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Physics for Scientists and Engineers II , Summer Semester 2009
1
Lecture 20: July 10th 2009
Physics for Scientists and Engineers II
Physics for Scientists and Engineers II , Summer Semester 2009
2
Transmission line economics
LR
TR
power)(1KW cleaner vacuumrunsConsumer
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Physics for Scientists and Engineers II , Summer Semester 2009
3
Transmission line economics – using transformers
LR
TR
21 NNer transformup-Step
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Physics for Scientists and Engineers II , Summer Semester 2009
4
Example: Problem 43 in Chapter 33
line?ion transmissin thepower of loss theisWhat
500KV toup dtransforme50.4V
power of5.00MW transmit toNeed
)(6.44x10 miles 400 :lineion transmissofLength
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Physics for Scientists and Engineers II , Summer Semester 2009
5
Example: Problem 43 in Chapter 33
:ansformerWithout tr
ed? transmittbecan much How be.cannot This
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Physics for Scientists and Engineers II , Summer Semester 2009
6
Example: Problem 43 in Chapter 33
.R when load toed transferrispower maximum that thefound we
wherebattery, a of resistance internal with as principle same BTW, d).transmitte
becan power lesseven casesother allIn .R when ONLY is this(and
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Physics for Scientists and Engineers II , Summer Semester 2009
7
The 500000 Volt Tesla Coil – featuring Adam Beehler succesfully trying to not electrocute himself
Physics for Scientists and Engineers II , Summer Semester 2009
8
Chapter 34: Electromagnetic Waves
carriers) chargeby (createdcurrent conduction a isdt
dqI where,B
law? sAmpere'Remember
0 Isd
Capacitor plates
1S1S
I
IPPath
. through passes none through passescurrent conduction a whileHowever,
path. same by the bound are and both but through passesonly I :Problem
21
211
SS
SSS
Physics for Scientists and Engineers II , Summer Semester 2009
9
General Form of Ampere’s Law
flux. electric theis and
space. free ofty permittivi where, I
:currentnt displaceme a defined He fields. electric varying-time
include tolaw sAmpere' dGeneralize :MaxellClark James
situation. for this inadequateclearly is,B
00d
0
AdE
dt
d
Isd
E
E
B
:Law) Maxwell-(Ampere
Law sAmpere' of form General
0000 dt
dIIIsd E
d
Physics for Scientists and Engineers II , Summer Semester 2009
10
Calculating displacement current: Example
2S
1S
I
I
Idt
dqq
dt
d
EAdt
d
dt
dIsd
IIsd
Ed
000
00
000002
001
0B:S Surface
0B:S Surface
Physics for Scientists and Engineers II , Summer Semester 2009
11
Major Point
B
:Law) Maxwell-(Ampere
Law sAmpere' of form General
0000 dt
dIIIsd E
d
Magnetic fields are produced both by conduction currents andby time-varying electric fields.
Physics for Scientists and Engineers II , Summer Semester 2009
12
Example: Chapter 34, Problem 1
AIdt
d
Cs
Nm
NmC
AI
dt
dq
dt
d
dt
d
A
E
E
E
100.01
I (b)
101.1310854.8
100.011q
qEA
qE :Capacitor Plate
plates. ebetween thcurrent nt displaceme theb) and
plates ebetween thflux electric of change of rate time thea) Find 4.00mm. is separation plate
The side.each on cm 5.00 plates square hasthat capacitor a charging iscurrent A -0.100A
000d
210
2
212000
00
Physics for Scientists and Engineers II , Summer Semester 2009
13
A Complete Description of All Classical Electromagnetic Interactions in a Vacuum
law Maxwell-Ampere B
law sFaraday'sdE
magnetismin law sGauss'0AdB
law sGauss'AdE
space freein Equations sMaxwell'
0000
0
dt
dIIIsd
dt
d
q
Ed
B
law force Lorentz BvqEqF
Physics for Scientists and Engineers II , Summer Semester 2009
14
Maxwell’s Prediction
law Maxwell-Ampere B
law sFaraday'sdE
magnetismin law sGauss'0AdB
law sGauss'0AdE
0I and 0q when space freein Equations sMaxwell'
00 dt
dsd
dt
d
E
B
Can be combined Result: Wave equations for electric and magnetic fields
Solution of wave equations shows that electric and magnetic field waves travel(“electromagnetic radiation”) with the speed of light, leading Maxwell to predict that light is a form of electromagnetic radiation.
Physics for Scientists and Engineers II , Summer Semester 2009
15
Hertz’s Experiment
Hertz showed with this apparatus that electro-magnetic waves exist.
Physics for Scientists and Engineers II , Summer Semester 2009
16
Hertz’s Experiment
Details of the apparatus:
How it works: Battery charges the capacitor in the primary circuit on the left. The interrupter periodically creates a short circuit across that capacitor and alternating charging and discharging of capacitor occurs. A large periodic change of flux occurs in the primary winding. The secondary winding picks up this large flux change and transforms the primary voltage fluctuation into a much higher voltage fluctuation in the secondary circuit. The secondary circuit is tuned (LC) creating a very large voltage across the spark balls. High electric fieldsoccur between the spark balls, causing a sudden charge transfer (spark). The electric fieldbreaks down but is then built up again. This fluctuating electric field induces a fluctuatingmagnetic field (Ampere-Maxwell law), which in turn creates a fluctuating electric field (Faraday’s law)….. electromagnetic radiation, which is then picked up by the detection ringcausing it to spark across it’s spark gaps (detection ring is also tuned to the same frequency).
Physics for Scientists and Engineers II , Summer Semester 2009
17
Hertz’s Experiment
Other experiments by Hertz:
em wave generator
metal plate reflectsem wave.
Standingem wave
Nodes can be detected wavelength can be determined
light. visibleof speed thec, vresult was The . using
calculated becan waveem theof speed theknow, isfrequency Since
fv
Physics for Scientists and Engineers II , Summer Semester 2009
18
Plane versus Spherical Waves
Let’s first look at mechanical waves: Imagine looking down on a pond. Someone throws rocks into the middle ofThe pond, creating spherical waves in two dimensions.
Direction of wave propagation
If instead, the person throws very long metal bars into the pond,plane waves are created.
Metalbar
All parts of the wave front have the samephase.
Physics for Scientists and Engineers II , Summer Semester 2009
19
Plane Electromagnetic Waves
Plane linearly polarized electromagnetic waves with propagation in x-direction.
y
zx
Properties:1)Wherever in the yz plane em wave comes from, it propagates in the x-direction. (all “rays” of this wave are parallel).2) All em waves coming from different parts of the yz plane are all in phase.3) Electric and magnetic waves oscillate perpendicular to each other (take this by faith for now).4) Electric field is in the same direction (here in y-direction) “linearly polarized”.5) Magnetic field is in the same direction (here in z-direction) “linearly polarized”.6) And B are only function of x and t and do not depend on y and z E(x,t), B(x,t).
E
B
cc
E
B
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