Transcript B - Purdue Physics - Purdue University

PHYS219 Fall semester 2014
Lecture 18: Maxwell’s Equations (1864)
and EM Radiation
Dimitrios Giannios
Purdue University
Second Midterm (EXAM II)
Lecture! Date)) Subject)
L01!
L02!
Chapter)
Aug.!25! !course!overview! !
Aug.!27! Charge,!
17.1>2!
Coulombs!law!
Aug.!29! Electric!Fields!
17.3>4!
Sep.!1!
Holiday!
!
Sep.!3!
Electric!Potential! 18.1>2!
Sep.!5!
Recitation)
!
Sep.!8!
Equipotential!
18.3>4!
surfaces!
Sep.!10! Capacitors!
18.4>5!
Sep.!12! Recitation!
!
Sep.!15! Electric!current,! 19.1>3!
resistance!
Sep.!17! Kirchoff’s!Rules! 19.4!
Sep.!19! Recitation!
!
Sep.!22! RC!circuits!
19.5>9!
Sep.!24! Magnetic!fields! 20.1>2!
Sep.!25! Exam)I:))
Chapters!17>19!!
8pm,)PHYS)112
Sep.!26! Recitation!
!
Sep.!29! Lorentz!Force!
20.3!
Oct.!1!
Magnetic!Force! 20.4>6!
on!elec.!currents!
Oct.!3!
Recitation!
!
Oct.!6!
Ampere’s!Law!
20.7>9!
Oct.!8!
Magnetic!
21.1>3!
Induction,!Lenz’s!
Law!!
Oct.!10! Recitation!
!
Oct.!15! RL!circuits!
21.4>6!
Oct.!17! Recitation!
!
Oct.!20! AC!Voltages!
22.1>3!
Oct.!22! AC!circuits!
22.4>6!
Oct.!24! Recitation!
!
Oct.!27! AC!circuits!
22.7>9!
Oct.!29! EM!waves!
23.1>4!
Oct.!31! Recitation!
!
Nov.!3!
Generating!EM!
23.5>7!
waves!
Nov.!5!
Gen.!EM!waves!
23.5>7!
Nov.!6!
Exam)II:))
Chapters!20>22!
8pm,)PHYS)112
Nov.!7!
Recitation!
!
• Date: November 6 @ 8pm
L03!
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L04!
R01!
L05!
• Place: Physics, Room 112
• Duration: 1 hour
L06!
R02!
L07!
Homework)
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CHIP!1!
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CHIP!2!
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• Material: Chapters 20, 21, 22, and 23
L08!
R03!
L09!
L10!
EXAM!I!
Note: this exam
replaces the
Wednesday,
November 5
lecture

NO LECTURE
ON November
5
R04!
L11!
L12!
R05!
L13!
L14!
R06!
L15!
R07!
L16!
L17!
R08!
L18!
L19!
R09!
L20!
L21!
EXAM!II!
R10!
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23
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CHIP!3!
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CHIP!4!
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CHIP!5!
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CHIP!6!
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CHIP!7!
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CHIP!8!
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CHIP!9!!
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CHIP!10!
7!
Maxwell’s Equations
Summarizes All Known Fundamental Properties of
Electricity and Magnetism (1864)
E
+
S
E diverges from point charge
I
N
Changing B induces current
B
I
B
B is continuous in space
PLUS Maxwell’s hypothesis that a changing
electric field can produce a magnetic field
Current produces B
Changing B fields
Changing E fields
Maxwell’s Prediction: an Electromagnetic Wave
No fields at all!
No fields at all!
E=E(x,t)
B=B(x,t)
Eo
Bo
c = f λ
Relating f and
λ: Units: [c] in m/s; [λ] in m; [f] in s-1 = Hz
Relating E and B:
E/B = c
(at any position and at any time)
Notation
You must be able to distinguish between three closelyrelated concepts
Symbol
Meaning
Comment
E,B
Instantaneous
values
Depends on exact
location and time
Eo , Bo
Amplitude,
maximum value
Characteristic of the
EM wave
Erms , Brms
Time-averaged
values
Characteristic of the
EM wave
Maxwell predicts the velocity c of an EM wave
c=
1
1
= 2.998 ×108 m s
=
εoμo
(8.85 ×10-12 C 2 N × m2 )(4π ×10-7 T × m A)
Date
Investigator
Technique
distance
result
1600’s
Galileo
Lanterns/hills
few km (?)
~10x faster than sound
1675
Roemer
Eclipse/Jupiter’s
moon
600 km
2 x 108 m/s
1728
Bradley
Stellar
aberration
Inter-stellar
3.01 x 108 m/s
1849
Fizeau
Rotating toothed
wheel
8.6 km
3.13 x 108 m/s
1862
Focault
Spinning mirror
35 km
299,790,000 m/s
1926
Michelson
Rotating 8-sided
mirrored “wheel”
35 km
(299,798,000 ± 4000) m/s
today
International
Agreement
Defined by
length of 1 m
-
2.99792458 x 108 m/s
Light is an Electromagnetic Wave!
The Electromagnetic Spectrum
visible light
wavelengths from
~4 x 10-7 m to ~7.6 x 10-7 m
(c = f λ )
Uses of EM radiation
Observing the Cosmos
Observing in different wave lengths
Different views of the Crab Nebula
Important Properties of EM waves
• No electric waves; no magnetic waves; ONLY EM waves
• Direction of E and B fields are perpendicular to each other AND to the
direction of travel – TRANSVERSE WAVE
• Strength of E and B fields vary in strength at a given point with time
• E and B fields occur simultaneously and have maxima and minima at SAME
time and place – they are “IN PHASE”
• EM waves can have a fixed POLARIZATION (plane containing E field)
• EM waves can travel in a vacuum
• Speed of wave depends on properties of medium in which they travel
• EM waves can be absorbed, reflected, change direction
• EM waves carry energy and momentum
• EM waves exhibit INTERFERENCE effects (constructive and
destructive)
• EM waves have a frequency and wavelength related by c=fλ
(ELECTROMAGNETIC SPECTRUM)
How to generate an EM wave?
http://phet.colorado.edu/sims/radiating-charge/radiating-charge_en.html
Heinrich Hertz 1888
H. Hertz is first to
produce and detect EM
radiation at ~100 MHz
R
L
Breakdown switch S
“closes” when spark I
formation occurs.
This event completes
an RLC circuit which
then produces a
rapidly
oscillating current.
~ 0.1 μs
t
Antennas and radio waves
Wavelength and frequency
1. Hertz produced EM radiation near 100 MHz. What is the wavelength
of this EM wave?
c = fλ
λ=
c
=
3×108 m / s
=3 m
f 100 ×106 s-1
2. WBAA broadcasts at 890 kHz. What is the wavelength of the
EM radio waves?
c 3 ×108 m / s
λ= =
= 337 m
3 -1
f 890 ×10 s
3. What is the frequency of a light wave with a wavelength of 5.0
x 10-7 m (green light)?
8
f = c = 3×10 m / s = 4.286 ×10 14 Hz
λ
7 ×10-7 m
Astrophysical sources send us EM radiation of
f = 3x1027 Hz, λ = 10-19 m
They oscillate 10 trillion times faster than green light!!!
Energy is transported by an EM wave!
The Poynting vector S specifies the instantaneous power
per unit area transported by an EM wave at a point in
space at an instant of time [E(t) and B(t) are
instantaneous values].
 1   E(t) B(t)
S = E ×B =
μo
μo
E
1
c=
=
B
εoμo

2(t
E
) = cεoE 2(t)
S=
cμo

Eo2
S AVERAGE = cεo
2
= cεoE2rms
Units: [W/m2]
Wave Intensity
The time-averaged value of S is called the
intensity I of the wave

1
2
I  S AVERAGE = cεoEo2 = cεo Erms
2
Eo
since c = = 1
Bo
εoμo

IS
=
AVERAGE
æ B2
1
1
= ceo (c 2B o2 ) = ceo ç o
çe m
2
2
è o o
ö
÷ = c B2
rms
÷ m
ø
o
The intensity I specifies the power
(in Watts per m2) carried by an EM
wave in free space averaged over
time.
The time averaged energy density of an EM
wave
KEY IDEA: Energy is stored in
both E and B fields
: Total absorber
time aver. power thru hole : P = IA W
time aver. energy thru hole : ΔU = PΔt J
Hole in mask,
area A
utot
Define time aver. energy density utot é
utot
u tot =
=
ΔU
(AcΔt)
I
1
=
PΔt
(AcΔt)
=
u tot = eoE rms =
2
1
mo
2
B rms
cΔt
(AcΔt )
Energy passing
thru hole in
time Δt
1
= eoE o =
B o2
c 2
2mo
2
IAΔt
J ù
in
êë
ú
m3 û
Units: J/m3
Time aver.
radiation,
intensity I