Nature of electromagnetic waves

An electromagnetic wave consists of oscillating electric and magnetic fields that travel through space. As the wave passes a point, the fields at that point change with time. The wave carries energy from one place to another.

Direction of the fields

In a plane electromagnetic wave, the electric field and magnetic field oscillate at right angles to each other. Both fields are also at right angles to the direction in which the wave travels. Because the oscillations are perpendicular to the direction of travel, the wave is transverse.

For example, if a plane electromagnetic wave travels forwards and its electric field oscillates up and down, its magnetic field oscillates from side to side.

Electromagnetic waves in a vacuum

Electromagnetic waves can travel through a vacuum, where there is no material medium. They do not need particles of a material to pass the wave along: the travelling electric and magnetic fields carry the wave and its energy through space.

Maxwell’s formula for electromagnetic wave speed

Electromagnetic waves travel through a vacuum at a speed determined by two properties of free space: its permittivity and its permeability. Maxwell’s formula connects these electric and magnetic properties to the speed of light:

Here, $$c$$ is the speed of electromagnetic waves in a vacuum, approximately $$3.00 \times 10^8\ \mathrm{m,s^{-1}}$$. The symbol $$\varepsilon_0$$ is the permittivity of free space, and $$\mu_0$$ is the permeability of free space.

What permittivity and permeability describe

Permittivity relates to the electric field produced by a charged object in free space. For a fixed charge distribution, the electric field strength is inversely proportional to $$\varepsilon_0$$: a greater permittivity corresponds to a weaker electric field.

Permeability relates to the magnetic flux density produced by a current-carrying wire in free space. For a fixed wire geometry and current, the magnetic flux density is proportional to $$\mu_0$$: a greater permeability corresponds to a greater magnetic flux density.

In Maxwell’s formula, these two properties appear together under the square root in the denominator. Their product therefore determines the speed of electromagnetic waves in a vacuum, which is the speed of light.

Hertz’s discovery of radio waves

Heinrich Hertz used electrical circuits to generate and detect radio waves. His experiment showed that electromagnetic waves could travel across the space between two separate circuits.

Generating and detecting the waves

Hertz’s transmitting circuit had a spark gap: a small break across which a spark could jump. The electrical activity in the circuit oscillated rapidly, producing electromagnetic waves that travelled away from it.

A separate receiving circuit also had a spark gap. When the waves reached it, they produced an electrical response in the circuit. A small spark across the receiving gap provided evidence that the waves had been detected.

Comparing radio-wave speed with light

Hertz measured the wavelength of the waves and used it with their frequency to determine their speed:

Here, $$v$$ is wave speed, $$f$$ is frequency and $$\lambda$$ is wavelength. Hertz’s measured speed was consistent with the speed of light. This supported the view that radio waves and light are both electromagnetic waves.

Fizeau’s measurement of the speed of light

Fizeau measured how long light took to travel to a distant mirror and back. He used a rotating toothed wheel to make that short time detectable.

Light passed through a gap in the wheel, travelled to the mirror and returned towards the same position on the wheel. While the light was travelling, the wheel continued to rotate. At a suitable rotation rate, a tooth moved into the light’s path and blocked the returning light.

Finding the speed of light

The wheel’s rotation rate and the spacing between a gap and a neighbouring tooth showed how long the wheel took to move the tooth into the gap’s position. This was the light’s round-trip time: the time taken to reach the mirror and return.

If the mirror was a distance $$d$$ from the wheel and the round-trip time was $$t$$, the light travelled a total distance of $$2d$$. Its speed was therefore:

The result showed that light takes a finite time to travel and provided a measurement of its speed on Earth. The measured speed can be compared with the speed of electromagnetic waves predicted by Maxwell’s theory. Their agreement supports the identification of light as an electromagnetic wave.