Electromagnetic waves are produced by:

Oscillating (accelerating) charges

Maxwell, Electromagnetic Waves and Spectra

In short: Maxwell showed that electricity and magnetism are linked and predicted electromagnetic waves travelling at the speed of light, so light itself is an electromagnetic wave. The spectra of light from stars show their temperature, what they are made of and how they move.

Maxwell's big idea

Before Maxwell, electricity, magnetism and light were thought of as separate topics. Maxwell unified electricity and magnetism with four equations. From them he predicted:

A changing electric field makes a magnetic field, and a changing magnetic field makes an electric field.
Together these can travel through empty space as an electromagnetic (EM) wave, with the two fields at right angles to each other and to the direction of travel.
These waves are made by accelerating (oscillating) charges.
They all travel at the same speed in a vacuum:

$c = \frac{1}{μ _{0} ε _{0}} = 3.00 \times 1 0^{8} m/s$

where $μ_{0}$ and $ε_{0}$ are constants measured from magnetism and electricity.

Light is one of these waves, and there should be others with wavelengths we cannot see.

Hertz proves it

In 1887, Heinrich Hertz used a spark gap to make charges oscillate rapidly. A small loop of wire across the room sparked too, so invisible waves had crossed the gap. He showed they reflected, refracted, interfered and could be polarised, just like light, and he measured their speed: the speed of light. These were the first radio waves, and they confirmed Maxwell's prediction.

The electromagnetic spectrum

All EM waves travel at $c$ in a vacuum and obey the wave equation:

$c = f λ$

From longest wavelength (lowest frequency, lowest energy) to shortest: radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays.

Measuring the speed of light

Who	Method
Fizeau (1849)	Shone light through the gaps of a fast-spinning toothed wheel to a mirror 8 km away and back. At the right speed, the returning light hit a tooth and was blocked. The time for one gap to be replaced by a tooth equals the round trip time.
Foucault (1850)	Used a rotating mirror. The mirror turned slightly while the light travelled to a distant mirror and back, so the returning beam was shifted. He also found light is slower in water than in air.

Three kinds of spectra

A spectroscope spreads light into its colours using a prism or a diffraction grating.

Spectrum	Looks like	Made by
Continuous	All colours, no gaps	Hot dense objects: a glowing filament, a star's surface
Emission (line)	Bright coloured lines on a dark background	Hot thin gas, such as a gas discharge tube
Absorption	Continuous spectrum with dark lines	Cooler gas in front of a hot source, such as a star's outer layers

Each element makes its own pattern of lines, like a barcode. The dark lines in an absorption spectrum are at exactly the same wavelengths as the bright lines in that element's emission spectrum.

What starlight tells us

By looking carefully at a star's spectrum, astronomers can find its:

Surface temperature: from the colour and the peak wavelength (see Light: the Quantum Model).
Chemical composition: from the absorption lines, matched to elements.
Translational velocity (moving towards or away from us): all the lines are shifted. Shifted to longer wavelengths (redshift) means moving away. Shifted to shorter wavelengths (blueshift) means moving towards us.
Rotational velocity: one side of a spinning star comes towards us and the other moves away, so each line is spread out (broadened). Faster spin, broader lines.
Density: denser stars, with higher pressure in their atmospheres, have broader lines.

Electromagnetic Waves

Maxwell

Unified electricity and magnetism
Predicted EM waves
c = 1 / √(μ₀ε₀)
Light is an EM wave

Hertz

Made radio waves
Same speed as light

Speed of light

Fizeau: toothed wheel
Foucault: rotating mirror
c = fλ

Spectra

Continuous
Emission lines
Absorption lines

Starlight

Temperature
Composition
Red and blue shift
Line broadening

Year 12Calculating a star's speed from a redshift

For speeds much less than $c$ , the shift in a spectral line gives the star's speed along our line of sight:

$\frac{Δ λ}{λ} \approx \frac{v}{c}$

Hydrogen's red line is at 656.3 nm in a lab. In a star it is measured at 658.5 nm. The shift is $Δ λ = 2.2$ nm, so $v = 3.00 \times 1 0^{8} \times \frac{2.2}{656.3} = 1.0 \times 1 0^{6}$ m/s, moving away (redshift).

Maxwell's limits. Maxwell's waves were thought to need a medium, the "aether", to travel through. The Michelson and Morley experiment (1887) failed to find it. This puzzle was solved by Einstein's special relativity (see Light and Special Relativity).

More on Fizeau. At exactly twice the blocking speed, the light that left through one gap returns through the next gap, so the observer sees it again. The blocking speed for a wheel with $N$ teeth at distance $d$ comes from: time for half a tooth spacing $= \frac{1}{2 N f}$ equals the round trip $\frac{2 d}{c}$ , so $f = \frac{c}{4 N d}$ .

Foucault and the models. Light being slower in water than in air supported the wave model and contradicted Newton's particle model, which needed light to speed up in water.

What an AC wire gives off. The charges oscillate at the AC frequency (50 Hz or radio frequencies for an antenna), so the wire gives off low-frequency radio waves.

What absorption lines prove. Matching lines show which elements are present. The absence of an element's lines suggests it is absent or very rare in the star's outer layers, but is not absolute proof.

Using the constants. $c = \frac{1}{μ _{0} ε _{0}} = \frac{1}{4 π \times 1 0 ^{- 7} \times 8.854 \times 1 0 ^{- 12}} \approx 3.00 \times 1 0^{8}$ m/s. In a material, $v = \frac{1}{μ ε}$ is slower, because $μ ε$ is bigger than in a vacuum.

Rotation from broadening. A line spread from $λ - Δ λ$ to $λ + Δ λ$ gives the edge speed $v = c \frac{Δ λ}{λ}$ , using the half-width. A star that is moving away and spinning has lines that are both shifted to the red and broadened.

Timing light. If one path is 6.0 m longer and its pulse arrives 20 ns later, $c = \frac{6.0}{20 \times 1 0 ^{- 9}} = 3.0 \times 1 0^{8}$ m/s.

Safety with discharge tubes. They run on high voltage (do not touch the terminals with the power on) and some give off ultraviolet (do not stare at them for long; use UV-blocking glasses).

Michelson and Morley. They found no difference in the speed of light in two directions at right angles, which suggested there is no aether and that light's speed is the same in every direction.

Quick summary

Maxwell unified electricity and magnetism and predicted EM waves travelling at $c = \frac{1}{μ _{0} ε _{0}}$ . Light is an EM wave.
EM waves are made by oscillating charges. Their electric and magnetic fields are at right angles.
Hertz made radio waves and confirmed Maxwell's prediction.
Fizeau and Foucault measured the speed of light. $c = f λ$ .
Continuous, emission and absorption spectra come from hot dense objects, hot thin gases and cool gas in front of a hot source.
Star spectra reveal temperature, composition, motion towards or away, rotation and density.

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Who first predicted that light is an electromagnetic wave?
1. A Newton
2. B Hertz
3. C Maxwell
4. D Einstein
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C: Maxwell
Maxwell's equations predicted EM waves moving at the speed of light.
Who first produced and detected radio waves, confirming the prediction?
1. A Maxwell
2. B Hertz
3. C Fizeau
4. D Planck
Show answer
B: Hertz
Hertz used a spark gap and showed the waves behaved like light.
Electromagnetic waves are produced by:
1. A Charges at rest
2. B Oscillating (accelerating) charges
3. C Steady magnetic fields
4. D Sound vibrations
Show answer
B: Oscillating (accelerating) charges
An oscillating charge makes changing electric and magnetic fields that travel outwards.