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Physics 211
Topic 23
E&M Waves- How they’re formed
- Poynting Vector (what the heck it means)- Doppler Effect for E&M waves
Electricity & Magnetism Lecture 23, Slide 1
What you thought…..
Poynting.
Didn't quite understand the waves of energy portion with the graphs
My understanding of the quantum mechanical theory of light is that the energy carried by light does depend on the angular frequency, right? That's what the photoelectric effect was all about?
The prelecture was making sense until after question 2. Once intensity (which looks just like current) was introduced along with power and poynting and 87 different averages, everything fell apart for me.
Because the prior lecture pulled the equations for the EM wave out of thin air, with little explanation, it was a bit hard to grasp the power portion of the pre-lecture.I'm starting to be ready for summer. Only about a month left.
Could you please explain the poynting vector and the importance of these average values mentioned in the prelecture (average pointing vector, average intensity, etc)? Also, what do we need to know about photons and waves as far as how we treat them in this class? Thank you.
Slide 2
First…..two comments
E&M waves like sounds waves (in many ways)
So I’m going to say
“Recall from Physics 2111….” a lot
Slide 3
The animations in the pre-lectures are really nice for this topic.
There are just some things that are tough to draw on the board.
Creating an Electromagnetic Wave
Slide 4
E
Dipole
Antenna
Signal
Generator
What does this Create?
Electric Field changing in
magnitude and direction
with time and space
Ex = Eo sin (kx – wt)
Key Point!!!
Slide 5
Not just single sine wave!
Same value of E
z
Plane wave!
Electricity & Magnetism Lecture 22, Slide 6
Past Confusion
Nothing is moving here.
Arrows only represent strength of field.
Ampere’s Law / Faraday’s Law
Slide 7
=• dAdt
dEldB oo
dAdt
dBldE −=•
Ampere’s Law – Changing Electric
Field causes Magnetic Field
Faraday’s Law – Changing Magnetic
Field causes Electric Field
Ex = Eo sin (kx – wt) By = Bo sin (kx – wt)
t
B
x
E
−=
Eo k cos (kx – wt) = Bo w cos (kx – wt)
Eo/Bo = w/k = wave velocity
Eo = c Bo = B/(oo)1/2
Question: When is this true?
For which situations does Eo = c*Bo?
A. Always
B. In all cases where the electric field is changing
C. In all cases where the magnetic field is changing
D. Only for a electro-magnetic wave
E. (B) and (C)
Slide 8
Plane Waves from Last Time
E and B are perpendicular and in phase
Oscillate in time and space
Direction of propagation given by E X B
E0 = cB0
Electricity & Magnetism Lecture 23, Slide 9
Ex
By
Not Really
CheckPoint 1(A): Direction of Wave
Electricity & Magnetism Lecture 23, Slide 10
Which equation correctly describes the electromagnetic wave
shown above?
A. Ex = Eo sin (kz + ω t)
B. Ey = Eo sin (kz - ω t)
C. By = Bo sin (kz - ω t)
CheckPoint 1(A): Direction of Wave
Electricity & Magnetism Lecture 23, Slide 11
Which equation correctly describes the electromagnetic wave
shown above?
A. Ex = Eo sin (kz + ω t)
B. Ey = Eo sin (kz - ω t)
C. By = Bo sin (kz - ω t)
Welcome to
Physics 2112
Hit “E” on your clicker.
Electricity & Magnetism Lecture 23, Slide 13
Slide 14
The Electromagnetic Spectrum
Clickers:
f =24Ghz
l ~ 12.5cm
Recall from 2111:
v = fl = c
Waves Carry Energy
Electricity & Magnetism Lecture 23, Slide 15
Recall:
Energy Density for E field = uE = ½ o E2
Energy Density for B field = uB = ½ 1/o B2
Average Total Energy Density = <u> = ½ (uE + uB) = EmaxBmax/2co
Recall from 2111:
Intensity = Power/Area
= Average Energy hitting a surface per unit time
Intensity = <u> c = EmaxBmax/2o
Define:
Poynting Vector
o
BES
=
Example 23.1: Sunshine Poynting Vector
Slide 17
Sunlight puts an average of 1000 Joules
of energy every second into each square
meter of the earth around the equator.
What is the magnitude of the average
Poynting vector for this light?
a) |Savg| = 1000 Watts/m2
b) |Savg| = 1000/ Watts/m2
c) |Savg| = 1000 Watts/m22
2
Example 23.1: Sunshine Poynting Vector
Slide 18
Sunlight puts an average of1000 Joules
of energy every second into each square
meter of the earth around the equator.
What is the magnitude of the average
Poynting vector for this light?
a) |Savg| = 1000 Watts/m2
b) |Savg| = 1000/ Watts/m2
c) |Savg| = 1000 Watts/m22
2
What is Emax and Bmax for these E&M waves?
Just another way to keep track of all this:
Its magnitude is equal to IIts direction is the direction of propagation of the wave
Comment on Poynting Vector
Electricity & Magnetism Lecture 23, Slide 20
CheckPoint 1(B): Energy of Wave
Which of the following actions will increase the energy carried by
this wave?
A. Increase E keeping ω constant
B. Increase ω keeping E constant
C. Both of the above actions will increase the energy of the
wave
D. Neither of the above actions will increase the energy of
the wave
Unit 23, Slide 21
Maybe some points of confusion?
Slide 23
Wasn’t there a frequency term
in the energy of sound wave in
2111? (Amplitude2*w2)
Good point!
But in sound, something
physical is moving so we have a
kinetic energy term
Maybe some points of confusion?
Slide 24
Why is it that I always hear that x-rays
are more dangerous than visible light
ray?
Isn’t that a frequency and energy deal?
Again, good point!
But now we’re in the area of quantum
mechanics and we’re thinking about light
in terms of photons. In high frequency
waves, there a higher energy photons,
but there are less of them.
Question: Wave Direction
An electromagnetic wave is described by: where is the unit vector in the +y direction.
A B C D
Which of the following graphs represents the z − dependence of Bx at t = 0?
x
y
z
j( )tkzEjE w−= cosˆ
0
Question: Wave Direction
Electricity & Magnetism Lecture 23, Slide 26
An electromagnetic wave is described by: where is the unit vector in the +y direction.
A B C D
Which of the following graphs represents the z − dependence of Bx at t = 0?
X X
x
y
z
E
B
x
y
z
Wave moves in +z direction
j( )tkzEjE w−= cosˆ
0
( )tkzEjE w−= cosˆ0
BE
Points in direction of propagation
( )tkzBiB w−−= cosˆ0
td
dp
m
p
td
dE
2
2=
Light has Momentum!
Electricity & Magnetism Lecture 23, Slide 27
If it has energy and its moving, then it also has momentum:
Analogy from mechanics:
td
dp
m
mv=
pressureA
F
c
I=
m
pKE
2
2
=
vF=
IAtd
dE
td
KEd tot =→)(
For E − M waves:
cFIA =
cv →
Radiation pressure
c
IP =
Example 23.2: Pressure from Sunshine
Slide 28
Sunlight puts an average of 1000 Joules
of energy every second into each square
meter of the earth around the equator.
What is the pressure this sunlight puts
on the earth assuming it is all absorbed?
What is the total force exerted on the earth by
this sunlight?
What is the pressure of this sunlight if it
reflected back?
Doppler Shift
The Big IdeaAs source approaches:Wavelength decreasesFrequency Increases
Electricity & Magnetism Lecture 23, Slide 31
Recall for sound from 2111:
If source is moving wrt to air:)/1/( soundsso vvff −=
If observer is moving wrt to air: )/1( soundoso vvff +=
)/1(
)/1(
sounds
soundoso
vv
vvff
−
+=If observer is moving wrt to air:
What’s Different from Sound or Water Waves ?
Sound /Water Waves : You can calculate (no relativity needed)
BUTResult is somewhat complicated: is source or observer moving wrt medium?
Electromagnetic Waves : You need relativity (time dilation) to calculate
BUTResult is simple: only depends on relative motion of source & observer
b > 0 if source & observer are approaching
b < 0 if source & observer are separating
b = v/c
Doppler Shift for E-M Waves
Electricity & Magnetism Lecture 23, Slide 32
2
1
1
1'
−
+=
b
bff
v
orf’
f
v
ff’
Doppler Shift for E-M Waves
Electricity & Magnetism Lecture 23, Slide 33
The Doppler Shift is the SAME for both cases!f ’/f only depends on the relative velocity
2
1
1
1'
−
+=
b
bff
A Note on Approximations
Doppler Shift for E-M Waves
Electricity & Magnetism Lecture 23, Slide 34
2
1
1
1'
−
+=
b
bff
if b <<< 1
( )b+ 1' ff
*f f b
A police k-band radar gun emits radio waves at a frequency of 24GHz which is reflected off an approaching car and received back at the gun.
Which car will provide a higher reflected frequency?a) A car approaching at 67 mphb) A car approaching at 69mphc) Both will provide the same
Electricity & Magnetism Lecture 23, Slide 36
Example 23.3: Police Radar
What are the reflected frequencies for these two speeds?
CheckPoint 2(A): Clicker Waves
Unit 23, Slide 38
Your iclicker operates at a frequency of
approximately 900 MHz (900x106 Hz). What is
the approximate wavelength of the EM wave
produced by your iclicker?
A. 0.03 meters
B. 0.3 meters
C. 3.0 meters
D. 30 meters
Unit 23, Slide 39
CheckPoint 2(B): Clicker Waves
If you wanted to see the EM wave produced by
the iclicker with your eyes, which of the following
would work? (Note: Your eyes are sensitive to EM
waves with frequency around 1014 Hz)
A. Run away from the iclicker when it is voting.
B. Run toward the iclicker when it is voting.
C. Neither will work, moving relative to the
iclicker won't change the frequency
reaching your eyes.
Your iclicker operates at a frequency of approximately 900 MHz (900x106 Hz).
How fast would you have to run towards your to see the EM wave produced by the iclicker with your eyes, which of the following would work?
(Note: Your eyes are sensitive to EM waves with a frequency around 1014Hz)
Electricity & Magnetism Lecture 23, Slide 40
Example 23.4: Running towards your clicker
Our Sun Star in a distant galaxy
wav
elen
gth
Wavelengths appear shifted higher lengths
Red Shift
Frequencies appear shifted lower
(c = lf)
Star separating from us(Expanding Universe)
Electricity & Magnetism Lecture 23, Slide 43
Light from
distant stars
Red Shift (the whole story!)
Electricity & Magnetism Lecture 23, Slide 44
Two additional effects can cause
frequency shifts from distant stars.
Gravity - Extreme case is a black hole. You
can think of a black hole a “redshifting” light
until l = infinity and f = 0
Expanding Universe - Can take so long to
reach Earth that universe expanded during
flight, stretching the wavelength
Exact mixture depends – How long was wave
in flight, how large was object emitting the wave
and how fast was it moving wrt Earth.
Spiral Arm galaxy
A spiral arm galaxy is rotating as shown above. Which portion of the galaxy will appear more “red shifted” (lower frequency)?
A. A
B. B
C. C
A
B
C
We believe the energy in an e-m wave is carried by photons
Question: What are Photons?
Answer: Photons are Photons.
Photons possess both wave and particle propertiesParticle:
Energy and Momentum localizedWave:
They have definite frequency & wavelength ( fl = c)
Question: How can something be both a particle and a wave?Answer: It can’t (when we observe it)What we see depends on how we choose to measure it!The mystery of quantum mechanics: More on this in PHYS 2115 (one cool class!)
h = 6.63e−34 J − s
Planck’s constantConnections seen in equations:
E = hf
p = h/l
Photons
Electricity & Magnetism Lecture 23, Slide 46