Download Electromagnetic Waves - Little Shop of Physics

Electromagnetic
Waves
•
Electromagnetic waves are
traveling waves of electric
and magnetic fields.
•
Electromagnetic waves
come in a wide range of
wavelengths. There is more
to the spectrum than the
rainbow.
•
Long wavelengths act like
waves, short wavelengths
like particles. Or, more
precisely, like photons.
1
Warming Up.
A metal wire is resting on
a U-shaped conducting
rail. The rail is fixed in
position, but the
wire is free to move.
If the magnetic field is increasing in strength, what is the
direction of the induced current?
a.Clockwise
b.Counterclockwise
What is the direction of the force on the wire?
a.To the left
b.To the right
2
Now, think...
A metal wire is resting on
a U-shaped conducting
rail. The rail is fixed in
position, but the
wire is free to move.
If the magnetic field is increasing in strength, this induces a
current in the wire.
How do the charges know to move?
3
A changing
magnetic field
induces an
electric field.
A changing
electric field
induces a
magnetic field
too.
One of the
10 coolest
things ever
discovered
4
The Inductor
L is the
inductance;
the unit is the
Henry. (H)
5
LC
Circuits
6
Tuned Circuits
7
Unifying Electricity and Magnetism
! ρ
∇⋅E =
ε0
!
∇⋅B = 0
!
!
∂B
∇×E =−
∂t
!
!
!
∂E
∇ × B = µ0 j + µ0ε 0
∂t
8
The electromagnetic pulse.
An accelerated charge emits a pulse of electric and
magnetic fields. This pulse travels through space.
Maxwell’s equations say the speed should be:
v=
1
= 3.00 × 10 8 m/s
ε 0 µ0
9
netism wondered about this and hypothesized th
an induced magnetic field.
This hypothesis leads to a surprising conclus
induce an electric field in the absence of any ch
can induce a magnetic field in the absence of any
establish self-sustaining electric and
magnetic f
u
currents. A changing electric field E creates a ma
just the right way to recreate the electric field, wh
to again recreate the magnetic field, with the f
electromagnetic induction. In fact, electric and m
free from any charges or currents, if they take the
The electromagnetic wave.
An oscillating charge will emit an electromagnetic wave.
It’s a wave of electric and magnetic fields.
electromagnetic wave.
1. The wave is a sinusoidal traveling wave,
Electromagnetic Waves
with frequency f and wavelength l.
u
E0
10
In order to sustain itself and travel through sp
have a very specific geometry, shown inu FIGUR
magnetic wave is a transverse wave. E and B
well as perpendicular to the direction of travel.
A mathematical analysis shows that such a w
FIGURE 25.25 A sinusoidal
y
Properties of Electromagnetic Wa
Wavelength l
E
vem =
u
E
u
vem
B0
u
B
z
u
u
E
u
B
x
u
2. E and B are
perpendicular to
each other and to
the direction of
u
u
3. E and B are in phase;
travel. Thus an
thatare
is, they
have
electromagnetic
Electromagnetic
Waves
Waves.
matching crests,
wave is a
troughs,
transverse wave. c =
f λ and zeros.
c 3.0 × 10 8 m/s
f = =
λ
λ
1
f ∝
λ
•
•
Increasing wavelength
Decreasing frequency
Increasing frequency
Decreasing wavelength
1
2P0m
where P0 and m0 are the permittivity and permea
for electric and magnetic fields. If you insert t
stants, you find vem = 3.00 * 108 m/s. This is a
speed of light!
In a vacuum, all electromagnetic waves must
we11call the speed of light and for which we use
the first to make this analysis, made a bold leap
tromagnetic wave. We studied the wave proper
we didn’t discuss just what is “waving.” Now w
and magnetic fields.
The amplitudes of the electric and magnetic
on the wave, the electric and magnetic field stre
E
=c
B
Figure 25.25 shows the values of the electric a
single line, the x-axis.
u
An E vector pointing in the y-dire
x-axis, where the vector’s tail is, the electric f
12
a certain strength. Nothing is “reaching” to a
NOTE ▶
FM vs. AM
An FM station transmits at 100 MHz, corresponding to a
wavelength of 3.0 m.
An AM station transmits at 1000 kHz, which is 1.0 MHz.
What is the corresponding wavelength?
Think
about ratios. The
frequency decreases
by a factor of 100.
What happens to
the wavelength?
c = fλ
13
FM & AM Radio
FM: Pick up electric field
AM: Pick up magnetic field
1
λ
4
14
Helpful Relationships
E = hf =
hc
λ
h = 4.14 × 10 −15 eVis
E (in eV) =
1240
λ (in nm)
15
Atomic Energies
16
Red vs. Blue, Part I.
A red pen laser emits light
of wavelength 670 nm.
A blue pen laser emits light
of wavelength 470 nm.
Which has a higher photon energy, the red or the blue?
E = hf
17
Red vs. Blue, Part II.
A red pen laser emits light
of wavelength 670 nm.
A blue pen laser emits light
of wavelength 470 nm.
Both lasers emit the same power, the same number of
joules per second.
Which laser emits more photons per second?
E = hf
18
The
Electromagnetic
Spectrum
Particle-y
Depends
Wave-ish
19
The Electromagnetic Spectrum
Wave
Wavelength Frequency
FM Radio
100 MHz
Microwave
1.9 GHz
Far IR
10 µm
Visible
500 nm
Ultraviolet
290 nm
Photon
energy
20
The
Electromagnetic
Spectrum
21
Basic Relationships
The speed of electromagnetic waves
A. depends on the wavelength
B. depends on the photon energy
C. is the same as the speed of sound
D. is the same for all waves regardless of wavelength
22
Basic Relationships
A typical analog cell phone has a frequency of 850 MHz; a
digital phone a frequency of 1950 MHz. Compared to the
signal from an analog cell phone, the digital signal has
! A. ! longer wavelength and lower photon energy
! B. ! longer wavelength and higher photon energy
! C. ! shorter wavelength and lower photon energy
! D. ! shorter wavelength and higher photon energy
23
Basic Relationships
A radio tower emits two 50 W signals, one an AM signal
at a frequency of 850 kHz, one an FM signal at a
frequency of 85 MHz. Which signal has more photons per
second? Explain.
! A. ! The AM signal has more photons per second.
! B. ! The FM signal has more photons per second.
! C. ! Both signals have the same photons per second.
24
Intensity
Intensity is
a ratio of
power to
area:
From
Chapter
15
P
I=
A
My laser pointer has a total output power of about 1.0
mW. When I shine it on the screen, it spreads out to
make a spot about 1.0 mm in diameter. What is the
intensity of the light in this spot?
How does this compare to the intensity of sunlight on
the ground at high noon on a summer day (which is
approximately 1100 W/m2)?
25
Energy and Field Strength
E0 =
2I
cε 0
B0 =
E0
c
E0 = cB0
26
The Microwave Oven
E0 =
2I
cε 0
B0 =
E0
c
E0 = cB0
Inside the cavity of a microwave oven, the 2.4 GHz
electromagnetic waves have an intensity of 5.0 kW/m2.
a. What is the strength of the electric field?
b. The magnetic field?
27
Intensity Variation for Spherical Wave
I=
Psource
4π r 2
28
A digital cell phone emits a 1.9 GHz
electromagnetic wave with total power
0.60 W.
• At a cell phone tower 2.0 km away,
what is the intensity of the wave?
(Assume that the wave spreads out
uniformly in all directions.)
• What are the electric and magnetic
field strengths at this distance?
I=
Psource
4π r 2
E0 =
2I
cε 0
B0 =
E0
c
29
Polarization
30
Navigating By The Sky
Polarization of skylight
Bee eyes
detect
polarization
31
Biological Effects of EM Radiation
Long wavelength
Wave-ish
Short wavelength
Particle-y
32
Talking On the Phone... How Dangerous?
P = 0.60 W
f = 1.9 GHz
Compute:
1) Intensity
2) Field strength
3) Photon energy
at 5.0 cm
33
What are the photon energies corresponding
to the following wavelengths?
a.
b.
c.
d.
Near IR, 1000 nm
Far red end of the spectrum, 750 nm
Far blue end of the spectrum, 400 nm
Near UV, 290 nm
E (in eV) =
1240
λ (in nm)
34
Atomic Radiation
Visible spectrum:
Approx. 400 - 750 nm
35
100 Watts = 4 Watts?
A typical incandescent lamp has a filament at a
temperature of approximately 2500 °C.
What is the peak wavelength of the emission?
36
Single-Photon Detection
Molecules are tuned to particular photon energies.
37
Visible Light, Near IR and UV
3 different cones
tuned to different
photon energies
38
The band gap of the silicon used to make the CCD
detector in a black and white security camera is 1.12 eV.
Photons with energy greater than this will be detected.
• What wavelength does this correspond to?
• In what part of the spectrum is this?
39
Radiation
N.B. e=0.97
for skin of any
color.
Seal thermal window
Pit viper
40
You Look Positively Radiant
A typical human has a surface area of about 1.8 m2. All
skin, regardless of color, has an emissivity of about e=0.97.
How much power does a person’s body radiate at normal
skin temperature? (About 33 °C, or 306 K)
What is the peak wavelength of the emission?
Pit Vipers
41
1600 cells
Raw
Processed
42
Short wavelength = high photon energy
Germicidal lamps
254 nm
4.9 eV
Tanning beds
365 nm
3.4 eV
43
Creating X rays
If an electron is accelerated through a 5.0 kV potential
difference, what is the maximum photon energy of the
resulting x ray? What is the wavelength?
44
Using X rays
45