Class 32: Outline
Hour 1:
Generating Electromagnetic Waves
Plane EM Waves
Electric Dipole EM Waves
Hour 2:
Experiment 12: Microwaves
Review Exam 3 Results
P32- 1
Recall:
Electromagnetic Radiation
P32- 2
Recall Electromagnetic
Radiation: Plane Waves
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/07-EBlight/07-EB_Light_320.html
P32- 3
Properties of EM Waves
Travel (through vacuum) with
speed of light
v=c=
m
= 3 × 10
s
µ 0ε 0
1
8
At every point in the wave and any instant of time,
E and B are in phase with one another, with
E E0
=
=c
B B0
E and B fields perpendicular to one another, and to
the direction of propagation (they are transverse):
G G
Direction of propagation = Direction of E × B
P32- 4
Generating Plane
Electromagnetic Radiation
P32- 5
Shake A Sheet of Charge Up
and Down
P32- 6
Java Applet for Generation of
Plane Waves
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/09-planewaveapp/09planewaveapp320.html
P32- 7
First Pull The Sheet of
Charge Down At Speed v
E1 vT v
tan θ =
=
=
E0 cT c
G ⎛ v ⎞ ⎛ vσ ⎞
ˆ
E1 = ⎜ E0 ⎟ ˆj = ⎜
⎟j
⎝ c ⎠ ⎝ 2ε 0 c ⎠
When you pull down, there is a back force up!
P32- 8
Rate of Work Done?
G
G
⎛ vσ ⎞ ˆ ⎛ vσ 2 dA ⎞ ˆ
dFe = dqE1 = (σ dA) ⎜
⎟j=⎜
⎟j
⎝ 2ε 0 c ⎠ ⎝ 2ε 0 c ⎠
G
G
⎛ vσ 2 dA ⎞ ˆ
dFext = −dFe = − ⎜
⎟j
⎝ 2ε 0 c ⎠
G
G
2 2
d Wext dFext d s ⎛ vσ 2 ˆ ⎞
v
σ
ˆ
j ⎟ ⋅ −v j =
=
⋅ = ⎜−
dA dt
dA dt ⎝ 2ε 0 c ⎠
2ε 0 c
2
( )
P32- 9
What About B Field?
G ⎛ v ⎞ ⎛ vσ ⎞
E1 = ⎜ E0 ⎟ ˆj = ⎜
⎟ ˆj
⎝ c ⎠ ⎝ 2ε 0 c ⎠
G ⎧⎪+ ( µ0σ v 2)kˆ , x > 0
B1 = ⎨
⎪⎩−( µ0σ v 2)kˆ , x < 0
P32- 10
Rate Energy Carried Away?
G 1 G G
1 ⎛ vσ ˆ ⎞ ⎛ µ0σ v ˆ ⎞ ⎛ v 2σ 2 ⎞ ˆ
S = E1 × B1 = ⎜
j⎟ × ⎜
k⎟ =⎜
⎟i
µ0
µ0 ⎝ 2ε 0c ⎠ ⎝ 2
⎠ ⎝ 4ε 0 c ⎠
Energy radiated to left and right is exactly equal to
the rate of work required to move sheet down P32- 11
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.
P32- 12
Generating Plane Wave Applet
P32- 13
PRS Question:
Generating A Plane Wave
P32- 14
Generating Electric Dipole
Electromagnetic Waves
P32- 15
Generating Electric Dipole
Radiation Applet
P32- 16
Quarter-Wavelength Antenna
Accelerated charges are the source of EM waves.
Most common example: Electric Dipole Radiation.
λ
4
λ
4
t=0
t = T/4
t = T/2
t=T
P32- 17
Why are Radio Towers Tall?
AM Radio stations have
frequencies 535 – 1605 kHz.
WLW 700 Cincinnati is at 700
kHz.
c
3 ×108 m/s
= 429 m
λ= =
3
f 700 ×10 Hz
λ / 4 ≈ 107m ≈ 350ft
The WLW 700 Cincinnati Tower is 747 ft tall
P32- 18
Quarter-Wavelength Antenna
P32- 19
Quarter-Wavelength Antenna
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/04QuarterWaveAntenna/04-MicrowaveDLICS_320.html
P32- 20
Spark Gap Transmitter
P32- 21
Spark Gap Generator:
An LC Oscillator
First: Example of “lumped” LC Oscillator
(Capacitor & Inductor together as one)
P32- 22
Group Problem: Lumped LC Circuit
Parallel
Plate
Capacitor
Cylindrical
Inductor Height (into page): h
Question: What is the resonance frequency?
Recall:
ε0 A
Φ
L=
C=
I
d
Bsolenoid = µo [ current per unit length]
1
ω0 =
LC
P32- 23
Our spark gap antenna
1) Charge gap (RC)
τ = RC = (4.5 × 106 Ω)(33 × 10−12 F) = 1.5 × 10−4 s
2) Breakdown! (LC)
1 c 3 ×10 cm/s
=
= =
12.4 cm
T 4l
9
= 2.4 ×10 Hz = 2.4 GHz 3) Repeat
10
f rad
P32- 24
Spark Gap Transmitter
P32- 25
PRS Question:
Spark Gap Antenna
P32- 26
Spark Gap Antenna
http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/light/03AntennaPattern/03-MicrowaveAntenna_320.html
P32- 27
Spark Gap Antenna
P32- 28
PRS Questions:
Angular Distribution &
Polarization of Radiation
P32- 29
Demonstration:
Antenna
P32- 30
Polarization
P32- 31
Polarization of TV EM Waves
Why oriented
as shown?
Why different
lengths?
P32- 32
Demonstration:
Microwave Polarization
P32- 33
Experiment 12:
Measure Wavelength by
Setting Up Standing Wave
P32- 34
Experiment 12:
Microwaves
P32- 35
Exam 3 Results
P32- 36