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Lecture 15.1 :!Electromagnetic Waves
Lecture Outline:!Maxwell’s Equations!
Electromagnetic Waves!Polarization!
April 21, 2015
Textbook Reading:!Ch. 34.3 - 34.7
Announcements
2
•Exam #3….a real mess due to printing mistake. My apologies.!
‣Average # points (out of 40 points you got to see): 31.27 (or 78.2%)!‣Standard Deviation: 5.71 points (or 14.3%)!‣Add 60 points to the grade you see in Blackboard. (e.g. if you got 25/40 points, your exam score will be counted as an 85%).!
•HW #11 due on Tuesday, April 28 at 9am.!
•Reminder: lecture on Thursday (April 23) and next Tuesday (April 28) will be review for the Final, which is cumulative.!
•My office hours today: 2-3pm. E-mail me to set up meeting times for the rest of the semester.!
•Online Evaluation e-mails should be sent to you this week.!
‣Please fill out the evaluation form...it is completely confidential.!
‣Remember that PHY212 and PHY222 (lab) are separate courses!!
Last Lecture...
3
E and B fields are observer dependent! We can transform fields measured in one inertial frame (A) to those in another inertial frame (B).
Last Lecture...
4
Maxwell introduced the idea of a “displacement current”, which modifies Ampere’s Law. This current is due to
changing electric flux (such as in a charging capacitor).
⇤⇥B · d⇥s = µ0
�Ithrough + �0
d�e
dt
⇥
Idisp = �0d�e
dt
The Displacement Current
5
⇤⇥B · d⇥s = µ0
�Ithrough + �0
d�e
dt
⇥
��E · d�s = �d�m
dt
Gauss’s Law for Magnetic Fields
6
(�m)closed surface =
��B · d �A = 0
No Isolated Magnetic Poles (Monopoles)!
POLE = POLE
Maxwell’s Equations
7
Maxwell’s Equations, plus Lorentz force law, form a complete theory of electromagnetism.
Electromagnetic Waves
8
“Source-free” Maxwell’s equations (no charge or current)
�⇥E · d ⇥A = 0
�⇥E · d⇥s = �d�m
dt�⇥B · d ⇥A = 0
�⇥B · d⇥s = �0µ0
d�e
dt
Electromagnetic Waves
9
Ey = E0sin (2⇥(x/�� ft))
Bz = B0sin (2⇥(x/�� ft))
�Ey
�x= ��Bz
�tCondition on EM Waves
from Faraday’s Law
⇥Bz
⇥x= ��0µ0
⇥Ey
⇥t
Condition on EM Waves from Ampere-
Maxwell Law
Electromagnetic Waves
10
Ey = E0sin (2⇥(x/�� ft))
Bz = B0sin (2⇥(x/�� ft))
Bx = By = 0
Ex = Ez = 0
Electromagnetic Waves
11
1
�0µ0vem= vem
E0 =B0
�0µ0vemE0 = vemB0
Electromagnetic Waves must travel at the Speed of Light!
vem wave =1
⇤�0µ0
⇥ 3.0� 108m/s = c
Applying Maxwell’s equations to our electromagnetic wave leads to two relations on E0 and B0 that both need to be true.
Electromagnetic Waves
12
Remember, electromagnetic waves do not just have to be visible light (wavelength ~ 100s of nanometers), but can be any wavelength.
� · f = c
Electromagnetic Waves
13
U.S. D
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INTER
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SATE
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Amate
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MARITIMEMOBILE
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FIXED
MOBILE
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FIXED
MOBIL
EFIX
EDSA
TELL
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SATE
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(E-S
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N
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HEX
PL. S
AT.
(Passi
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300
325
335
405
415
435
495
505
510
525
535
1605
1615
1705
1800
1900
2000
2065
2107
2170
2173
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90.5
2194
2495
2501
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2505
2850
3000
RADIO-LOCATION
BROA
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TING
FIXED
MOBILE
AMAT
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RADI
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ATIO
N
MOBIL
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EDMA
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MARI
TIME
MOBIL
E (TE
LEPH
ONY)
MARIT
IME
MOBIL
ELA
NDMO
BILE
MOBIL
EFIX
ED
30.0
30.5
6
32.0
33.0
34.0
35.0
36.0
37.0
37.5
38.0
38.2
5
39.0
40.0
42.0
43.6
9
46.6
47.0
49.6
50.0
54.0
72.0
73.0
74.6
74.8
75.2
75.4
76.0
88.0
108.
0
117.
975
121.
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123.
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128.
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7.03
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7.18
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161.
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162.
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173.
217
3.4
174.
0
216.
0
220.
022
2.0
225.
0
235.
0
300
ISM – 6.78 ± .015 MHz ISM – 13.560 ± .007 MHz ISM – 27.12 ± .163 MHz
ISM – 40.68 ± .02 MHz
ISM – 24.125 ± 0.125 GHz 30 GHz
ISM – 245.0 ± 1GHzISM – 122.5 ± .500 GHzISM – 61.25 ± .250 GHz
300.
0
322.
0
328.
6
335.
4
399.
9
400.
0540
0.15
401.
0
402.
0
403.
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0
420.
0
450.
045
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455.
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2.737
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7.537
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7.737
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0
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061
4.0
698
746
764
776
794
806
821
824
849
851
866
869
894
896
9019
0190
2
928
929
930
931
932
935
940
941
944
960
1215
1240
1300
1350
1390
1392
1395
2000
2020
2025
2110
2155
2160
2180
2200
2290
2300
2305
2310
2320
2345
2360
2385
2390
2400
2417
2450
2483
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0026
5526
9027
00
2900
3000
1400
1427
1429
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1430
1432
1435
1525
1530
1535
1544
1545
1549
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5916
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10.6
1613
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26.5
1660
1660
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68.4
1670
1675
1700
1710
1755
1850
MARIT
IME M
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(space
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T.(Sp
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TE (R
)(sp
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3.0
3.1
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3.5
3.6
3.65
3.7
4.2
4.4
4.5
4.8
4.94
4.99
5.0
5.15
5.25
5.35
5.46
5.47
5.6
5.65
5.83
5.85
5.92
5
6.42
5
6.52
5
6.70
6.87
5
7.02
57.
075
7.12
5
7.19
7.23
57.
25
7.30
7.45
7.55
7.75
7.90
8.02
5
8.17
5
8.21
5
8.4
8.45
8.5
9.0
9.2
9.3
9.5
10.0
10.4
510
.510
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10.6
10.6
8
10.7
11.7
12.2
12.7
12.7
5
13.2
513
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13.7
514
.0
14.2
14.4
14.4
714
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515
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5
15.3
5
15.4
15.4
3
15.6
315
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.617
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17.2
17.3
17.7
17.8
18.3
18.6
18.8
19.3
19.7
20.1
20.2
21.2
21.4
22.0
22.2
122
.5
22.5
5
23.5
5
23.6
24.0
24.0
5
24.2
524
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24.6
5
24.7
5
25.0
5
25.2
525
.527
.0
27.5
29.5
29.9
30.0
ISM – 2450.0 ± 50 MHz
30.0
31.0
31.3
31.8
32.0
32.3
33.0
33.4
36.0
37.0
37.6
38.0
38.6
39.5
40.0
40.5
41.0
42.5
43.5
45.5
46.9
47.0
47.2
48.2
50.2
50.4
51.4
52.6
54.2
555
.78
56.9
57.0
58.2
59.0
59.3
64.0
65.0
66.0
71.0
74.0
75.5
76.0
77.0
77.5
78.0
81.0
84.0
86.0
92.0
95.0
100.
0
102.
0
105.
0
116.
0
119.
98
120.
02
126.
0
134.
0
142.
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149.
0
150.
0
151.
0
164.
0
168.
0
170.
0
174.
5
176.
5
182.
0
185.
0
190.
0
200.
0
202.
0
217.
0
231.
0
235.
0
238.
0
241.
0
248.
0
250.
0
252.
0
265.
0
275.
0
300.
0
ISM – 5.8 ± .075 GHz
ISM – 915.0 ± 13 MHz
INTER
-SATE
LLITE
RADIO
LOCA
TION
SATE
LLITE
(E-S)
AERO
NAUT
ICAL
RADIO
NAV.
PLEASE NOTE: THE SPACING ALLOTTED THE SERVICES IN THE SPEC-TRUM SEGMENTS SHOWN IS NOT PROPORTIONAL TO THE ACTUAL AMOUNTOF SPECTRUM OCCUPIED.
AERONAUTICALMOBILE
AERONAUTICALMOBILE SATELLITE
AERONAUTICALRADIONAVIGATION
AMATEUR
AMATEUR SATELLITE
BROADCASTING
BROADCASTINGSATELLITE
EARTH EXPLORATIONSATELLITE
FIXED
FIXED SATELLITE
INTER-SATELLITE
LAND MOBILE
LAND MOBILESATELLITE
MARITIME MOBILE
MARITIME MOBILESATELLITE
MARITIMERADIONAVIGATION
METEOROLOGICALAIDS
METEOROLOGICALSATELLITE
MOBILE
MOBILE SATELLITE
RADIO ASTRONOMY
RADIODETERMINATIONSATELLITE
RADIOLOCATION
RADIOLOCATION SATELLITE
RADIONAVIGATION
RADIONAVIGATIONSATELLITE
SPACE OPERATION
SPACE RESEARCH
STANDARD FREQUENCYAND TIME SIGNAL
STANDARD FREQUENCYAND TIME SIGNAL SATELLITE
RADI
O AS
TRON
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FIXED
MARITIME MOBILE
FIXED
MARITIMEMOBILE Aeronautical
Mobile
STAN
DARD
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ALLOCATION USAGE DESIGNATIONSERVICE EXAMPLE DESCRIPTION
Primary FIXED Capital LettersSecondary Mobi le 1st Capital with lower case letters
U.S. DEPARTMENT OF COMMERCENational Telecommunications and Information AdministrationOffice of Spectrum Management
October 2003
MOBIL
EBR
OADC
ASTIN
G
TRAVELERS INFORMATION STATIONS (G) AT 1610 kHz
59-64 GHz IS DESIGNATED FORUNLICENSED DEVICES
Fixed
AERO
NAUT
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RADI
ONAV
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ION
SPAC
E RES
EARC
H (Pa
ssive
)
* EXCEPT AERO MOBILE (R)
** EXCEPT AERO MOBILE WAVELENGTH
BANDDESIGNATIONS
ACTIVITIES
FREQUENCY
3 x 107m 3 x 106m 3 x 105m 30,000 m 3,000 m 300 m 30 m 3 m 30 cm 3 cm 0.3 cm 0.03 cm 3 x 105Å 3 x 104Å 3 x 103Å 3 x 102Å 3 x 10Å 3Å 3 x 10-1Å 3 x 10-2Å 3 x 10-3Å 3 x 10-4Å 3 x 10-5Å 3 x 10-6Å 3 x 10-7Å
0 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz 10 MHz 100 MHz 1 GHz 10 GHz 100 GHz 1 THz 1013Hz 1014Hz 1015Hz 1016Hz 1017Hz 1018Hz 1019Hz 1020Hz 1021Hz 1022Hz 1023Hz 1024Hz 1025Hz
THE RADIO SPECTRUMMAGNIFIED ABOVE3 kHz 300 GHz
VERY LOW FREQUENCY (VLF)Audible Range AM Broadcast FM Broadcast Radar Sub-Millimeter Visible Ultraviolet Gamma-ray Cosmic-ray
Infra-sonics Sonics Ultra-sonics Microwaves InfraredP L S XC Radar
Bands
LF MF HF VHF UHF SHF EHF INFRARED VISIBLE ULTRAVIOLET X-RAY GAMMA-RAY COSMIC-RAY
X-ray
ALLOCATIONSFREQUENCY
BRO
AD
CA
STIN
GFI
XED
MO
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*
BRO
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BRO
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FIXED
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BROA
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FIXED
BROA
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FIXED
BROA
DCAS
TING
FIXED
BROA
DCAS
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FIXED
BROA
DCAS
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FIXED
FIXED
FIXED
FIXED
FIXED
FIXED
LAND
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FIXE
D
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NAUT
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This chart is a graphic single-point-in-time portrayal of the Table of Frequency Allocations used by theFCC and NTIA. As such, it does not completely reflect all aspects, i.e., footnotes and recent changesmade to the Table of Frequency Allocations. Therefore, for complete information, users should consult theTable to determine the current status of U.S. allocations.
Properties of Electromagnetic Waves
14
Poynting vector, S, defines the flow of energy in an electromagnetic wave. It has units of Power/Area.
�S ⇥ 1
µ0
�E � �B
S =EB
µ0=
E2
cµ0= c�0E
2
I =P
A= Savg =
c�02
E20
Average Intensity over one cycle
Clicker Question #1
15
An electromagnetic plane wave is coming toward you, out of the screen. At one instant, the electric field looks as shown. Which is the wave’s magnetic field at this instant?
Eis in the direction of motion.
Clicker Question #2
16
In which direction is this electromagnetic wave traveling? !!A. Up. B. Down. C. Into the screen. D. Out of the screen. E. These are not allowable fields for an electromagnetic wave.
is in the direction of motion.
Properties of Electromagnetic Waves
17
When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5E9 km from earth. It sent a signal with 21 W of power back to earth. Assuming the transmitter broadcast equally in all directions, what signal intensity was received on earth? What electric field amplitude was detected? What magnetic field amplitude was detected?
Properties of Electromagnetic Waves
18
Electromagnetic waves exert a “radiation pressure” when they are incident on a surface.
Solar Sail
�p =energy absorbed
c
prad =F
A=
P/A
c=
I
c
F =�p
�t=
(energy absorbed/�t)
c=
P
c
Properties of Electromagnetic Waves
19
Properties of Electromagnetic Waves
20
An 80 kg astronaut has gone outside her space capsule to do some repair work. Unfortunately, she forget to lock her safety tether in place, and she has drifted 5.0m away from the capsule. Fortunately, she has a 1000 W portable laser with fresh batteries that will operate it for 1.0h. Her only chance is to accelerate herself toward the space capsule by firing the laser in the opposite direction. She has a 10-h supply of oxygen. How long will it take her to reach safety?
Properties of Electromagnetic Waves
21
Alternating current in an antenna creates an electromagnetic wave.
Properties of Electromagnetic Waves
22
Polarization
23
Plane defined by the Poynting vector and the Electric Field vector is called the Plane of Polarization.
Polarization
24
Polarization
25
Light reflecting off of a horizontal surface (such as a lake) has significant horizontal polarization.
Appropriate sunglasses can reduce the “glare”.
Which way are the “polymers” in your sunglasses oriented?
Polarization
26
Itransmitted = I0cos2�
Polarizer removes energy from the incident wave by diminishing it’s electric field amplitude.
Clicker Question #3
27
Unpolarized light, traveling in the direction shown, is incident on polarizer 1. Does any light emerge from polarizer 3? !!A. Yes. B. No.
Reminders
28
!
•On Thursday (4/23) and Tuesday (4/28) we will review course material in preparation for the Final. !
•HW #11 due on Tuesday, 4/28, at 9am.!•Final Exam is Monday, May 4th from 3-5pm at
Watson Theatre in Watson Hall (corner of University Place and Comstock)!!
•My office hours today are 2-3pm. If you would like to meet ahead of the Final, please feel free to e-mail me and setup a meeting time.
