A charging capacitor’s wire carries current i. What total current does the Ampere–Maxwell law use around this wire?

i. The two surfaces give equal currents, which must not be added.

Which radiates: a circling charge or one moving straight at constant velocity?

The circling charge. Its changing direction means acceleration, even at constant speed.

Electric field points along positive y; magnetic field points along positive z. Which direction carries energy?

Positive x. The right-hand rule takes the electric field first, then the magnetic field.

In vacuum, electric amplitude is 120 V/m. What is the magnetic amplitude?

4×10^-7 T. Divide electric amplitude by the vacuum speed, rather than multiplying.

In the same medium, field amplitude triples. By what factor does intensity increase?

Nine. Intensity depends on amplitude squared, so the factor is three squared.

One photon has twice another’s wavelength. How does its energy compare?

Half as much. Energy per photon varies inversely with wavelength.

For a narrower radar beam, how should wavelength change if antenna width stays fixed?

It should decrease. Shorter wavelengths produce less diffraction spreading for the same antenna.

Which radiation comes from a nucleus dropping to a lower energy level?

Gamma rays. The emitting transition occurs inside the nucleus.

Teach Electromagnetic Waves in eight steps.

For each idea: show it, ask before you tell, then say one line.

Gather paper and a pencil.

Common misconceptions & worked visual for this chapter · 15 practice questions with answers

Why it matters

Radio waves carry signals without needing matter along their path.
Microwave ovens heat food when its contents absorb electromagnetic energy.
Infrared signals let remotes control appliances.

What to teach

How to teach it

How electromagnetic waves arise

Capacitor diagram showing wire current, an empty gap, electric field and magnetic loop.

1. Displacement current

Changing electric flux has a magnetic effect.

Show: Find the capacitor plates and wire-current arrows in the diagram. Follow the gap-field arrows, then find the surrounding magnetic-field loop.
Ask: Must charges cross the gap?
Say: The changing field has a magnetic effect without charges crossing.
Used in: Capacitors pass changing audio signals while separating steady voltages.

If your child says…“The wire and gap currents add together.”

Ask: Are we counting the same charging twice?
What’s true: For this loop, choose a surface through the wire or through the gap. Each gives current i. Do not add results from different surfaces.

Oscillating transmitter charges send electromagnetic waves towards a separate receiver.

2. Sources of electromagnetic waves

Accelerating charges emit waves that can cross empty space.

Show: Look at the diagram’s transmitter on the left. Follow the charge oscillation, then the wave towards the receiver.
Ask: Could this transmitter send energy to the receiver across empty space?
Say: Yes, oscillating charges accelerate and radiate electromagnetic waves. These waves carry energy from the transmitter, even through empty space.
Used in: In antennas, charges oscillate to send radio signals for communication.

If your child says…“Any moving charge gives off waves.”

Ask: Does moving straight at steady speed change a charge’s speed or direction?
What’s true: Charges radiate when their velocity changes, including changes of direction.

Fields, speed and energy

Perpendicular electric and magnetic wave patterns have aligned peaks and travel along positive x.

3. Transverse electromagnetic waves

Both fields oscillate together, perpendicular to each other and wave travel.

Show: Find the electric field E and magnetic field B in the diagram. Compare their peaks and zeros along x.
Ask: As this wave passes through empty space, what will oscillate?
Say: The electric and magnetic fields oscillate, reaching their peaks together. Both are perpendicular to travel and each other.
Used in: Polarising sunglasses reduce reflected glare by filtering light according to its electric field’s direction.

If your child says…“I find the travel direction using B × E.”

Ask: Curl your right-hand fingers from the electric towards the magnetic field. Where does your thumb point?
What’s true: Reversing the order reverses the predicted direction; reversing both fields leaves travel unchanged.

$\lambda=\frac{3.0\times10^8}{1.0\times10^8}=3.0\,\mathrm{m}$

$B_0=\frac{E_0}{c}$

4. Wave speed, frequency and amplitude

Wave speed links wavelength, frequency and field amplitudes.

Show: Write these lines for a vacuum wave: frequency 100 MHz, electric amplitude 3 V/m. Name wavelength lambda, frequency f, and vacuum speed c. Call electric and magnetic amplitudes E-zero and B-zero.
Ask: What magnetic amplitude completes this calculation?
Say: The magnetic amplitude is ten nanotesla.
Used in: Lenses redirect light to focus images.

If your child says…“I multiply electric amplitude by light’s speed to find magnetic amplitude.”

Ask: Which operation isolates magnetic amplitude in the last line?
What’s true: In vacuum, magnetic amplitude equals electric amplitude divided by light’s speed.

Waves reach absorbers; doubled field amplitudes give four times the intensity and forward force.

5. Energy, intensity and momentum

Both fields carry energy; waves also carry momentum.

Show: Follow each wave to the absorber in the diagram. Compare field amplitudes and the forward force arrows. Explain that intensity measures energy arriving per unit area per second.
Ask: Could absorbing sunlight push a surface as well as warm it?
Say: Yes, absorption transfers energy and forward momentum to the surface.
Used in: Microwave ovens transfer electromagnetic energy into food, heating it.

If your child says…“Doubling the field strength doubles the intensity.”

Ask: When a quantity is squared, does doubling it give twice or four times the result?
What’s true: A vacuum plane wave shares energy equally between its fields, and doubling amplitude quadruples intensity.

The spectrum and its uses

Spectrum places visible light between infrared and ultraviolet, with frequency increasing rightwards.

6. Electromagnetic spectrum, infrared and ultraviolet

Longer wavelengths mean less energy per photon.

Show: Read the diagram from radio waves towards gamma rays. Find infrared beside visible red, then ultraviolet beside visible violet.
Ask: Would our eyes detect the bands just beyond red and violet?
Say: Our eyes detect neither infrared beyond red nor ultraviolet beyond violet.
Used in: Ultraviolet kills germs in water purifiers.

If your child says…“Longer wavelengths mean more energy.”

Ask: Which side shows longer wavelengths, and which side gives each photon more energy?
What’s true: Longer wavelengths mean less photon energy.

Equal-sized dishes have wider receiving beams for longer wavelengths and narrower beams for shorter wavelengths.

7. Radio waves and microwaves

Shorter wavelengths allow a fixed antenna to produce narrower beams.

Show: Find the equal-sized dishes in the diagram. Compare their receiving beams for longer and shorter wavelengths.
Ask: Which wavelength would make this dish need more precise aiming towards its source?
Say: The shorter wavelength needs more precise aiming. For the same dish size, shorter wavelengths produce a narrower receiving beam.
Used in: Microwave radar images farmland through clouds and darkness.

If your child says…“Longer wavelengths make a narrower radar beam.”

Ask: If longer wavelengths spread more, which wavelengths would help this dish select a narrower direction?
What’s true: For the same antenna width, beam spreading grows with wavelength.

Paired diagrams showing an electron striking metal and a nucleus emitting radiation.

8. X-rays and gamma rays

Electron processes produce X-rays; nuclear transitions produce gamma rays.

Show: Find the electron, metal target and nucleus in the diagram. Compare where each outgoing wave begins.
Ask: What radiation would this nucleus emit as it drops to a lower energy level?
Say: Striking metal, electrons can emit X-rays. Nuclear transitions can emit gamma rays.
Used in: X-rays reveal bones inside the body.

If your child says…“Nuclei make X-rays; electrons make gamma rays.”

Ask: Which panel shows a nuclear process?
What’s true: Their wavelengths overlap, but their sources differ.

A real problem

RISAT-1 could image farmland through clouds and darkness.

It launched on 26 April 2012.

Its microwave sensing enabled imaging through clouds, by day and at night.

Its applications included monitoring paddy during the kharif growing season.

ISRO Wikipedia

Green paddy field beneath thick monsoon clouds.

Concept Lab · Common misconception

The tempting mistake in Electromagnetic Waves

Open standalone misconception page →

Do higher-frequency electromagnetic waves travel faster in a vacuum?

Wrong

X-rays cross a vacuum faster than radio waves because their frequency is higher.

Why it feels right. Frequency appears in the wave speed equation, so I increase it while holding wavelength fixed.

Right

All electromagnetic waves travel at the same speed in a vacuum. Higher frequency comes with shorter wavelength.

Worked example

Radio pulse

Longer wavelength→Same path at speed c→Arrives at time t

X-ray pulse

Shorter wavelength→Same path at speed c→Arrives at time t

The wavelengths differ. Both pulses cover the same vacuum path in the same time.

Send a radio pulse and an X-ray pulse across the same vacuum path at the same time.
They arrive together even though the X-rays have shorter wavelengths.

Ask your child eight quick questions.

One per step. The answer and the reason are given.

A charging capacitor’s wire carries current i. What total current does the Ampere–Maxwell law use around this wire?

i. The two surfaces give equal currents, which must not be added.
Which radiates: a circling charge or one moving straight at constant velocity?

The circling charge. Its changing direction means acceleration, even at constant speed.
Electric field points along positive y; magnetic field points along positive z. Which direction carries energy?

Positive x. The right-hand rule takes the electric field first, then the magnetic field.
In vacuum, electric amplitude is 120 V/m. What is the magnetic amplitude?

$4\times10^{-7}$ T. Divide electric amplitude by the vacuum speed, rather than multiplying.
In the same medium, field amplitude triples. By what factor does intensity increase?

Nine. Intensity depends on amplitude squared, so the factor is three squared.
One photon has twice another’s wavelength. How does its energy compare?

Half as much. Energy per photon varies inversely with wavelength.
For a narrower radar beam, how should wavelength change if antenna width stays fixed?

It should decrease. Shorter wavelengths produce less diffraction spreading for the same antenna.
Which radiation comes from a nucleus dropping to a lower energy level?

Gamma rays. The emitting transition occurs inside the nucleus.

15 more questions with answers, 3 with pictures

Teach Electromagnetic Waves in eight steps.

Why it matters