The Doppler Effect Electromagnetic Waves - Hadroncrede/FILES/FALL2014/EM... · 2014-10-12 ·...
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College Physics B EM Waves Properties of EM Waves Polarization The Doppler Effect College Physics B - PHY2054C Electromagnetic Waves 10/13/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building
Transcript of The Doppler Effect Electromagnetic Waves - Hadroncrede/FILES/FALL2014/EM... · 2014-10-12 ·...
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
College Physics B - PHY2054C
Electromagnetic Waves
10/13/2014
My Office Hours:Tuesday 10:00 AM - Noon
206 Keen Building
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Outline
1 EM WavesProperties of EM Waves
2 Polarization
3 The Doppler Effect
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Symmetry of ~E and ~B
The correct form of Ampère’s Law (due to Maxwell) says thata changing electric flux produced a magnetic field.
• Since a changing electric flux can be caused by achanging E , we can also say that a changing electricfield produces a magnetic field.
Faraday’s Law says that a changing magnetic flux produces aninduced emf; emf is always associated with an electric field.
• Since a changing magnetic flux can be caused by achanging B, we can say that a changing magnetic fieldproduces an electric field.
Self-sustaining oscillations involving E and B are possible.➜ The oscillations are an electromagnetic wave.
(also referred to as electromagnetic radiation)
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Perpendicular Fields
According to Faraday’s Law, a changingmagnetic flux through a given area doesproduce an electric field perpendicular tothe initial magnetic field.
Similarly, the magnetic field induced by achanging electric field is perpendicular tothe electric field that produced it.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Transverse Waves
An electromagnetic wave involves both an electric field and amagnetic field:
• These fields are perpendicular to each other.
• The propagation direction of the wave is perpendicular toboth the electric field and the magnetic field.
➜ The wave is a transverse wave.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Properties of EM Waves
Maxwell found that the speed of an electromagnetic wave canbe expressed in terms of two universal constants:
1 The permittivity of free space, ǫ0
2 The magnetic permeability of free space, µ0
Speed of an electromagnetic wave in vacuum is denoted by c:
c =1
√ǫ0 µ0
= 299, 792, 458 m/s ≈ 3.0 × 108 m/s
The value of the speed of an electromagnetic wave is the sameas the speed of light.
Why?
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Properties of EM Waves
Maxwell found that the speed of an electromagnetic wave canbe expressed in terms of two universal constants:
1 The permittivity of free space, ǫ0
2 The magnetic permeability of free space, µ0
Speed of an electromagnetic wave in vacuum is denoted by c:
c =1
√ǫ0 µ0
= 299, 792, 458 m/s ≈ 3.0 × 108 m/s
The value of the speed of an electromagnetic wave is the sameas the speed of light.
Maxwell answered the question of the nature of light – it is anelectromagnetic wave.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 1
Which of these is NOT a form of electromagnetic radiation?
A gamma rays
B infrared
C sound
D visible light
E radio
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 1
Which of these is NOT a form of electromagnetic radiation?
A gamma rays
B infrared
C sound
D visible light
E radio
Sound comes from pressure waves; all others are types ofEM radiation of different wavelengths.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Electromagnetic Spectrum
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Example
speed of light = wavelength · frequency
c = λ · ν
c ≈ 3 · 108 m/s
1 Commercial AM radio: 550 kHz – 1600 kHz
λ = c/ν = 3 · 108 m/s / 1000 kHz
= 300 m
2 Microwave oven uses 2.45 GHz
λ = c/ν = 3 · 108 m/s / 2, 450, 000, 000 Hz
≈ 12.2 cm
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 2
If an electric field wave oscillates north and south (horizontally),and the electromagnetic wave is traveling vertically straight up,then what direction does the magnetic field wave oscillate?
A It does not oscillate: the situation is impossible.
B East and west (horizontally)
C North and south (horizontally)
D Up and down (vertically)
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 2
If an electric field wave oscillates north and south (horizontally),and the electromagnetic wave is traveling vertically straight up,then what direction does the magnetic field wave oscillate?
A It does not oscillate: the situation is impossible.
B East and west (horizontally)
C North and south (horizontally)
D Up and down (vertically)
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves in Material Substances
When an electromagnetic wave travels through a substance,its speed depends on the properties of the substance:
• The speed of the wave is always less than c.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves in Material Substances
When an electromagnetic wave travels through a substance,its speed depends on the properties of the substance:
• The speed of the wave is always less than c.
Electromagnetic Waves Carry Energy
Electromagnetic waves carryenergy in the electric andmagnetic fields associatedwith the waves.
Assume a wave interactswith a charged particle: theparticle will experience anelectric force.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves Carry Energy
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 total energy (of a wave) per unit volume is the sum of itselectric and magnetic energies:
u total = u elec + u mag
As the wave propagates, the energies per unit volume oscillate.The electric and magnetic energies are equal:
12
ǫ0 E20 =
12µ0
B20
E20 = 1/(ǫ0 µ0) B2
0
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves Carry Energy
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 total energy (of a wave) per unit volume is the sum of itselectric and magnetic energies:
u total = u elec + u mag
As the wave propagates, the energies per unit volume oscillate.The electric and magnetic energies are equal:
12
ǫ0 E20 =
12µ0
B20
E0 = c B0
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Synchrotron Radiation
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Intensity of an EM Wave
The strength of an electromagnetic wave is usually measuredin terms of its intensity:
• Unit is W/m2.
• Intensity is the amount of energy transported per unittime across a surface of unit area.
• Intensity also equals the energy density multiplied by thespeed of the wave:
I total = u total × c =
(
12
ǫ0 E20 +
12µ0
B20
)
c = ǫ0 c E20
I avg =12
ǫ0 c E20
The intensity is thus proportional to the square of the electricfield amplitude. Since E = c B, the intensity is also propor-tional to the square of the magnetic field amplitude.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Example
On a typical summer day, the intensity of sunlight at the Earth’ssurface is approximately I = 1000 W/m2. What is the amplitudeof the electric field associated with this electromagnetic wave?
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Example
On a typical summer day, the intensity of sunlight at the Earth’ssurface is approximately I = 1000 W/m2. What is the amplitudeof the electric field associated with this electromagnetic wave?
The electric field amplitude and the intensity are related by(previous slide):
I avg =12
ǫ0 c E20 → E0 =
√
2 Iǫ0 c
Solve:
E0 =
√
2 (1000) W/m2
(8.85 · 10−12 C2/(N · m2)) (3.0 · 108 m/s)= 870 V/m
The electric field is very large!
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves Carry Momentum
An electromagnetic wave has nomass, but it does carry momentum.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves Carry Momentum
The momentum is carried by thewave before the collision and by theparticle after the collision:
• When the charge absorbs anelectromagnetic wave, there isa magnetic force on the chargein the direction of propagationof the original wave: F = q v B.
• Charge’s velocity originatesfrom its oscillation due to thewave’s electric field.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
EM Waves Carry Momentum
The momentum is carried by thewave before the collision and by theparticle after the collision:
• When the charge absorbs anelectromagnetic wave, there isa magnetic force on the chargein the direction of propagationof the original wave: F = q v B.
• Force on charge is related tocharge’s change in momentum:
FB = ∆p/∆t
p wave = E total/c
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Radiation Pressure
The momentum is carried by thewave before the collision and by theparticle after the collision:
• When the charge absorbs anelectromagnetic wave, there isa magnetic force on the chargein the direction of propagationof the original wave: F = q v B.
• Radiation pressure is the forceof the electromagnetic forcedivided by the exposed area:
P radiation =FA
=Ic
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Example
A spacecraft designer wants to use radiation pressure topropel a spacecraft as sketched. Near the Earth, the intensityof sunlight is about 1000 W/m2 and the exposed area of thespacecraft is 500 m2. If the sunlight is completely absorbed,what is the force on the spacecraft?
The radiation pressure is relatedto the intensity of the radiation:
F = P radiation A =I Ac
=(1000 W/m2) (500 m2)
3.0 · 108 m/s
= 1.7 · 10−3 N
Equal to the weight of a penny!
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 3
When light is absorbed by an object, the radiation pressure isP radiation = I/c. Suppose the exposed surface of an object hasinstead a reflective coating so that it reflects electromagneticwaves. Which of the following statements is true?
A The force on the object due to radiation pressure is thesame whether the light is absorbed or reflected.
B The force on the object due to radiationpressure is greater by a factor of twowhen the light is reflected.
C There is no force on the object due toradiation pressure when the light isreflected.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Question 3
When light is absorbed by an object, the radiation pressure isP radiation = I/c. Suppose the exposed surface of an object hasinstead a reflective coating so that it reflects electromagneticwaves. Which of the following statements is true?
A The force on the object due to radiation pressure is thesame whether the light is absorbed or reflected.
B The force on the object due to radiationpressure is greater by a factor of twowhen the light is reflected.
C There is no force on the object due toradiation pressure when the light isreflected.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Outline
1 EM WavesProperties of EM Waves
2 Polarization
3 The Doppler Effect
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Polarization
There are many directions of the electric field of an electromag-netic wave that are perpendicular to the direction of propagation.
Most light in nature is unpolarized.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Polarizers
Polarized light can be created using a polarizer.(e.g. a thin plastic film)
The polarizer absorbs radiation with electric fields that are notalong the axis. When unpolarized light strikes a polarizer, thelight that comes out islinearly-polarized.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Polarizers
If the electric field is parallel to thepolarizer’s axis:
E out = E in
If the electric field is perpendicularto the polarizer’s axis:
E out = 0
If the electric field makes an angle θrelative to the polarizer’s axis:
E out = E in cos θ
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Malus’ Law
If the electric field is parallel to thepolarizer’s axis:
E out = E in
If the electric field is perpendicularto the polarizer’s axis:
E out = 0
If the electric field makes an angle θrelative to the polarizer’s axis:
E out = E in cos θ
I out = I in cos2 θ
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Examples
Unpolarized light can be thought of as a collection of manyseparate light waves, each linearly-polarized in different andrandom directions.
A The intensity is reduced to 1/2 by the first polarizer:
I out = (I in cos2 θ) avg =12
I in
B Three polarizers are used: a non-zero intensity results.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Summary
When analyzing light as it passes through several polarizers insuccession, always analyze the effect of one polarizer at a time:
• The light transmitted by a polarizer is always linearlypolarized.
• The transmitted wave has no “memory” of its originalpolarization.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Applications
When analyzing light as it passes through several polarizers insuccession, always analyze the effect of one polarizer at a time:
• The light transmitted by a polarizer is always linearlypolarized.
• The transmitted wave has no “memory” of its originalpolarization.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Outline
1 EM WavesProperties of EM Waves
2 Polarization
3 The Doppler Effect
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Effect
Moving (sound) source and observer at rest:If the source is moving toward you, the wavelengthsseem shorter; if moving away, they seem longer.
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Effect
Similar situation for moving observer and source at rest
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
f obs = f source
√
1 − v rel/c√
1 + v rel/c
v rel: velocity of the source rel. tothe observer
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Shift
Waves from movingsource tend to pile upin direction of motion(blue shift) and bestreched out on theother side (red shift).
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Shift
The Doppler effect shifts an object’s entire spectrum eithertowards the red or towards the blue.
Example
Astronomer observes Hα line in spectrum of star to have awavelength of 657 nm instead of 656.3 nm:
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Shift
The Doppler effect shifts an object’s entire spectrum eithertowards the red or towards the blue.
Example
Astronomer observes Hα line in spectrum of star to have awavelength of 657 nm instead of 656.3 nm:
(657 / 656.3 − 1) · c ≈ 0.0011 · speed of light ≈ 320 km/s
CollegePhysics B
EM WavesProperties of EMWaves
Polarization
The DopplerEffect
Doppler Shift
The Doppler effect shifts an object’s entire spectrum eithertowards the red or towards the blue.
Example
Astronomer observes Hα line in spectrum of star to have awavelength of 655 nm instead of 656.3 nm:
(655 / 656.3 − 1) · c ≈ −0.002 · speed of light ≈ −594 km/s
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