E. The Wave Nature of Light · The Wave Nature of LightElectromagnetic Waves from Oscillating Charges
E2.1 E3.4 A1.12About 65 minutes
Learning goals- I can describe, in qualitative terms, how an oscillating electric dipole produces electromagnetic radiation.
- I can describe an electromagnetic wave as perpendicular, changing electric and magnetic fields travelling at c.
- I can relate the frequency of the radiation to the frequency of the oscillating charges, and use c = fλ.
- I can identify how radio transmitters, microwave emitters, X-ray tubes and atoms produce different parts of the electromagnetic spectrum.
Words to know
electromagnetic (EM) wave
A transverse wave of changing electric and magnetic fields, perpendicular to each other and to the direction of travel, moving at c = 3.00 × 10⁸ m/s in a vacuum.
oscillate
To move or vary back and forth repeatedly.
electric dipole
A pair of equal and opposite charges separated by a small distance.
antenna
A conductor in which oscillating charges produce (or detect) electromagnetic waves.
electromagnetic spectrum
The full range of electromagnetic waves, from radio waves to gamma rays, ordered by wavelength or frequency.
accelerating charge
A charge that is speeding up, slowing down or changing direction; only accelerating charges radiate electromagnetic waves.
A wave without a medium
Sound needs air; water waves need water. Light crosses 150 million kilometres of nearly empty space from the Sun. What is waving? The answer came in the 1860s from James Clerk Maxwell: light is a wave of electric and magnetic fields, and it is made by charges that oscillate. A radio station, a microwave oven and a glowing neon sign are all, at heart, ways of shaking charges back and forth.
Fields that make each other
In Gravitational, Electric and Magnetic Fields you studied fields around charges and currents. Maxwell put two key ideas together:
- A changing magnetic field produces an electric field (this is electromagnetic induction, which you met in Grade 11).
- A changing electric field produces a magnetic field.
So a changing E field makes a changing B field, which makes a changing E field, and so on. The disturbance keeps itself going and travels outward as an electromagnetic wave. Maxwell calculated its speed from two constants measured in electricity experiments:
c = 1/√(μ₀ε₀) = 1/√[(4π × 10⁻⁷)(8.85 × 10⁻¹²)] ≈ 3.00 × 10⁸ m/s
This matched the measured speed of light, so Maxwell concluded that light is an electromagnetic wave. In 1887 to 1888, Heinrich Hertz confirmed the theory by making and detecting radio waves in his laboratory.
How an oscillating dipole radiates
A charge sitting still has an electric field but makes no wave. A charge moving at a constant velocity makes no wave either. Only accelerating charges radiate.
The simplest radiator is an oscillating electric dipole: a straight antenna connected to an alternating-current (AC) source. Electrons surge up and down the antenna, so one end becomes positive while the other becomes negative, then they switch, f times every second.
- The electric field near the antenna keeps reversing. Its changes cannot reach far points instantly; they spread outward at speed c. Loops of field "break away" and travel outward.
- The frequency of the wave equals the frequency of the oscillation. The wavelength is λ = c/f.
- The electric field of the wave is parallel to the antenna, so a vertical antenna sends out vertically polarized waves. The magnetic field circles around the antenna, perpendicular to E.
- The radiation is strongest perpendicular to the antenna and nearly zero straight off its ends.
- Receiving works in reverse: the wave's electric field pushes electrons up and down a receiving antenna, making a tiny alternating current. Reception is best when the receiving antenna is parallel to the transmitter's (same polarization).
A common design, the half-wave dipole, has a total length of about λ/2, which makes it resonate at the station's frequency.
Worked exampleExample 1: An FM antenna
An FM radio station broadcasts at 99.9 MHz. Find the wavelength and the length of a half-wave dipole antenna for this station.
- λ = c/f = 3.00 × 10⁸ ÷ 99.9 × 10⁶ = 3.00 m.
- Half-wave dipole: length ≈ λ/2 = 1.50 m.
λ ≈ 3.00 m; the antenna is about 1.5 m long. The charges in the transmitting antenna oscillate 99.9 million times per second.
Worked exampleExample 2: Checking Maxwell's prediction
Use μ₀ = 4π × 10⁻⁷ T·m/A and ε₀ = 8.85 × 10⁻¹² C²/(N·m²) to calculate the speed of electromagnetic waves.
- μ₀ε₀ = (1.2566 × 10⁻⁶)(8.85 × 10⁻¹²) = 1.112 × 10⁻¹⁷.
- √(1.112 × 10⁻¹⁷) = 3.335 × 10⁻⁹.
- c = 1 ÷ 3.335 × 10⁻⁹ = 3.00 × 10⁸ m/s.
3.00 × 10⁸ m/s, the speed of light: electricity and magnetism predict light.
Different sources, one spectrum
All electromagnetic waves travel at c in a vacuum; they differ in frequency and wavelength. The way they are produced depends on how fast the charges can be made to oscillate or change:
- Radio waves: an AC current in an antenna (a radio transmitter, a cellphone tower, a Wi-Fi router). In December 1901, Guglielmo Marconi reported receiving a radio signal sent across the Atlantic Ocean at Signal Hill in St. John's, Newfoundland.
- Microwaves: in a microwave oven, a device called a magnetron makes electrons circle in a magnetic field, radiating at about 2.45 GHz. Radar and Wi-Fi also use microwave frequencies.
- Infrared: charged particles in vibrating molecules of warm objects; your body glows in infrared.
- Visible and ultraviolet light: electron energy transitions in atoms: when an electron drops from a higher energy level to a lower one, the atom emits light of a specific frequency (that is where emission lines come from; details in Quantum Mechanics).
- X-rays: fast electrons slamming into a metal target in an X-ray tube decelerate violently and radiate, and electrons in the target's inner shells also make transitions.
- Gamma rays: changes inside atomic nuclei (radioactive decay).
The boundaries between regions are approximate: they overlap.
| Region | Typical wavelength | Typical source |
|---|
| Radio | metres to kilometres | AC in antennas |
| Microwave | about 1 mm to 1 m | magnetron, radar, Wi-Fi |
| Infrared | about 700 nm to 1 mm | warm objects |
| Visible | about 400 to 700 nm | hot objects, electron transitions in atoms |
| Ultraviolet | about 10 to 400 nm | the Sun, electron transitions |
| X-ray | about 0.01 to 10 nm | fast electrons hitting metal |
| Gamma | less than about 0.01 nm | nuclear changes |
Worked exampleExample 3: Wi-Fi and microwave ovens
Wi-Fi often uses frequencies near 2.4 GHz and 5 GHz. A microwave oven uses about 2.45 GHz. Find each wavelength.
- 2.4 GHz: λ = 3.00 × 10⁸ ÷ 2.4 × 10⁹ = 0.125 m (12.5 cm).
- 5 GHz: λ = 3.00 × 10⁸ ÷ 5.0 × 10⁹ = 0.060 m (6.0 cm).
- 2.45 GHz: λ = 3.00 × 10⁸ ÷ 2.45 × 10⁹ = 0.122 m (12.2 cm).
12.5 cm, 6.0 cm and 12.2 cm. The 2.4 GHz Wi-Fi band and the oven use similar wavelengths, which is why a running microwave oven can sometimes interfere with 2.4 GHz Wi-Fi nearby (the oven's metal screen is designed to keep most of its microwaves inside).
Just for funEvery time you turn on a radio, you are listening to electrons being shaken back and forth about a hundred million times a second in an antenna far away. Talk about a station that never stops dancing.
Hands-on activityAntenna polarization
You need: a portable FM radio with a telescoping (pull-out) antenna, or a TV with a "rabbit ears" antenna. Optional: a phone app that shows Wi-Fi signal strength.
- Tune the radio to a weak FM station (one that hisses a little). Pull the antenna all the way out.
- Point the antenna straight up, then horizontally (try a few horizontal directions), then at 45°. Note how the hiss and the signal change.
- Measure the length of the extended antenna. Calculate λ/2 for the station's frequency (λ = c/f) and compare.
- Optional: stand in one spot and note the Wi-Fi signal strength while you hold the phone upright, then sideways.
What to look for: many FM stations transmit with both horizontal and vertical components, so results vary, but you should find positions where reception is clearly better or worse. For 100 MHz, λ/2 = 1.5 m; a radio's telescoping antenna is usually shorter, so it works but is not perfectly matched. Write a short explanation using the idea that the wave's E field must push electrons along the antenna.
Your turn
1What kind of charge motion produces electromagnetic waves?
Accelerating charges (for example, charges oscillating back and forth).
2How is the frequency of the radiated wave related to the oscillation of the charges?
3An AM station broadcasts at 1010 kHz. Find the wavelength.
λ = 3.00 × 10⁸ ÷ 1.010 × 10⁶ = 297 m.
4Find the length of a half-wave dipole for an FM station at 94.1 MHz.
λ = 3.00 × 10⁸ ÷ 94.1 × 10⁶ = 3.19 m, so λ/2 ≈ 1.59 m.
5Describe the directions of E, B and travel in an electromagnetic wave.
All three are mutually perpendicular: E and B are perpendicular to each other and to the direction of travel.
6A vertical transmitting antenna sends out waves. How should a receiving antenna be held for the best signal, and why?
Vertically, parallel to the transmitter: the wave's E field is vertical, so it pushes electrons along the antenna.
7Name the source of each: X-rays in a hospital, visible light from a neon sign.
X-rays: fast electrons hitting a metal target. Neon sign: electron energy transitions in neon atoms.
More practice: warm-up
1What is the speed of all EM waves in a vacuum?
2Who showed in the 1860s that light is an electromagnetic wave?
3Who first made and detected radio waves in a laboratory?
Heinrich Hertz (1887 to 1888).
4Does a charge moving at constant velocity radiate EM waves?
5Which has the longer wavelength: microwaves or X-rays?
More practice: on your own
1Power lines carry 60 Hz AC. Find the wavelength of the EM waves they produce, and explain why power lines are very poor antennas for these waves.
λ = 3.00 × 10⁸ ÷ 60 = 5.0 × 10⁶ m (5000 km). A good antenna is about λ/2 long; even very long power-line spans are tiny compared with 2500 km, so they radiate very little.
2Explain why a dipole antenna radiates almost nothing straight along its own axis.
The wave's E field is parallel to the antenna and must also be perpendicular to the direction of travel. Along the axis these two conditions cannot both be met, so very little radiation goes that way.
3Visible light of 500 nm: find its frequency and explain why no ordinary antenna circuit can produce it.
f = c/λ = 3.00 × 10⁸ ÷ 5.00 × 10⁻⁷ = 6.0 × 10¹⁴ Hz. Electronic circuits cannot drive currents back and forth that fast; instead visible light comes from electron transitions in atoms (and from very hot objects).
4Explain in your own words how a changing electric field and a changing magnetic field keep an EM wave going through empty space.
A changing E field creates a B field; as that B field changes it creates an E field, and so on. Each field regenerates the other, so the wave sustains itself without needing a medium.
5A radar uses λ = 3.0 cm. Find f and identify the part of the spectrum.
f = 3.00 × 10⁸ ÷ 0.030 = 1.0 × 10¹⁰ Hz (10 GHz): microwave.
Challenge
1Light was shown to be a transverse wave by polarization. Explain how the dipole model predicts that EM waves are polarized, and give an everyday piece of evidence.
An oscillating dipole makes an E field parallel to the antenna, so the wave has a definite polarization direction. Evidence: reception changes as you rotate a radio or TV antenna; TV and radio antennas are mounted with a particular orientation.
2An X-ray tube produces X-rays of wavelength 3.0 × 10⁻¹⁰ m. Find their frequency and suggest why accelerating electrons by stopping them suddenly in metal makes such high frequencies.
f = 3.00 × 10⁸ ÷ 3.0 × 10⁻¹⁰ = 1.0 × 10¹⁸ Hz. The electrons stop in an extremely short time, so the change in their motion (and in their fields) is very rapid; a very rapid change produces very high-frequency radiation.
3Use Maxwell's equation c = 1/√(μ₀ε₀) to explain why measuring electric and magnetic forces in a lab could tell scientists the speed of light without ever timing a light beam.
μ₀ and ε₀ can be found from measurements of magnetic forces between currents and electric forces between charges. Putting them into c = 1/√(μ₀ε₀) gives 3.00 × 10⁸ m/s, a prediction made purely from electricity and magnetism. That it matches timed measurements of light is strong evidence that light is an EM wave.
Quiz
1. Which produces electromagnetic radiation?
2. In an EM wave, the electric and magnetic fields are…
3. A vertical dipole antenna produces waves whose electric field is…
4. Charges in an antenna oscillate at 150 MHz. The wavelength of the radio waves is…
5. Visible light emitted by a neon sign comes mainly from…
6. Maxwell's prediction c = 1/√(μ₀ε₀) was important because…
Big idea: expectation E3.4 asks students to describe qualitatively how an oscillating electric dipole produces electromagnetic radiation, with examples (radio transmitter, microwave emitter, X-ray emitter, electron transitions in atoms). Calculations here are limited to c = fλ and the antenna length.
How to help: the radio activity is a quick way to make polarization of radio waves real. Ask your teen to explain why rotating the antenna matters.
Common difficulties:
- Thinking any moving charge radiates. Only accelerating charges do.
- Mixing up the directions: E is parallel to the antenna; the wave travels perpendicular to it.
- Treating the spectrum boundaries as exact. They overlap.
- Forgetting MHz = 10⁶ Hz and GHz = 10⁹ Hz.