1. Electromagnetic Waves
Chapter 32
Electromagnetic Waves
© 2016 Pearson Education Inc. – Modfied by Scott Hildreth – Chabot College 2017

2. Learning Goals for Chapter 32
How are electromagnetic waves generated?
Why speed of light is related to fundamental E&M constants.
Describe propagation of sinusoidal electromagnetic wave.
Determine energy & momentum carried by EM wave.
Describe standing electromagnetic waves.
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3. Introduction Why do metals reflect light? Visible light is EM wave.
Many other examples: x-rays, radiowaves, microwaves
Unlike sound or waves on a string, EM waves do NOT require a medium to travel.
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4. James Clerk Maxwell
Scottish physicist James Clerk Maxwell (1831–1879) shows fundamental nature of light mathematically
Proved in 1865 EM “disturbance” propagates in free space w/ speed equal to “c”
Deduced correctly that light was an electromagnetic wave
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5. Maxwell’s Equation’s in integral form
Gauss’s Law
Gauss’s Law for Magnetism
Faraday’s Law
dS = n dA
Flux = field integrated over a surface
No magnetiic monopoles
E .dl is an EMF (volts)
Ampere’s Law

6. Maxwell’s Equations Differential Form

8. Electricity, magnetism, and light
According to Maxwell’s equations, accelerating electric charge must produce electromagnetic waves.
Overhead power lines carry strong AC; substantial amount of charge accelerates back & forth, generating EM (radio) waves.
These waves can produce a buzzing sound from your car radio when you drive near the lines.
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9. Electromagnetic spectrum
Frequencies & wavelengths of EM waves in nature extend over wide range! Use logarithmic scale to show all bands.
Boundaries between bands are (somewhat) arbitrary.
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10. Visible light Extends from violet end (400 nm) to red (700 nm).
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11. Ultraviolet vision Many insects & birds can see UV that humans cannot.
Left photo shows how “black-eyed Susans” look to us.
Right photo (in false color), taken with UV camera, shows how flowers appear to bees that pollinate them.
Note prominent central spot invisible to humans.
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12. Ultraviolet vision

13. A simple plane electromagnetic wave
Imagine space divided into two regions by plane perpendicular to x-axis.
At every point to left uniform electric & magnetic fields
Boundary plane (wave front) moves in +x-direction with constant speed c.
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14. Gauss’s laws & simple plane wave
Create rectangular Gaussian surface simple plane wave is traveling through.
Box encloses no electric charge.
No flux! So E & B fields must be perpendicular to direction of propagation.
Wave must be transverse.
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15. Faraday’s law & simple plane wave
In time dt, magnetic flux through rectangle in xy-plane increases by dΦB.
Increase equals flux through shaded rectangle w/ area ac dt: dΦB = Bac dt
So dΦB/dt = Bac
Faraday’s law implies:
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16. Faraday’s Law

17. Ampere’s law & simple plane wave
In time dt, electric flux through rectangle in xz-plane increases by dΦE.
Increase equals flux through shaded rectangle w/ area ac dt: dΦE = Eac dt
Thus dΦE/dt = Eac and….
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18. Properties of electromagnetic waves
Maxwell’s equations imply in an EM wave, BOTH E & B fields are perpendicular to direction of propagation of wave & to each other.
For electromagnetic waves, ratio between magnitudes of electric & magnetic fields E = cB
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19. Properties of electromagnetic waves
Travel in vacuum with definite (and unchanging) speed: c = 3.00 × 108 m/s.
Unlike mechanical waves, EM waves require no medium.

20. Properties of electromagnetic waves
Direction of propagation of EM wave is direction of vector cross product of electric & magnetic fields.
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21. Sinusoidal electromagnetic waves
EM waves produced by oscillating point charge are not plane waves.
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22. Sinusoidal electromagnetic waves
EM waves produced by oscillating point charge are not plane waves.
Restrict observations to relatively small region of space at a sufficiently great distance from source, these waves are well approximated by plane waves.
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23. Fields of a sinusoidal wave
Linearly polarized, sinusoidal EM wave traveling +x-direction.
One wavelength shown at time t = 0.
Fields shown for a few points along x-axis.
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24. Polarization of sinusoidal wave
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25. Variation in Polarization of sinusoidal wave
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26. Elliptical Polarization of sinusoidal wave
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27. Traveling sinusoidal EM waves
Describe EM waves with wave functions:
Wave travels right w/ speed c = ω/k.
Amplitudes related by:
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28. Electromagnetic waves in matter
When electromagnetic waves travel in nonconducting materials— dielectrics — speed v of waves depends on dielectric constant of material.
Ratio of speed c in vacuum to speed v in material is index of refraction n
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29. Energy in electromagnetic waves
EM waves transport energy
British physicist John Poynting introduced Poynting vector, S
Magnitude of Poynting vector = power per unit area in wave [W/m2]
Direction of Poynting vector = direction of propagation
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30. Energy in electromagnetic waves
British physicist John Poynting
Worked with Maxwell
Worked with JJ Thompson
Wrote THE physics textbook used for 50+ years!
Coined “greenhouse effect”!
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31. Energy in electromagnetic waves
Poynting vector, S
Magnitude of Poynting vector = power per unit area [W/m2]
[E] = Newtons/Coulomb (from F = qE!)
[B] = Teslas = Newtons/[Coulomb-meter/sec] (from F = qvxB!!)
[m0] = Tesla-meter/Amp (from Ampere’s Law !!!)
[S] = (N/C) x (T) x (Amps/Tm) = N/m-sec = Nm/m2-sec = W/m2
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32. Energy in electromagnetic waves
Magnitude of average value of = intensity [W/m2]
Rooftop solar panels tilted face-on to sun so panels absorb maximum amount of wave energy.
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33. Electromagnetic radiation pressure
EM waves carry momentum & exert radiation pressure on a surface:
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35. Electromagnetic radiation pressure
Solar Constant: 1370 W/m2 at Earth’s Surface
If solar panels on earth-orbiting satellite are perpendicular to sunlight, & radiation completely absorbed, average radiation pressure is 4.7 × 10−6 N/m2
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36. Electromagnetic radiation pressure

37. Solar Sails!

38. Standing waves in a cavity
Typical microwave oven @ 2.45 GHz sets up standing EM wave w/ λ = 12.2 cm
Strongly absorbed by water!
Because standing wave has nodes spaced λ/2 = 6.1 cm apart, food must be rotated while cooking.
Otherwise, portion at a node — where E-field amplitude = 0 will remain cold!
Measure the speed of light yourself using Butter – or Peeps!
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39. Standing electromagnetic waves
EM waves reflected by conductor or dielectric, leading to standing waves.
Remember E field in conductor MUST be zero!!
So E(ends) = 0 permanently!
Just like displacement wavefunction for closed pipes!
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40. Standing electromagnetic waves
Pattern does not move; instead, at every point E & B field vectors oscillate.
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