Lecture 15.1 :
Electromagnetic Waves
Lecture Outline:
Electromagnetic Waves
Properties of Electromagnetic Waves
Polarization
Textbook Reading:
Ch. 34.5 - 34.7
April 23, 2013
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Announcements
•Quiz #6 on Thursday (34.1-34.5 material)
•Online Evaluation e-mails should be sent to you this week.
‣Please fill out the evaluation form...it is completely confidential.
May 8 is
deadline.
‣Remember that PHY212 and PHY222 (lab) are separate courses!
•Society of Physics Student (SPS) is planning to offer “clinic”
services during Finals week. The regular clinic will also be open.
‣Date: May 1st
‣Time: 10am-4pm
‣Location: Rooms 104N and 106 in the Physics building.
‣Come with specific questions!
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Last Lecture...
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).
Idisp
�
�
�
dΦe
�
B · d�s = µ0 Ithrough + �0
dt
3
dΦe
= �0
dt
Last Lecture...
Maxwell’s Equations, plus Lorentz force law, form a
complete theory of electromagnetism.
4
Last Lecture...
Ey = E0 sin (2π(x/λ − f t))
Bz = B0 sin (2π(x/λ − f t))
∂Ey
∂Bz
=−
∂x
∂t
Condition on EM Waves
from Faraday’s Law
E0 = vem B0
5
Electromagnetic Waves
∂Bz
∂Ey
= −�0 µ0
∂x
∂t
Condition on EM Waves
from Ampere-Maxwell Law
6
Electromagnetic Waves
We now have two relations on E0 and B0 that both need to be true.
B0
E0 =
�0 µ0 vem
E0 = vem B0
1
= vem
�0 µ0 vem
Electromagnetic Waves must travel at the Speed of Light!
vem
wave
1
=√
≈ 3.0 × 108 m/s = c
� 0 µ0
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Electromagnetic Waves
Remember, electrogmagnetic waves do not just have to be visible light
(wavelength ~ 100s of nanometers), but can be any wavelength.
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Properties of Electromagnetic Waves
Poynting vector, S, defines the flow of energy in an electromagnetic wave.
1
�≡
� ×B
�
S
E
µ0
E2
EB
=
= c�0 E 2
S=
µ0
cµ0
Average Intensity
over one cycle
9
P
c�0 2
I=
= Savg =
E0
A
2
Clicker Question #1
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?
is in the direction of motion.
10
E
Clicker Question #2
In which direction is this
electromagnetic wave
traveling?
A.
B.
C.
D.
E.
is in the direction of motion.
Up.
Down.
Into the screen.
Out of the screen.
These are not allowable fields for an
electromagnetic wave.
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Properties of Electromagnetic Waves
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
one earth? What electric field amplitude was detected?
What magnetic field amplitude was detected?
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Properties of Electromagnetic Waves
Electromagnetic waves exert a “radiation pressure”
when they are incident on a surface.
energy absorbed
∆p =
c
∆p
(energy absorbed/∆t)
P
F =
=
=
∆t
c
c
prad
Solar Sail
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F
P/A
I
=
=
=
A
c
c
Properties of Electromagnetic Waves
Alternating current in an antenna creates an
electromagnetic wave.
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Properties of Electromagnetic Waves
15
Polarization
Plane defined by the Poynting vector and the Electric
Field vector is called the Plane of Polarization.
16
Polarization
17
Polarization
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?
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Polarization
Polarizer removes energy from the incident wave by
diminishing it’s electric field amplitude.
Itransmitted = I0 cos2 θ
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Clicker Question #3
Unpolarized light, traveling in the direction shown, is incident
on polarizer 1. Does any light emerge from polarizer 3?
Yes.
B. No.
A.
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Reminders
•Quiz #6 on Thursday (34.1-34.5 material)
•Don’t miss out on opportunities for Final exam
preparation (SPS “clinic”, regular “clinic”, review in
class on Thu./Tue.).
•Final Exam is May 6th from 3-5pm.
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