1. Electromagnetic Waves
Chapter 23
Electromagnetic Waves

2. Electromagnetic Theory
Theoretical understanding
Well developed by middle 1800’s
Coulomb’s Law and Gauss’ Law explained electric fields and forces
Ampère’s Law and Faraday’s Law explained magnetic fields and forces
The laws were verified in many experiments

3. Unanswered Questions
What was the nature of electric and magnetic fields?
What is the idea of action at a distance?
How fast do the field lines associated with a charge react to a movement in the charge?
James Clerk Maxwell studied some of these questions in the mid-1800’s
His work led to the discovery of electromagnetic waves

4. Discovery of EM Waves
A time-varying magnetic field gives rise to an electric field
A magnetic field can produce an electric field
Maxwell proposed a modification to Ampère’s Law
A time-varying electric field produces a magnetic field
This gives a new way to create a magnetic field
Also gives equations of electromagnetism a symmetry
Section 23.1

5. Symmetry of E and B
The correct form of Ampère’s Law (due to Maxwell) says that a changing electric flux produced a magnetic field.
Since a changing electric flux can be caused by a changing E, was an indication that a changing electric field produces a magnetic field
Faraday’s Law says that a changing magnetic flux produces an induced emf, and an emf is always associated with an electric field
Since a changing magnetic flux can be caused by a changing B, we can also say that a changing magnetic field produces an electric field
Section 23.1

6. Symmetry of E and B, cont.
Section 23.1

7. Electromagnetic Waves
Self-sustaining oscillations involving E and B are possible
The oscillations are an electromagnetic wave
Electromagnetic waves are also referred to as electromagnetic radiation
Both the electric and magnetic fields must be changing with time
Although Maxwell worked out the details of em waves in great mathematical detail, experimental proof of the existence of the waves wasn’t carried out until 1887
Section 23.1

8. Perpendicular Fields
According to Faraday’s Law, a changing magnetic flux through a given area produces an electric field
The direction of the electric field is perpendicular to the magnetic field that produced it
Similarly, the magnetic field induced by a changing electric field is perpendicular to the electric field that produced it
Section 23.1

9. Properties of EM Waves
An electromagnetic wave involves both an electric field and a magnetic field
These fields are perpendicular to each other
The propagation direction of the wave is perpendicular to both the electric field and the magnetic field
Section 23.1

10. EM Waves are Transverse Waves
Imagine a snapshot of the electromagnetic wave
The electric field is along the x-axis
The wave travels in the z-direction
Determined by the right-hand rule #2
The magnetic field is along the y-direction
Because both fields are perpendicular to each other, the wave is a transverse wave
Section 23.2

11. Light is an EM Wave
Maxwell found the speed of an em wave can be expressed in terms of two universal constants
Permittivity of free space, εo
Magnetic permeability of free space, μo
The speed of an em wave is denoted by c
Inserting the values, c = 3.00 x 108 m/s
The value of the speed of an electromagnetic wave is the same as the speed of light
Section 23.2

12. Light as an EM Wave, cont.
Maxwell answered the question of the nature of light – it is an electromagnetic wave
He also showed that the equations of electricity and magnetism provide the theory of light

13. EM Waves in a Vacuum
Remember that mechanical waves need a medium to travel through
Many physicists searched for a medium for em waves to travel through
EM waves can travel through many materials, but they can also travel through a vacuum
All em waves travel with speed c through a vacuum
The frequency and wavelength are determined by the way the wave is produced
Section 23.2

14. EM Waves in Material Substances
When an em wave travels through a material substance, its speed depends on the properties of the substance
The speed of the wave is always less than c
The speed of the wave depends on the wave’s frequency
Section 23.2

15. EM Waves Carry Energy
An em wave carries energy in the electric and magnetic fields associated with the waves
Assume a wave interacts with a charged particle
The particle will experience an electric force
Section 23.3

16. EM Waves Carry Energy, cont.
As the electric field oscillates, so will the force
The electric force will do work on the charge
The charge’s kinetic energy will increase
Energy is transferred from the wave to the particle
The wave carries energy
The total energy per unit volume is the sum of its electric and magnetic energies
utotal = umag + uelec
Section 23.3

17. EM Waves Carry Energy, final
As the wave propagates, the energies per unit volume oscillate
The electric and magnetic energies are equal and this leads to the proportionality between the peak electric and magnetic fields
Section 23.3

18. Intensity of an EM Wave
The strength of an em wave is usually measured in terms of its intensity
Units W/m2
Intensity is the amount of energy transported per unit time across a surface of unit area
Intensity also equals the energy density multiplied by the speed of the wave
I = utotal x c = ½ εo c Eo2
Since E = c B, the intensity is also proportional to the square of the magnitude field amplitude
Section 23.3

19. Quiz time!
The miners recently rescued in Chile wore sunglasses at night when they came out of the mine.
If their eyes could only handle 10W/m^2 what was the amplitude of the E field [V/m]?
A) 53
B) 87
C) 115
D) 135
E) 3.14

20. EM Waves Carry Momentum
An electromagnetic wave has no mass, but it does carry momentum
Consider the collision shown
The momentum is carried by the wave before the collision and by the particle after the collision
Section 23.3

21. EM Waves Carry Momentum, cont.
The absorption of the wave occurs through the electric and magnetic forces on charges in the object
When the charge absorbs an electromagnetic wave, there is a force on the charge in the direction of propagation of the original wave
The force on the charge is related to the charge’s change in momentum: FB = Δp / Δt
According to conservation of momentum, the final momentum on the charge must equal the initial momentum of the electromagnetic wave
The momentum of the wave is p = Etotal / c
Section 23.3

22. Radiation Pressure
When an electromagnetic wave is absorbed by an object, it exerts a force on the object
The total force on the object is proportional to its exposed area
Radiation pressure is the force of the electromagnetic force divided by the area
This can also be expressed in terms of the intensity
Section 23.3

23. Electromagnetic Spectrum
All em waves travel through a vacuum at the speed c
c = x 108 m/s ~ 3.00 x 108 m/s
c is defined to have this value and the value of a meter is derived from this speed
Electromagnetic waves are classified according to their frequency and wavelength
The wave equation is true for em waves: c = ƒ λ
The range of all possible electromagnetic waves is called the electromagnetic spectrum
Section 23.4

24. Quiz time! If the Death Star’s green laser has a wavelength of 530nm
What is the frequency in Hz?
A) 2*10^16
B) 1*10^15
C) 7*10^13
D) 5*10^14
E) 3*10^8

25. EM Spectrum, Diagram
Section 23.4

26. EM Spectrum, Notes
There is no strict lower or upper limit for electromagnetic wave frequencies
The range of frequencies assigned to the different types of waves is somewhat arbitrary
Regions may overlap
The names of the different regions were chosen based on how the radiation in each frequency interacts with matter and on how it is generated
Section 23.4

27. Radio Waves Frequencies from a few hertz up to about 109 hertz
Corresponding wavelengths are from about 108 meters to a few centimeters
Usually produced by an AC circuit attached to an antenna
A simple wire can function as an antenna
Antennas containing multiple conducting elements are usually more efficient and more common
Radio waves can be detected by an antenna similar to the one used for generation

28. Radio Waves, cont. Parallel wires can act as an antenna
The AC current in the antenna is produced by time-varying electric fields in the antenna
This then produces a time-varying magnetic field and the em wave
As the current oscillated with time, the charge is accelerated
In general, when an electric charge is accelerated, it produces electromagnetic radiation
Section 23.4

29. Microwaves
Microwaves have frequencies between about 109 Hz and 1012 Hz
Corresponding wavelengths are from a few cm to a few tenths of a mm
Microwave ovens generate radiation with a frequency near 2.5x109 Hz
The microwave energy is transferred to water molecules in the food, heating the food
Section 23.4

30. Infrared
Infrared radiation has frequencies from about 1012 Hz to 4 x 1014 Hz
Wavelengths from a few tenths of a mm to a few microns
We sense this radiation as heat
Blackbody radiation from objects near room temperature fall into this range
Also useful for monitoring the Earth’s atmosphere
Section 23.4

31. Visible Light Frequencies from about 4 x1014 Hz to 8 x1014 Hz
Wavelengths from about 750 nm to 400 nm
The color of the light varies with the frequency
Low frequency; high wavelength – red
High frequency; low wavelength – blue
The speed of light inside a medium depends on the frequency of the radiation
The effect is called dispersion
White light is separated into different colors
Section 23.4

32. Dispersion Example
Section 23.4

33. Ultraviolet
Ultraviolet (UV) light has frequencies from about 8 x 1014 Hz to 1017 Hz
Corresponding wavelengths are about 3 nm to 400 nm
The UV portion of the spectrum is commonly subdivided into several regions
UV-A: 315 nm to 400 nm
UV-B: 280 nm to 315 nm
UV-C: 200 nm to 280 nm
Greatest potential for damaging tissue
Section 23.4

34. X-Rays Frequencies from about 1017 Hz to about 1020 Hz
Discovered by Wilhelm Röntgen in 1895
X-rays are weakly absorbed by skin and other soft tissue and strongly absorbed by dense material such as bone, teeth, and metal
In the 1970’s CAT scans were developed
Allows X-rays to be taken from many different angles and combined through computer analysis
Section 23.4

35. X-Ray Example
Section 23.4

36. Gamma Rays
Gamma rays are the highest frequency electromagnetic waves, with frequencies above 1020 Hz
Wavelengths are less than m
Gamma rays are produced by processes inside atomic nuclei
They are produced in nuclear power plants and in the Sun
Gamma rays reach us from outside the solar system
Section 23.4

37. Astronomy and EM Radiation
Different applications generally use different wavelengths of em radiation
Astronomy uses virtually all types of em radiation
The pictures show the Crab Nebula at various wavelengths
Colors indicate intensity at that wavelength
Section 23.4

38. Generation of EM Waves
A radio wave can be generated by using an AC voltage source connected to two wires
The two wires act as an antenna
As the voltage of the AC source oscillates, the electric potential of the two wires also oscillate
Electric charges are also flowing onto and off the wires as the voltage alternates
Section 23.5

39. Generation of EM Waves, cont.
The electric field continues to oscillate in size and direction
The wave propagates away from the antenna
The charges are accelerated
The charges undergo simple harmonic motion with a given frequency which is also the frequency of the AC voltage source and the frequency of the wave
Section 23.5

40. Antennas The simple antenna with two wires is called a dipole antenna
At any particular moment, the two wires are oppositely charged
The waves propagate perpendicular to the antenna’s axis
Section 23.5

41. Antennas, cont.
Electromagnetic waves also propagate inside the antenna wires
For a very long antenna, these tend to cancel
Therefore, most dipole antennas have a total length of λ/4
More complicated antennas also have the same cancellation effect, so the length of the antenna is usually comparable to the wavelength of the radiation

42. Antenna to Detect Radiation
The same antenna that generates an em wave can also be used to detect the wave
The electric field associated with the wave exerts a force on the electrons in the antenna
This produces a current and an induced voltage across the antenna wires
This is the voltage source of the circuit in the receiver
Section 23.5

43. Intensity
There are cases where the charges are not confined to one direction
In these cases, the radiation can propagate outward in all directions
The idea case of a very small source producing spherical wave fronts is called a point source
The intensity of a spherical wave decreases with distance: I  1/r2
The intensity decreases as the constant amount of energy spreads out over greater areas
This intensity relationship applies to many other situations, including the strength of a radio signal from a distant station
Section 23.5

44. Polarization
There are many directions of the electric field of an em wave that are perpendicular to the direction of propagation
Knowing the actual direction of the electric field is important to determining how the wave interacts with matter
The previous wave (fig ) was linearly polarized
The electric field was directed parallel to the z-axis
Most light is unpolarized
Section 23.6

45. Polarizers Polarized light can be created using a polarizer
The type of polarizer shown consists of a thin, plastic film that allows an em wave to pass through it only if the electric field of the wave is parallel to a particular direction called the axis of the polarizer
Section 23.6

46. Polarizers, cont.
The polarizer absorbs radiation with electric fields that are not along the axis
When the unpolarized light strikes a polarizer, the light that come out is linearly polarized
Assume linearly polarized light strikes a polarizer
If the incident light is polarized parallel to the axis of the polarizer and the outgoing electric field is equal in amplitude to the incoming field
All the incident energy is transmitted through the polarizer
Section 23.6

47. Polarizers, final
If the incident light is polarized perpendicular to the axis of the polarizer, no light is transmitted
If the incident light is polarized at an angle θ relative to the axis of the polarizer, only a component of electric field is transmitted

48. Polarizers and Malus’ Law
If the electric field is parallel to the polarizer’s axis: Eout = Ein
If the electric field is perpendicular to the polarizer’s axis, Eout = 0
If the electric field makes some angle θ relative to the polarizer’s axis, Eout = Ein cos θ
This relationship can be expressed in terms of intensity and is then called Malus’ Law:
Iout = Iin cos2 θ
Section 23.6

49. Malus’ Law and Unpolarized Light
Unpolarized light can be thought of as a collection of many separate light waves, each linearly polarized in different and random directions
Each separate wave is transmitted through the polarizer according to Malus’ Law
The average outgoing intensity is the average of all the incident waves:
Iout = (Iin cos2 θ)ave = ½ Iin
Since the average value of the cos2 θ is ½
Section 23.6

50. Polarization Examples
In figure A, the unpolarized light passes through polarized oriented at 90°
The intensity is reduced to ½ by the first polarizer and to 0 by the second
In figure B, three polarizers are used and a non-zero intensity results
Section 23.6

51. Polarizers, Summary
When analyzing light as it passes through several polarizers in succession, always analyze the effect of one polarizer at a time
The light transmitted by a polarizer is always linearly polarized
The polarization direction is determined solely by the polarizer axis
The transmitted wave has no “memory” of its original polarization
Section 23.6

52. Operation of a Polarizer
Most applications use a sandwich structure with certain types of long molecules placed between thin sheets of plastic
When the molecules are aligned parallel to each other, the sheets act as a polarizer with the axis perpendicular to the direction of the molecules
Section 23.6

53. Operation, cont.
Electrons in the polarizer molecules respond to electric fields
When the electric field is parallel to the molecules light is absorbed
When the electric field is perpendicular to the molecular direction the light is transmitted
The polarization axis is always perpendicular to the molecular direction
Section 23.6

54. Polarization by Reflection
Light can be polarized by scattering
Air molecules act as antennas
Charged particles respond to sunlight by oscillating in the direction of the electric field
These particles produce new outgoing waves that are polarized
The outgoing waves are called scattered waves
The light is said to be polarized by reflection
Section 23.6

55. Optical Activity
When linearly polarized light passes through certain materials, the polarization direction is rotated
This effect is called optical activity
These materials generally contain molecules with a screw-like or helical structure
Section 23.6

56. Applications of Polarized Light
Many objects use LCD’s
Liquid Crystal Displays
Incident light is linearly polarized by a polarizing sheet
The light encounters an optically active material called a liquid crystal
The molecules in the liquid crystal rotate the light by 90° so that it can pass through an “output” polarizer
Voltages can be applied to rotate the light with respect to the output polarizer and the make the display appear dark
Section 23.6

57. Spectral Lines
Astronomers use spectral lines to determine properties of stars
Each dark line in the spectrum corresponds to a color absorbed by the atoms in the object
The location of each line corresponds to a particular wavelength of light
Some spectra are observed to be shifted
Section 23.7

58. Red Shifts
Observations by Edwin Hubble showed that distant galaxies were shifted to longer wavelengths relative to the wavelength of the same spectral line on Earth
This is called a red shift
Hubble proposed that those galaxies must be moving away from us
This would cause the frequency to appear lower
This is similar to the Doppler Effect seen for sound
The size of the frequency shift can be used to determine the velocity of the galaxy emitting the light
Section 23.7

59. Expanding Universe
Most galaxies in the observable universe were found to be moving away from us
The farther the galaxy is from the Earth, the faster it is receding
From any viewpoint, the galaxies would appear to be moving away from you
Section 23.7

60. Doppler Shift for Light
The Doppler Shift relationships for light are different than for sound
For light:
vrel is the velocity of the source relative to the observer
A positive value of vrel corresponds to a source moving away from the observer
Section 23.7

61. Fields
The existence of electromagnetic waves means that electric and magnetic fields are real
There is no other way to explain how an em wave can propagate through a vacuum, carrying energy and momentum
The analogy with gravitational fields suggests the existence of gravitational waves
Work is now being done to detect these waves
Section 23.8

62. Traveling Through a Vacuum
Since all mechanical waves travel through some material, physicists of Maxwell’s time thought there was a material called the ether that supported em waves
The ether permeated all space, including vacuums
The ether would allow objects to travel through it without experiencing any frictional force due to the ether
Many experiments were designed to study the ether and its properties
In 1900, the existence of the ether was disproved
Therefore, em waves can carry energy even through a vacuum
Section 23.8

63. EM Waves and Quantum Theory
Newton proposed that light was made up of particles
Other physicists thought light was a wave
Maxwell’s work seemed to show conclusively that light is a wave
It is now known that light has both wavelike and particle-like properties
The “particles” of light are called photons
Subsequent chapters will discuss experiment evidence of both natures
Section 23.8