Transcript From Last Time…

From last time…
Inductors in circuits
I?
+
EM waves
Tue. Nov. 11, 2008
Physics 208, Lecture 21
1
• A Transverse wave.
• Electric/magnetic fields perpendicular to
propagation direction
• Can travel in empty space
f = v/, v = c = 3 x 108 m/s (186,000 miles/second)
Tue. Nov. 11, 2008
Physics 208, Lecture 21
2
Quick Quiz
A microwave oven irradiates food with electromagnetic
radiation that has a frequency of about 1010 Hz. The
wavelengths of these microwaves are on the order of
A. kilometers
B. meters
C. centimeters
D. micrometers
3 10 8 m /s
 c/ f 
 3cm
10
10 /s
Tue. Nov. 11, 2008
Physics 208, Lecture 21
3

Electromagnetic waves
x
y
E  E o coskz   t
2
2
k
, 

f
B  Bo coskz   t
Bo  E o /c
z
EB

c  1/ oo  1/ 8.85 1012 C 2 /N  m 2 4 107 N / A 2 

 2.9986108 m /s
Tue. Nov. 11, 2008
Physics 208, Lecture 21
4
Energy and EM Waves
Energy density in E-field
Energy density in B-field
uE  o E r,t /2
2
uB  B2 r,t /2o
2
2

u


E
/2

B
/2o
Total Tot
o
 o E 2 /2
 E 2 /2c 2o  o E 2 r,t   B 2 r,t / o
uTot  o E 2  o E o2 cos2 kz   t moves w/ EM wave

Tue. Nov. 11, 2008
at speed c
Physics 208, Lecture 21
5
Power and intensity in EM waves


Energy density uE moves at c
Instantaneous energy transfer =
energy passing plane per second.
2
2
 = cuTot  co E r,t   cB r,t / o

This is power density W/m2

Time average of this is Intensity = co E max /2  cBmax /2o
2
2

Tue. Nov. 11, 2008
Physics 208, Lecture 21

6
Example: E-field in laser pointer

1 mW laser pointer.

Beam diameter at board ~ 2mm
103 W
 318W /m 2

Intensity =

How big is max E-field?
 0.001m
2
2
2
co E
/2

318W
/m
max
E max 
Tue. Nov. 11, 2008
2318W /m 2 
3 10 m /s8.8510
8
12
C /N  m
2
Physics 208, Lecture 21
2

 489N /C  489V /m
7
Spherical waves

Sources often radiate EM wave in all directions





Light bulb
The sun
Radio/tv transmission tower
Spherical wave, looks like plane wave far away
Intensity decreases with distance

Power spread over larger area

I
Psource
4 r 2
Source power
Spread over this
surface area
 Tue. Nov. 11, 2008
Physics 208, Lecture 21
8
Question
A radio station transmits 50kW of power from its
antanna. What is the amplitude of the electric
field at your radio, 1km away.
A. 0.1 V/m
B. 0.5 V/m
I
50,000W
4  1000m
2
 4 103W / m2
C. 1 V/m
2
co E max
/2  4 103W /m 2
D. 1.7 V/m
E. 15 V/m
Tue. Nov. 11, 2008

E max 
24 103 W /m 2 
3 10 m /s8.8510
8
12
C 2 /N  m 2 
 1.73N /C  1.73V /m
 Physics 208, Lecture 21
9
The Poynting Vector

Rate at which energy flows through a unit area perpendicular
to direction of wave propagation

Instantaneous power per unit area (J/s.m2 = W/m2) is also
S


1
o
E  B  Poynting Vector
Its direction is the direction of propagation of
the EM wave
This is time dependent
 Its magnitude varies in time
 Its magnitude reaches a maximum at the
same instant as E and B
Tue. Nov. 11, 2008
Physics 208, Lecture 21
10

Radiation Pressure



Saw EM waves carry energy
They also have momentum
When object absorbs energy U from EM wave:




Momentum p is transferred
p  U /c ( Will see this later in QM )
U /t
Result is a force F  p/t 
 P /c
c
Pressure = Force/Area =
prad
Power
Intensity
P/A

 I /c
c
Radiation pressure

on perfectly absorbing object
Tue. Nov. 11, 2008
Physics 208, Lecture 21
11
Radiation pressure & force
EM wave incident on surface exerts a radiation pressure
prad (force/area) proportional to intensity I.
Perfectly absorbing (black) surface: prad  I /c
Perfectly reflecting (mirror) surface: prad  2I /c
Resulting force = (radiation pressure) x (area)


Tue. Nov. 11, 2008
Physics 208, Lecture 21
12
Question
A perfectly reflecting square solar sail is 107m X 107m. It has
a mass of 100kg. It starts from rest near the Earth’s orbit,
where the sun’s EM radiation has an intensity of 1300 W/m2.
How fast is it moving after 1 hour?
A. 100 m/s
B. 56 m/s
C. 17 m/s
D. 3.6 m/s
E. 0.7 m/s
Tue. Nov. 11, 2008
prad  2I /c
Frad  prad A  2IA/c 
21300W /m 2 1.145104 m 2 
3 10 m /s
8
 0.1N
a  Frad /m  103 m /s2
v  at  103 m /s2 3600s  3.6m /s
Physics 208, Lecture 21
13
Polarization of EM waves


Usually indicate the polarization direction by
indicating only the E-field.
Can then be indicated with a line:
Unpolarized
Plane Polarized
x
z
y
E  E o coskz   txˆ
B  Bo coskz   tyˆ
Tue. Nov. 11, 2008
Superposition of
plane polarized waves
Physics 208, Lecture 21
14
Producing polarized light

Polarization by selective absorption: material that transmits
waves whose E-field vibrates in a plain parallel to a certain
direction and absorbs all others
This polarization
absorbed
This polarization
transmitted
transmission axis
Long-chain hydrocarbon
molecules
Tue. Nov. 11, 2008
Polaroid sheet
Demo on MW and metal grid
15
Physics 208, Lecture 21

Transmission at an angle
Plane-polarized
incident wave
y
Einc  Eo coskx  t
Incident wave is equivalent
to 
superposition


x
polarizer
E inc cos xˆ  E inc sinyˆ
transmitted

absorbed
Transmitted wave =
E trans  E o cos coskx  t xˆ
Tue. Nov. 11, 2008
Physics 208, Lecture 21
transmission
16
Detecting polarized light

Polarizer



transmits component of E-field parallel to transmission axis
absorbs component of E-field perpendicular to transmission axis
Transmitted intensity: I = I0cos2 I0 = intensity of polarized
beam on analyzer (Malus’ law)
Allowed component
parallel to analyzer axis
Tue. Nov. 11, 2008
Polaroid
Physicssheets
208, Lecture 21
17
Malus’ law



Transmitted amplitude is Eocos
(component of polarization along polarizer axis)
Transmitted intensity is Iocos2
( square of amplitude)
Perpendicular polarizers give zero intensity.
Tue. Nov. 11, 2008
Physics 208, Lecture 21
18
Polarization by reflection

Unpolarized light reflected
from a surface becomes
partially polarized

Degree of polarization
depends on angle of
incidence
Unpolarized
Incident light
Reflection
polarized
with E-field
parallel to
surface
n
Refracted
light
Tue. Nov. 11, 2008
Physics 208, Lecture 21
19
Reducing glare


Reflected sunlight partially
polarized.
Horizontal reflective surface ->the
E-field vector of reflected light has
strong horizontal component.
Transmission axis
Tue. Nov. 11, 2008
Physics 208, Lecture 21
20
Circular and elliptical polarization


Circularly polarized light is a superposition
of two waves with orthogonal linear
polarizations, and 90˚ out of phase.
The electric field
rotates in time with
constant magnitude.
Tue. Nov. 11, 2008
Physics 208, Lecture 21
21