On the vacuum energy between a sphere and a plane at finite temperature
Maxwell’s equations Plane waves in a vacuum.
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Transcript of Maxwell’s equations Plane waves in a vacuum.
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0 Bv Dt
x
D
jH
tx
B
E
Maxwell’s equations
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0 Bv D
t
EεjxH o
t
HμxE o
Plane waves in a vacuum
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Plane waves in a vacuum
t
HμxE o
t
xHμxEx o
t
EεxH o
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Plane waves in a vacuum
t
xHμxEx o
ttE
εμ
o
o
EE 2
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Plane waves in a vacuum
0t
EεμE
2
2
oo2
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BvEQF HvEQ
2
2
2 L
QQE
T
LM
3
22
22
2
ML
TQ
LTL
M
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Q
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LQ
T
LM
2 2
2
2
2
Q
ML
TQTL
M
ML
Q
TQ
ML 2
22
31
2
T
L
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02
22
too
EE
22
2
secondmeter
volts
t
E
22
metermeter
volts E
2
meter
second
oo
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oo
c
1
97 10
361
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1
c
second103 8 metersc
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01
2
2
22
tc
EE
second103 8 metersc
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1638 - Galileo attempts to measure the speed of light by a lantern relay between distant hilltops. He gets a very large answer.
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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."
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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.
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one dimensional wave equation
yEE
0 and 0x y z
xy zEy
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01
2
2
22
tc
EE
2 2y y
2 2 2
E E10
z c t
x
y zEy
one dimensional wave equation
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• 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
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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
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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
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• Q. E. D.
• Ey = a F(z - ct) + b G(z + ct)
• = a Fb G
• is a solution of the wave equation!!!
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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
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Ey = aF(z - ct) + bG(z + ct)
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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
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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
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perturbation transverse to the direction of
propagation“transverse waves”
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perturbation transverse to the direction of
propagation“transverse waves”“trajectory”
z
t* **
*
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the flood
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whips and chains
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“the slinky wave”
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“the slinky wave”
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“the slinky wave”
perturbation is in the direction of propagation
“longitudinal wave”sound waves--compression &
rarefaction of air
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ion acoustic wave in a plasma
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nerve propagation test for MS
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nerve propagation test for MS
Pulsegenerator
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general properties of linear waves
01
2
2
22
2
tcz
ctzGctzFtz ,
wavesnonlinearccif ,,,, chaossolitonsshocks
magneticandelectric kineticandpotential
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soliton - soliton collision
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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.
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