← All printables Chapter 07 · Electromagnetism · 2 sheets · read the chapter →
Vedatom Physics
FORMULA CARD · PHYSICS.VEDATOM.COM
Chapter 07 · Part V · Electromagnetism
Revised on ____________________
Chapter 07 · Electromagnetic Waves

Fields that carry themselves, at one fixed speed

2 sheets
2 diagrams
20 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

Displacement current

FLUX CHANGING, NOT CHARGE MOVING
I.Definition  ID = ε0 dΦEdt nothing crosses the gap
II.Ampère–Maxwell  ∮ B·dl = μ0 (I + ID)
III.In a charging capacitor  ID = I by identity, not by conduction
IV.Gauss, electric  ∮ E·dA = qε0
V.Gauss, magnetic  ∮ B·dA = 0 no monopoles
VI.Faraday  ∮ E·dl = − dΦBdt
The displacement current exists to keep Ampère's law consistent whichever surface you stretch across the loop. Maxwell added it on paper; the wave it predicted arrived twenty years later.
II

The wave itself

E AND B PEAK TOGETHER
I.Speed in vacuum  c = 1√(μ0 ε0) 3.00×108 m s−1
II.In a medium  v = cn , n = √(μr εr)
III.Field ratio  E0B0 = c
IV.Geometry  E ⊥ B ⊥ direction of travel transverse, and in phase
V.Frequency in a medium  unchanged λ and v both drop by n
VI.Energy density  u = 12 ε0 E² + B²2μ0 the two halves are equal
VII.Intensity  I = 12 ε0 c E0² = ε₀ c Erms²
VIII.Poynting vector  S = 1μ0 E × B
x (propagation)EBλE ⊥ B ⊥ x, in phase, E = cB
III

Momentum and pressure

A MIRROR FEELS TWICE AS MUCH
I.Momentum carried  p = Uc
II.Perfect absorber  P = Ic
III.Perfect reflector  P = 2 Ic the momentum reverses
IV.Reflectivity R  P = (1 + R) Ic
V.Photon  p = hλ = Ec
VI.Source at distance r  I = Psource4π r²
IV

The spectrum

ONE PHENOMENON, TWENTY DECADES
Band
Wavelength
Produced by
Used for
Radio
> 0.1 m
oscillating circuits
broadcast, mobile
Microwave
1 mm – 0.1 m
klystron, magnetron
radar, ovens
Infrared
700 nm – 1 mm
hot bodies, molecules
heat, remote controls
Visible
400 – 700 nm
atoms, LEDs
sight
Ultraviolet
1 – 400 nm
arcs, the Sun
sterilisation
X-ray
0.01 – 1 nm
inner-shell transitions
imaging
Gamma
< 0.01 nm
nuclear transitions
therapy
RadioMicro-​waveInfraredVisibleUVX-rayγ-rayf, E=hf increaseλ increasesOne continuum · all travel at c in vacuum
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Treating displacement current as charge crossing the gap. It is a rate of change of electric flux.
2Changing the frequency in a medium. Speed and wavelength drop by n; the frequency is set by the source.
3Imagining E and B take turns. They oscillate in phase and carry half the energy each.
4Using I/c for a mirror. A perfect reflector feels 2I/c; reflectivity R gives (1 + R)I/c.