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Electromagnetic Waves
Electromagnetic Waves
Concept and Nature of EM Waves Frequency, Wavelength, Speed Energy Transport Doppler Effect Polarization
Electromagnetic Waves
Connect conducting rods to the terminals of an AC generator:
Generator EMF produces
current as charges separate
Current produces magnetic
field
+
-
B
E
Electromagnetic Waves
Current reverses: magnetic field also reverses
After current has reversed,
charges are again separated
with reverse polarity
Electric field is then reversed
+
-
B
E
Electromagnetic Waves
Magnitude and direction of electric and magnetic field vectors then travel away from the conducting rods. Traveling disturbance: wave.
Electromagnetic Waves
The electric and magnetic field vectors oscillate in perpendicular planes. Both planes are perpendicular to the direction of the wave’s motion (transverse wave).
Electromagnetic Waves
Just as the electric and magnetic fields require no material in which to exist, the electromagnetic wave needs no “medium.” It can travel in a vacuum, or in (some) materials.
Electromagnetic Waves
James Clerk Maxwell
1831 – 1879
Scottish mathematician
Established the
theoretical basis
for electromagnetic
waves
Frequency, Wavelength, Speed
Maxwell’s work in electrodynamics predicted: the existence of electromagnetic waves their transverse nature their ability to travel without any material medium their speed:
(in vacuum; slower in materials)
m/s 103.00 A / m T 104 /NmC 108.85
11 8
7-2212-00
c
Frequency, Wavelength, Speed
Velocity, frequency, and wavelength
are related in the same way as with other waves:
m/s 103.00 1 8
00
c
c
ff
cfc
Frequency, Wavelength, Speed
Electromagnetic waves are called by different names, and produced, handled, and detected by different technologies – depending on their frequency and wavelength.
radio waves microwaves infrared radiation visible light ultraviolet light gamma waves
Energy Transport
Like all waves, electromagnetic waves carry energy from one place to another.
The time rate at which the energy passes a given location is power:
The unit of power, as always, is the watt (W).
time
energyP
Energy Transport
If an area A has a power P passing perpendicularly through it, we define a quantity intensity:
Intensity can be expressed in terms of the electric and magnetic field peak magnitudes, individually:
A
PS SI unit: W/m2
20
2
0
EcSBc
S
Energy Transport
If an element of area A intercepts an electromagnetic wave of intensity S, traveling in a direction that makes an angle with the normal to the area element’s normal, the power within the area is
A
cosSAP
Energy Transport
Energy per unit volume in a space traversed by an electromagnetic wave:
area = A
intensity = S
length = c t
volume = V = A c t
20
2
0
20
2
0
1 EB
c
SuEcB
cS
c
S
tAc
tSA
V
Eu
tSAtPE
SAP
Doppler Effect
Similar to sound waves: observed frequency depends on velocity of source and/or observer
Different from sound waves: No “medium” (depends only on relative
source/observer velocity) All observers, regardless of velocity, measure the
same speed for light Assumption: source/observer velocity small
compared to the speed of light
Doppler Effect
Governing equation:
c
vff relsourceobs 1
observed frequency source frequency
relative source/observer velocity
speed of light
“+” means approaching; “ – “ means receding
Polarization
The state of polarization of an electromagnetic wave refers to the orientation of the plane in which the electric field vector oscillates.
Polarization
Some materials (polarizers) have a preferred direction for the electric field in the electromagnetic waves that they will transmit.
An efficient polarizer
transmits about half
the randomly-polarized
incident intensity.
Polarization
If two polarizers are encountered in series, the transmitted intensity depends on the relative orientation of their transmission axes.
Polarization
Etienne Louis Malus
French artillery officer and engineer
1775 – 1812
Malus’ Law: 20 cosSS
