Download Lecture 14 - Purdue Physics

Chapter 23 Electromagnetic Waves – Lecture 14
23.1 The Discovery of Electromagnetic Waves
23.2 Properties of Electromagnetic Waves
23.3 Electromagnetic Waves Carry Energy and
Momentum
23.4 Types of Electromagnetic Radiation: The
Electromagnetic Spectrum
23.5 Generation and Propagation of Electromagnetic
Wave
23.6 Polarization
23.7 Doppler Effect
Electromagnetic Theory
• Theoretical understanding of electricity and
magnetism
• Seemed complete by around 1850
• 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
Introduction
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
Introduction
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
B
L  o Ienclosed
closed
path
Section 23.1
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, there 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
Symmetry of E and B, cont.
Section 23.1
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 (Maxwell
equations), experimental proof of the existence of
the waves wasn’t carried out until 1887
Section 23.1
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
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
EM Waves are Transverse Waves
• Imagine a snapshot of the electromagnetic (em) 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 the direction of
propagation, the wave is a transverse wave
Section 23.2
Light is an EM Wave
• Maxwell found the speed of an em wave can be expressed
in terms of two universal constants (from the Maxwell
equations)
• Permittivity of free space, εo
• Magnetic permeability of free space, μo
• The speed of an em wave is denoted by c
c
1
 o o
(from the Maxwell equations)
• Inserting the values of εo and μo, we obtain c = 3.00 x 108 m/s !
• The value of the speed of an electromagnetic wave is the same as
the speed of light
• 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
Section 23.2
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
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
EM Waves Carry Energy
• An em wave carries
energy in the electric
and magnetic fields
associated with the
wave
• Assume a wave
interacts with a charged
particle
• The particle will
experience an electric
force
Section 23.3
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 = uelec + umag
1
uelec 
umag 
2
 o E 2 , Eq. 18.48  and
1 2
B , Eq.  21.35 
2 o
Section 23.3
EM Waves Carry Energy, final
• As the wave propagates, the energies per unit
volume oscillate
• It turns out that the electric and magnetic energies
are equal, and this leads to the proportionality
between the peak electric and magnetic fields
uelect  umag
uelec
umag
1
1 2
2
  o Eo 
Bo
2
2 o
Eo  c Bo
c
1
  o E 2 , Eq. 18.48  and
2
1 2

B , Eq.  21.35 
2 o
1
 o o
Section 23.3
Intensity of an EM Wave
• The strength of an em wave is usually measured in
terms of its intensity
• SI unit is 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 × c = ½ εo c Eo2
• Since E = c B, the intensity is also proportional to the
square of the magnetic field amplitude
1
1
1
1 2
2
2
2
Bo
I  utotal  c   o cEo 
cBo   o Eo 
1
2
2 o
2
2 o
c
Eo  c Bo
 o o
Section 23.3
Solar Cells
• The intensity of sunlight on a typical sunny day is
•
•
•
•
about 1000 W/m²
A solar cell converts the energy from sunlight into
electrical energy
Current photovoltaic cells capture only about 15% of
the energy that strikes them
Also must account for nights and cloudy days
Making better and more practical solar cells is an
important engineering challenge
Section 23.3
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
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
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 electromagnetic force
divided by the area
F
Pradiation 
A
• This can also be expressed
in terms of the intensity
Pradiation
 Pradiation 
F I
 
A c
F F  L Work
I


 utotal 
A A  L Volume
c
 I  utotal  c
Section 23.3
Electromagnetic Spectrum
• All em waves travel through a vacuum at the speed c
• c = 2.99792458 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
Light is an
Electromagnetic
Wave
f   c
Figure 23-8 p797
Radio Waves
• Frequencies from a few hertz up to about 109 hertz
• Corresponding wavelengths are from about 108 meters to
a few centimeters
• 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 oscillates with time,
the charge is accelerated
• In general, when an electric charge
is accelerated, it produces
electromagnetic radiation
Section 23.4
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 2.5 x 109 Hz
• The microwave energy is
transferred to water
molecules in the food,
heating the food
Section 23.4
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
• Also useful for monitoring
the Earth’s atmosphere
Section 23.4
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
Dispersion Example
Section 23.4
Ultraviolet
• Ultraviolet (UV) light has frequencies from about 8 x
1014 Hz to 1017 Hz
• Corresponding wavelengths are about 3 nm to 400
nm
• UV radiation stimulates the production of vitamin D
in the body
• Excessive exposures to UV light can cause sunburn,
skin cancer and cataracts
Section 23.4
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 CT (CAT) scans were developed
Section 23.4
X-Ray Example
Section 23.4
CT Scan
• With a single X-ray image,
there will always be parts
of the person’s body that
are obscured
• Images can be taken from
different angles
• A CT scan takes many Xray images at many
different angles
• Computer analysis is used
to combine the images into
a three-dimensional
representation of the object
Section 23.4
Gamma Rays
• Gamma rays are the highest frequency
•
•
•
•
electromagnetic waves, with frequencies above 1020
Hz
Wavelengths are less than 10-12 m
Gamma rays are produced by processes inside
atomic nuclei
They are produced in nuclear power plants and in
the Sun
Gamma rays also reach us from outside the solar
system
Section 23.4
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 each wavelength
Section 23.4