Download Lecture_20

Chapter 31
Maxwell’s Equations and
Electromagnetic Waves
Copyright © 2009 Pearson Education, Inc.
31-7 Measuring the Speed of Light
The speed of light
was known to be
very large,
although careful
studies of the
orbits of Jupiter’s
moons showed
that it is finite.
One important
measurement, by
Michelson, used a
rotating mirror:
Copyright © 2009 Pearson Education, Inc.
31-7 Measuring the Speed of Light
Over the years, measurements have become
more and more precise; now the speed of light
is defined to be
c = 2.99792458 × 108 m/s.
This is then used to define the meter.
Copyright © 2009 Pearson Education, Inc.
31-8 Energy in EM Waves; the
Poynting Vector
Energy is stored in both electric and magnetic
fields, giving the total energy density of an
electromagnetic wave:
Each field contributes half the total energy
density:
Copyright © 2009 Pearson Education, Inc.
31-8 Energy in EM Waves; the
Poynting Vector
This energy is
transported by
the wave.
Copyright © 2009 Pearson Education, Inc.
31-8 Energy in EM Waves; the
Poynting Vector
The energy transported through a unit area
per unit time is called the intensity:
Its vector form is the Poynting vector:
Copyright © 2009 Pearson Education, Inc.
31-8 Energy in EM Waves; the
Poynting Vector
Typically we are interested in the average
S
value of S:
.
Copyright © 2009 Pearson Education, Inc.
31-8 Energy in EM Waves; the
Poynting Vector
Example 31-6: E and B from the Sun.
Radiation from the Sun reaches the Earth
(above the atmosphere) at a rate of about
1350 J/s·m2 (= 1350 W/m2). Assume that this
is a single EM wave, and calculate the
maximum values of E and B.
Copyright © 2009 Pearson Education, Inc.
31-9 Radiation Pressure
In addition to carrying energy, electromagnetic
waves also carry momentum. This means that a
force will be exerted by the wave.
The radiation pressure is related to the average
intensity. It is a minimum if the wave is fully
absorbed:
and a maximum if it is fully reflected:
Copyright © 2009 Pearson Education, Inc.
31-9 Radiation Pressure
Example 31-7: Solar pressure.
Radiation from the Sun that reaches
the Earth’s surface (after passing
through the atmosphere) transports
energy at a rate of about 1000 W/m2.
Estimate the pressure and force
exerted by the Sun on your
outstretched hand.
Copyright © 2009 Pearson Education, Inc.
31-9 Radiation Pressure
Example 31-8: A solar sail.
Proposals have been made to use the
radiation pressure from the Sun to help
propel spacecraft around the solar
system. (a) About how much force
would be applied on a 1 km x 1 km
highly reflective sail, and (b) by how
much would this increase the speed of
a 5000-kg spacecraft in one year? (c) If
the spacecraft started from rest, about
how far would it travel in a year?
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
This figure illustrates the process by which a
radio station transmits information. The audio
signal is combined with a carrier wave.
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
The mixing of signal and carrier can be done
two ways. First, by using the signal to modify
the amplitude of the carrier (AM):
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
Second, by using the signal to modify the
frequency of the carrier (FM):
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
At the receiving end, the wave is received,
demodulated, amplified, and sent to a
loudspeaker.
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
The receiving
antenna is
bathed in
waves of many
frequencies; a
tuner is used to
select the
desired one.
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
A straight antenna will have a current induced
in it by the varying electric fields of a radio
wave; a circular antenna will have a current
induced by the changing magnetic flux.
Copyright © 2009 Pearson Education, Inc.
31-10 Radio and Television; Wireless
Communication
Example 31-9: Tuning a station.
Calculate the transmitting wavelength
of an FM radio station that transmits
at 102.3 MHz.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 31.3
Before the days of cable,
televisions often had two
antennae on them, one straight
and one circular. Which antenna
picked up the magnetic
oscillations?
TV Antennas
1) the circular one
2) the straight one
3) both equally; they were
straight and circular for
different reasons
ConcepTest 31.3
Before the days of cable,
televisions often had two
antennae on them, one straight
and one circular. Which antenna
picked up the magnetic
oscillations?
The varying B field in the loop
means the flux is changing and
therefore an emf is induced.
TV Antennas
1) the circular one
2) the straight one
3) both equally; they were
straight and circular for
different reasons
ConcepTest 31.4
If a radio transmitter has a vertical
antenna, should a receiver’s
antenna be vertical or horizontal
to obtain the best reception?
Radio Antennas
1) vertical
2) horizontal
3) doesn’t matter
ConcepTest 31.4
If a radio transmitter has a vertical
antenna, should a receiver’s
antenna be vertical or horizontal
to obtain the best reception?
Radio Antennas
1) vertical
2) horizontal
3) doesn’t matter
If a wave is sent out from a vertical
antenna, the electric field oscillates
up and down. Thus, the receiver’s
E field
antenna should also be vertical so
of wave
that the arriving electric field can set
the charges in motion.
E field
of wave
Summary of Chapter 31
• Maxwell’s equations are the basic equations
of electromagnetism:
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 31
• Electromagnetic waves are produced by
accelerating charges; the propagation speed
is given by
• The fields are perpendicular to each other
and to the direction of propagation.
Copyright © 2009 Pearson Education, Inc.
Summary of Chapter 31
• The wavelength and frequency of EM waves
are related:
• The electromagnetic spectrum includes
all wavelengths, from radio waves through
visible light to gamma rays.
• The Poynting vector describes the
energy carried by EM waves:
Copyright © 2009 Pearson Education, Inc.
Chapter 35
Diffraction and Polarization
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Light is polarized when
its electric fields
oscillate in a single
plane, rather than in any
direction perpendicular
to the direction of
propagation.
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Polarized light will not
be transmitted through
a polarized film whose
axis is perpendicular
to the polarization
direction.
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
When light passes through a polarizer, only the
component parallel to the polarization axis is
transmitted. If the incoming light is planepolarized, the outgoing intensity is:
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
This means that if initially unpolarized light
passes through crossed polarizers, no light
will get through the second one.
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Example 35-13: Two Polaroids at 60°.
Unpolarized light passes through two
Polaroids; the axis of one is vertical and
that of the other is at 60° to the vertical.
Describe the orientation and intensity of
the transmitted light.
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Conceptual Example
35-14: Three Polaroids.
When unpolarized
light falls on two
crossed Polaroids
(axes at 90°), no light
passes through.
What happens if a
third Polaroid, with
axis at 45° to each of
the other two, is
placed between
them?
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Light is also partially polarized after reflecting
from a nonmetallic surface. At a special angle,
called the polarizing angle or Brewster’s angle,
the polarization is 100%:
.
Copyright © 2009 Pearson Education, Inc.
35-11 Polarization
Example 35-15: Polarizing angle.
(a) At what incident angle is sunlight
reflected from a lake plane-polarized? (b)
What is the refraction angle?
Copyright © 2009 Pearson Education, Inc.
35-12 Liquid Crystal Displays (LCD)
Liquid crystals are unpolarized in the absence
of an external voltage, and will easily transmit
light. When an external voltage is applied, the
crystals become polarized and no longer
transmit; they appear dark.
Liquid crystals can be found in many familiar
applications, such as calculators and digital
watches.
Copyright © 2009 Pearson Education, Inc.
35-13 Scattering of Light by the
Atmosphere
Skylight is partially
polarized due to scattering
from molecules in the air.
The amount of polarization
depends on the angle that
your line of sight makes
with the Sun.
Google: “Sunstones” … not now! After class.
Copyright © 2009 Pearson Education, Inc.
ConcepTest 35.3
Polarization
If unpolarized light is incident
1) only case 1
from the left, in which case will
2) only case 2
some light get through?
3) only case 3
4) cases 1 and 3
5) all three cases
ConcepTest 35.3
Polarization
If unpolarized light is incident
1) only case 1
from the left, in which case will
2) only case 2
some light get through?
3) only case 3
4) cases 1 and 3
5) all three cases
In cases 1 and 3, light is
blocked by the adjacent
horizontal and vertical
polarizers. However, in case
2, the intermediate 45°
polarizer allows some light
to get through the last
vertical polarizer.