Lesson 11 of 11 · 14 min

Chapter review

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20 facts

1Displacement current id = ε₀ dΦE/dt; it produces a magnetic field exactly as a conduction current does.
2In a charging capacitor: ic = i in the wires, id = i in the gap; total current is continuous.
3Ampere-Maxwell law: ∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt.
4Maxwell's four equations: Gauss (E), Gauss (B), Faraday, Ampere-Maxwell.
5∮B·dA = 0 because no magnetic monopoles are known.
6Accelerated charges radiate; charges at rest or in uniform motion do not.
7The frequency of the wave equals the frequency of the oscillating charge.
8Hertz produced and detected em waves in 1887; J. C. Bose produced waves of 25 mm to 5 mm.
9E, B and the direction of travel are mutually perpendicular; travel is along E × B.
10Ex = E₀ sin(kz − ωt), By = B₀ sin(kz − ωt): E and B in phase.
11c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s; ω = ck; νλ = c; B₀ = E₀/c.
12In a medium v = 1/√(με).
13em waves need no medium, and all of them travel at c in vacuum.
14Spectrum by decreasing wavelength: radio, microwave, infrared, visible, UV, X-rays, gamma.
15Visible: about 400-700 nm, 4 × 10¹⁴ to 7 × 10¹⁴ Hz.
16FM 88-108 MHz, AM 530-1710 kHz, TV 54-890 MHz.
17Microwaves: klystron, magnetron, Gunn diode; radar and ovens.
18Infrared = heat waves; used in remotes and physical therapy; causes the greenhouse effect.
19Ozone layer (40-50 km) absorbs most solar UV; glass absorbs UV.
20X-rays: electrons striking a metal target; gamma rays: radioactive nuclei.

Common traps

Saying no current flows between the plates of a charging capacitor, so there is no magnetic field there.

No conduction current flows, but a displacement current id = ε₀ dΦE/dt equal to i does, and it makes the same B.

Taking B₀ = E₀ for an em wave.

B₀ = E₀/c. For E₀ = 6.3 V/m, B₀ is only 2.1 × 10⁻⁸ T.

Thinking a steady current or a charge moving at constant velocity radiates.

Only accelerated charges radiate em waves.

Believing that higher-frequency em waves travel faster in vacuum.

Every em wave has the same speed c in vacuum; frequency and wavelength trade off through νλ = c.

Putting X-rays between visible and UV, or microwaves beyond infrared, when ordering the spectrum.

Decreasing wavelength: radio, micro, IR, visible, UV, X, gamma. Wavelength falls and frequency rises along it.

Assuming E and B in an em wave are a quarter cycle apart, as in an LC circuit.

In a travelling em wave E and B are in phase: both are sin(kz − ωt).

Thinking em waves, like sound, need a medium to travel.

They are self-sustaining oscillations of E and B and travel through vacuum.

Believing you can get a tan or sunburn through a closed glass window.

Ordinary glass absorbs UV, which is also why welders' goggles are made of glass.

6 to know

Displacement current

id = ε₀ dΦE/dt

Equals the conduction current in the leads of a charging capacitor.

Ampere-Maxwell law

∮B·dl = μ₀ic + μ₀ε₀ dΦE/dt

Total current i = ic + id.

Plane em wave

Ex = E₀ sin(kz − ωt), By = B₀ sin(kz − ωt)

k = 2π/λ, ω = 2πν.

Speed in vacuum

c = 1/√(μ₀ε₀) = ω/k = νλ

About 3 × 10⁸ m/s.

Field amplitudes

B₀ = E₀/c

E in V/m, B in T.

Speed in a medium

v = 1/√(με)

ε and μ of the medium.

14 terms

Conduction current: Current carried by charges moving through a conductor.
Displacement current: ε₀ times the rate of change of electric flux; acts as a source of B like a real current.
Ampere-Maxwell law: Ampere's law with the displacement current added to the conduction current.
Maxwell's equations: The four laws of electromagnetism: Gauss's laws for E and B, Faraday's law and the Ampere-Maxwell law.
Electromagnetic wave: Coupled E and B fields oscillating at right angles to each other and to the direction of travel.
Wave vector (k): Vector of size 2π/λ pointing along the direction of travel.
Transverse wave: A wave whose oscillations are perpendicular to the direction it travels.
Electromagnetic spectrum: The full range of em waves arranged by frequency or wavelength.
Microwaves: Short-wavelength radio waves in the GHz range, from 0.1 m to 1 mm.
Infrared (heat waves): Waves from 1 mm to 700 nm that set molecules vibrating and so heat matter.
Greenhouse effect: Warming of the earth as CO₂ and water vapour trap the infrared the ground re-radiates.
Ozone layer: Layer about 40-50 km up that absorbs most of the sun's ultraviolet.
Klystron, magnetron: Vacuum tubes that generate microwaves.
Gunn diode: A solid-state source of microwaves.