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1P32-
Class 32: Outline
Hour 1:Generating Electromagnetic Waves
Plane EM WavesElectric Dipole EM Waves
Hour 2:Experiment 12: MicrowavesReview Exam 3 Results
2P32-
Recall:Electromagnetic Radiation
3P32-
Recall Electromagnetic Radiation: Plane Waves
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/07-EBlight/07-EB_Light_320.html
4P32-
Properties of EM Waves
8
0 0
1 3 10 mv csµ ε
= = = ×
0
0
EE cB B= =
Travel (through vacuum) with speed of light
At every point in the wave and any instant of time, E and B are in phase with one another, with
E and B fields perpendicular to one another, and to the direction of propagation (they are transverse):
Direction of propagation = Direction of ×E B
5P32-
Generating Plane Electromagnetic Radiation
6P32-
Shake A Sheet of Charge Up and Down
7P32-
Java Applet for Generation of Plane Waves
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/09-planewaveapp/09-planewaveapp320.html
8P32-
First Pull The Sheet of Charge Down At Speed v
1
0
tan E vT vE cT c
θ = = =
1 00
ˆ ˆ2
v vEc c
σε
⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠
E j j
When you pull down, there is a back force up!
9P32-
Rate of Work Done?2
10 0
ˆ ˆ( )2 2ev v dAd dq dAc c
σ σσε ε
⎛ ⎞ ⎛ ⎞= = =⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠F E j j
2
ext0
ˆ2ev dAd d
cσε
⎛ ⎞= − = −⎜ ⎟
⎝ ⎠F F j
( )2 2 2 2
ext ext
0 0
ˆ ˆ2 2
d W d d v vvdAdt dA dt c c
σ σε ε
⎛ ⎞= ⋅ = − ⋅ − =⎜ ⎟
⎝ ⎠
F s j j
10P32-
What About B Field?
01
0
ˆ( 2) , 0
ˆ( 2) , 0
v x
v x
µ σ
µ σ
⎧+ >⎪= ⎨− <⎪⎩
kB
k1 0
0
ˆ ˆ2
v vEc c
σε
⎛ ⎞⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠
E j j
11P32-
Rate Energy Carried Away?
2 20
1 10 0 0 0
1 1 ˆ ˆˆ2 2 4
vv vc c
µ σσ σµ µ ε ε
⎛ ⎞ ⎛ ⎞⎛ ⎞= × = × =⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠
S E B j k i
Energy radiated to left and right is exactly equal to the rate of work required to move sheet down
12P32-
To generate plane wave, move sheet up and down sinusoidally
The work you do in moving the sheet is carried away as electromagnetic radiation, with 100% efficiency.
13P32-
Generating Plane Wave Applet
14P32-
PRS Question:Generating A Plane Wave
15P32-
Generating Electric Dipole Electromagnetic Waves
16P32-
Generating Electric Dipole Radiation Applet
17P32-
Quarter-Wavelength AntennaAccelerated charges are the source of EM waves. Most common example: Electric Dipole Radiation.
4λ
4λ
t = 0 t = T/4 t = T/2 t = T
18P32-
Why are Radio Towers Tall?AM Radio stations have frequencies 535 – 1605 kHz. WLW 700 Cincinnati is at 700 kHz.
8
3
3 10 m/s 429 m700 10 Hz
/ 4 107m 350ft
cf
λ
λ
×= = =
×≈ ≈
The WLW 700 Cincinnati Tower is 747 ft tall
19P32-
Quarter-Wavelength Antenna
20P32-
Quarter-Wavelength Antenna
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/04-QuarterWaveAntenna/04-MicrowaveDLICS_320.html
21P32-
Spark Gap Transmitter
22P32-
Spark Gap Generator:An LC Oscillator
First: Example of “lumped” LC Oscillator (Capacitor & Inductor together as one)
23P32-
Group Problem: Lumped LC Circuit
Height (into page): h
Parallel Plate
Capacitor
Cylindrical Inductor
Question: What is the resonance frequency?
Recall:
01LC
ω =0ACdε
= LIΦ
=
[ ]solenoid current per unit lengthoB µ=
24P32-
Our spark gap antenna
6 12 4(4.5 10 )(33 10 F) 1.5 10 sτ RC − −= = × Ω × = ×
rad1
4cf
T l= =
103 10 cm/s12.4cm×
=
92.4 10 Hz 2.4GHz= × =
1) Charge gap (RC)
2) Breakdown! (LC)
3) Repeat
25P32-
Spark Gap Transmitter
26P32-
PRS Question:Spark Gap Antenna
27P32-
Spark Gap Antenna
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/03-AntennaPattern/03-MicrowaveAntenna_320.html
28P32-
Spark Gap Antenna
29P32-
PRS Questions:Angular Distribution &
Polarization of Radiation
30P32-
Demonstration:Antenna
31P32-
Polarization
32P32-
Polarization of TV EM Waves
Why oriented as shown?
Why different lengths?
33P32-
Demonstration:Microwave Polarization
34P32-
Experiment 12:Measure Wavelength by
Setting Up Standing Wave
35P32-
Experiment 12:Microwaves
36P32-
Exam 3 Results