Module 30:
Generating
g EM Waves,,
Dipole Radiation,
Polarization
1
Module 30: Outline
Generating EM Waves
Electric Dipole EM Waves
Experiment 9: Microwaves
2
Electromagnetic
g
Waves
Hz
Remember:
λf =c
3
Summary:
Traveling Electromagnetic
Waves
4
Properties of EM Waves
Travel (through vacuum) with
speed of light
v=c=
m
= 3 × 10
s
μ0ε 0
1
8
At every
yp
point in the wave and any
y 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):
r r
Direction of propagation = Direction of E × B
5
Traveling
g E & B Waves
G
G G
Wavelength: λ
ˆ E sin(k ⋅ r − ωt )
E
=
E
0
Frequency : f
W
Wave
Number:
N b
k=
2π
λ
Angular Freq
Freq.:: ω = 2π f
1 2π
Period: T = =
f
ω
ω
S
Speed:
d v= =λf
k
ˆ × Bˆ
Direction: + kˆ = E
E E0
=
=v
B B0
In vacuum...
=c=
m
= 3 × 10
s
μ0ε 0
1
8
6
Generating
G
ti Plane
Pl
Electromagnetic Radiation
7
Shake a Sheet of Charge
g
Link to application
8
Problem: B Field Generation
Sheet (blue) has uniform
charge
h
d
density
it σ
Starting time T ago pulled
down at velocity v
1) What is B field?
sheet
(ω t )
(HINT: Change drawing perspective)
y(t)) = y0 sin
2)) If sheet p
position is y(
What is B(x,t)?
What is E(x,t)? What Direction?
9
You Made a Plane Wave!
Link
10
How to Think About E-Field
E-Field
E
Field lines like strings tied to plane
This is the field
you calculated &
that propagates
11
Problem: Energy
gy in Wave
You Found:
B1 = μ0σ v 2
1) What is total power per unit area radiated away?
2) Wh
Where iis tthat
h t energy coming
i ffrom?
?
3) Calculate power generated to see efficiency
12
Generating
g Electric Dipole
p
Electromagnetic Waves
13
Generating
Ge
e a g Electric
ec c Dipole
po e
Radiation Applet
Link to applet
pp
14
Half-Wavelength
g Antenna
Accelerated charges are the source of EM waves.
M t common example:
Most
l Electric
El t i Dipole
Di l R
Radiation.
di ti
λ
4
λ
4
t=0
t = T/4
t = T/2
t=T
15
Why
y are Radio Towers Tall?
AM Radio stations have
f
frequencies
i 535 – 1605 kH
kHz.
WLW 700 Cincinnati is at 700
kHz.
kH
c
3 × 10 m/s
λ= =
=
429
m
f 700 × 103 Hz
λ / 4 ≈ 107m ≈ 350ft
8
The WLW 700 Cincinnati Tower is 747 ft tall; with
reflection One wavelength antenna
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Quarter-Wavelength
Quarter
Wavelength Antenna
17
Quarter-Wavelength
Q
g Antenna
18
Spark
p
Gap
p Transmitter
19
Spark Gap Generator:
An LC Oscillator
20
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
= = =
12.4cm
T 4l
10
f rad
= 2.4 × 10 Hz = 2.4GHz
9
3) Repeat
21
Spark Gap Transmitter
22
Concept Question Question:
Spark
p
Gap
p Antenna
23
Concept
p Question: Spark
p
Gap
p
At the time shown the
charge
h
on the
h top h
half
lf off our
1/2 wave antenna is positive
and
d att its
it maximum
i
value.
l
At this time the current
across the
th sparkk gap iis
1.
2.
3.
4.
5.
Zero
A maximum and downward
A maximum and upward
g
Can’t tell from the information given
I don’t know
Spark
p
Gap
p Antenna
25
Spark
p
Gap
p Antenna
26
Demonstration:
Antenna
27
Polarization
28
Polarization of TV EM Waves
Why oriented
as shown?
Why different
lengths?
29
Demonstration:
Microwave Polarization
30
Experiment 10:
Microwaves
31
Concept
C
t Question
Q
ti
Questions:
Angular
g
Distribution &
Polarization of Radiation
32
Concept
p Q.: Angular
g
Dependence
p
As you moved your receiving antenna around
p
g
gap
p transmitting
g antenna as above,,
the spark
you saw
1.
1
2.
3
3.
4.
Increased power at B compared to A
Decreased power at B compared to A
N change
No
h
iin power att B compared
d tto A
I don’t know
33
Concept Question: Polarization
When located as shown, your receiving antenna
saw maximum power when oriented such that
1 Its straight portion was parallel to the
1.
straight portion of the transmitter
2 Its straight portion was perpendicular to the
2.
straight portion of the transmitter
3. I don
don’tt know
34
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8.02SC Physics II: Electricity and Magnetism
Fall 2010
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