed of electromagnetic waves in vacuum depends on two properties of free space: electric permittivity \(\varepsilon_0\) and magnetic permeability \(\mu_0\).

This was one of the biggest discoveries in physics because it linked light with electricity and magnetism.

When electromagnetic waves travel through glass, water, or any other material, they usually slow down. The new speed becomes:

where \(n\) is the refractive index of the medium.

The speed of a wave is related to its frequency and wavelength by:

For electromagnetic waves in vacuum, \(v = c\), so:

If the frequency increases, the wavelength automatically decreases, because their product must always equal the speed of the wave.

For example:

• Radio waves have very large wavelengths and low frequencies.
• Gamma rays have very tiny wavelengths and extremely high frequencies.

Mechanical waves like sound or water waves need particles to vibrate. Without particles, they cannot propagate.

In electromagnetic waves, the disturbance is in the electric and magnetic fields themselves, not in matter. Because a changing electric field produces a changing magnetic field and vice versa, the wave keeps moving forward even in empty space.

The energy in an electromagnetic wave is shared between the electric field and the magnetic field. In a plane wave, both fields carry equal amounts of energy.

The intensity of an electromagnetic wave is the energy flowing per unit area per unit time.

Intensity is proportional to the square of the electric field amplitude:

If you point your index finger along the direction of the electric field \(\vec{E}\), and your middle finger along the direction of the magnetic field \(\vec{B}\), then your thumb gives the direction in which the wave propagates.

This cross-product relation shows that the wave travels perpendicular to both fields.

If the electric field oscillates only in a single plane, the wave is said to be linearly polarised.

Polaroid sunglasses block certain orientations of light waves. They reduce glare because they absorb waves whose electric field oscillates in specific directions.