maxwell’s equations plane waves in a vacuum
TRANSCRIPT
0 Bv Dt
x
D
jH
tx
B
E
Maxwell’s equations
0 Bv D
t
EεjxH o
t
HμxE o
Plane waves in a vacuum
Plane waves in a vacuum
t
HμxE o
t
xHμxEx o
t
EεxH o
Plane waves in a vacuum
t
xHμxEx o
ttE
εμ
o
o
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Plane waves in a vacuum
0t
EεμE
2
2
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BvEQF HvEQ
2
2
2 L
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T
LM
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22
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ML
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LTL
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T
LM
2 2
2
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ML
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22
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2
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02
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EE
22
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secondmeter
volts
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E
22
metermeter
volts E
2
meter
second
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oo
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361
104
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second103 8 metersc
01
2
2
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second103 8 metersc
1638 - Galileo attempts to measure the speed of light by a lantern relay between distant hilltops. He gets a very large answer.
Albert Einstein, when asked to describe radio, replied: "You see, wire telegraph is a kind of a very, very long cat. You pull his tail in New York and his head is meowing in Los Angeles. Do you understand this? And radio operates exactly the same way: you send signals here, they receive them there. The only difference is that there is no cat."
There was a young lady named Bright,
Whose speed was far faster than light;
She set out one day,
In a relative way,
And returned home the previous night.
one dimensional wave equation
yEE
0 and 0x y z
xy zEy
01
2
2
22
tc
EE
2 2y y
2 2 2
E E10
z c t
x
y zEy
one dimensional wave equation
• MOST GENERAL SOLUTION!!
• Ey = a F(z - ct) + b G(z + ct)
• = a Fb G
• where F & G are arbitrary functions that depend on the excitation
2 2y y
2 2 2
E E10
z c t
2 2y y
2 2 2
E E10
z c t
yE dF dG
a bd z d zz
2 2 22 2y
2 2 2
E d F d Ga b
z zz d d
2 2 2
2 2y2 2 2
E d F d Ga 1 b 1
z d d
ctzψ
ctzθ
yE dF dGa b
d t d tt
2 2 22 2y
2 2 2
E d F d Ga b
t tt d d
2 2 2
2 2y2 2 2
E d F d Ga c b c
t d d
2 2y y
2 2 2
E E10
z c t
ctzψ
ctzθ
• Q. E. D.
• Ey = a F(z - ct) + b G(z + ct)
• = a Fb G
• is a solution of the wave equation!!!
Ey = aF(z - ct) + bG(z + ct) = aFbG
z
Ey
t = T
z
Ey
t = 2T
2 2y y
2 2 2
E E10
z c t
Ey = aF(z - ct) + bG(z + ct)
0
-10
10z
Ey = aF(z - ct) + bG(z + ct) = aFbGLet c = 2
z - ct = z + ct = t zz 5 t
2 2y y
2 2 2
E E10
z c t
0
-10
10z
Ey = aF(z - ct) + bG(z + ct) = aFbGLet c = 2
z - ct = z + ct = t zz 5 t
2 2y y
2 2 2
E E10
z c t
perturbation transverse to the direction of
propagation“transverse waves”
perturbation transverse to the direction of
propagation“transverse waves”“trajectory”
z
t* **
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the flood
whips and chains
“the slinky wave”
“the slinky wave”
“the slinky wave”
perturbation is in the direction of propagation
“longitudinal wave”sound waves--compression &
rarefaction of air
ion acoustic wave in a plasma
nerve propagation test for MS
nerve propagation test for MS
Pulsegenerator
general properties of linear waves
01
2
2
22
2
tcz
ctzGctzFtz ,
wavesnonlinearccif ,,,, chaossolitonsshocks
magneticandelectric kineticandpotential
soliton - soliton collision
Twinkie shortage looms March 21, 2000PORTLAND, Maine (AP) - A Teamsters strike against a bakery company is creating shortage of Twinkies across parts of the Northeast. A Philadelphia bakery was shut down after pickets appeared Monday, and Teamsters planned to set up pickets in Buffalo, N.Y., as well. A New York City bakery also was shut down over the weekend. "It's a wave that's going to go right across the country," said Richard Volpe, director for the union in the United States and Canada.