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Chapter 34
Electromagnetic
Waves
LAWS of Electromagnetism
charges produce E
Magnetic “charges” do
not exist (monopole)
Currents produce B
Change in E produces B
Change in B produces an E
LAWS of Electromagnetism
charges produce E
Magnetic “charges” do
not exist (monopole)
Currents produce B
Change in E produces B
Change in B produces an E
 Maxwell’s equations
All electromagnetism in just 4
equations
LAWS of Electromagnetism
divergence:
source or sink of a
vector field
curl: rotation of
a vector field
 Maxwell’s equations
All electromagnetism in just 4
equations
LAWS of Electromagnetism
 large divergence
zero divergence
large curl, zero divergence
divergence:
source or sink of a
vector field
curl: rotation of
a vector field
 Maxwell’s equations
All electromagnetism in just 4
equations
LAWS of Electromagnetism
In empty space (zero charges and currents)
LAWS of Electromagnetism
In empty space (zero charges and currents)
LAWS of Electromagnetism
=0
r
BE
In empty space (zero charges and currents)
For example:
=0
equation of a wave that propagates in the x direction
with speed
c
1
 o o
c=
1
e o mo
=
( 8.85 ´ 10
1
-12
(
C2 N × m 2
)) ( 4p ´ 10
-7
T×m A
)
= 3.00 ´ 10 8 m s
c is the speed of light
The properties and speed of electromagnetic waves are predicted
by Maxwell’s equations
The Nature of Electromagnetic Waves
The wire has oscillating charge, that produces
an oscillating E.
The oscillating Electric Field generates a
oscillating Magnetic Field (Ampere’sMaxwell’s Law)
The oscillating Magnetic Field generates
an oscillating Electric field (Faraday’s
Law)
…..
A straight wire connected to
the terminals of an AC generator
can create an electromagnetic
wave.
Only the electric wave traveling to the
right is shown here.
The Nature of Electromagnetic Waves
This picture shows the wave of the radiation field far from the
antenna.
Once away from the antenna the Fields generate in vacuum forever.
The speed of an electromagnetic wave in a vacuum is:
c == 3.00 ´ 10 m s
8
The Nature of Electromagnetic Waves
Properties of the wave
c = 3.00 ´ 108 m s
(in vacuum)
E=cB
E and B are perpendicular to each other
E and B are perpendicular to the direction of propagation
The wave is TRANSVERSE
c = fl
The Electromagnetic Spectrum
Like all waves, electromagnetic waves have a wavelength and
frequency, related by:
c = fl
The Electromagnetic Spectrum
EM waves that we can see are called “light”, or visible light
The ONLY difference between visible light and the other
EM waves is the frequency and wavelength
The Electromagnetic Spectrum
ORIGIN OF LIGHT
fast stopping of
electrons
antennas with
oscillating charge
excitation and decay of
electrons in atoms
vibration of atoms
or molecules
Stars emit light in all the spectra
nuclear reactions
The Electromagnetic Spectrum
Example 1 The Wavelength of Visible Light
Find the range in wavelengths for visible light in the frequency range
between 4.0x1014Hz and 7.9x1014Hz.
c 3.00 ´108 m s
-7
l= =
= 7.5 ´10 m = 750 nm
14
f
4.0 ´10 Hz
c 3.00 ´108 m s
-7
l= =
= 3.8 ´10 m = 380 nm
14
f
7.9 ´10 Hz
The Speed of Light
Conceptual Example 3 Looking Back in Time
A supernova is a violent explosion that occurs at the death of certain
stars. The figure shows a photograph of the sky before and after a
supernova. Why do astronomers say that viewing an event like this
is like looking back in time?
The Energy Carried by Electromagnetic Waves
The total energy density carried by an electromagnetic
wave
Total energy 1
1 2
2
u
 oE 
B
Volume
2
2 o
energy stored in an
electric field (per
volume)
u  oE 
2
B
energy stored in
a magnetic field
(per volume)
2
o
E  cB
c  1 /  o o
The Energy Carried by Electromagnetic Waves
P Total energy uctA
S= =
=
= cu
A
tA
tA
INTENSITY
The energy travels with the wave.
S  cu  c o E  c
2
B
2
o

EB
o
The Energy Carried by Electromagnetic Waves
Electromagnetic waves, like water waves, carry energy.
•Microwaves penetrate food and deliver their energy to it.
•The electric field delivers the energy to the water molecules in the food.
•The oscillating electric field makes the water molecules oscillate with the
frequency of the wave (2.4 × 109 Hz)
•Transfer of energy is very efficient, only for water (resonance)
•In the process, bonds break between neighboring water molecules, energy is
released as internal energy.
•As the internal energy increases, the temperature of the water increases, and
the food cooks.
Example
An electromagnetic wave that delivers a cellular phone call to a car has an
average intensity of 7.4 × 10-7 W/m2. The wave passes perpendicularly
through an open window, the area of which is 0.31 m2. How much energy
does this wave carry through the window during a 24-s phone call?
Mathematical Description of Traveling EM Waves
Electric Field:
Magnetic Field:
E = Em sin (kx - w t )
B = Bm sin (kx - w t )
Wave Speed:
1
c=
m0e 0
All EM waves travel a c in vacuum
Wavenumber:
k=
2p
Angular frequency:
Vacuum Permittivity:
Vacuum Permeability:
Amplitude Ratio:
Em
=c
Bm
Magnitude Ratio:
E (t )
=c
B (t )
l
w=
2p
e0
m0
t
A Most Curious Wave
• Unlike other waves (sound, guitar string…), EM waves require no medium
through/along which to travel. EM waves can travel through empty space
(vacuum)!
• Speed of light is independent of speed of observer! You could be heading
toward a light beam at the speed of light, but you would still measure c as the
speed of the beam!
c = 299 792 458 m/s