phy 712 electrodynamics 11-11:50 am mwf olin 107 plan for...
TRANSCRIPT
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 1
PHY 712 Electrodynamics11-11:50 AM MWF Olin 107
Plan for Lecture 36:
General review
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 2
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 3
Signup for presentations:Schedule for PHY712 presentations -- please enter your own name replacing “presenter” and also list your presentation title replacing “title”. Of course, please do not change other student entries without their permission.
Monday April 29, 201311:00 - 11:15 -- Pete Diemer Magnetrons and Microwaves11:15 - 11:30 -- Jiajie Xiao Negative Refraction11:30 - 11:45 -- (Chaochao Dun) (Antireflection Thin Film)
Wednesday May 1, 201311:00 - 11:15 -- Katelyn Goetz Space Charge Limited Current Measurements11:15 - 11:30 -- Zach Lamport Dielectric properties of monolayer11:30 - 11:45 -- Xiaohua Liu Electron paramagnetic resonance
Thursday May 2, 20139:00 - 9:15 -- (David Montgomery) (Auroras)9:15 - 9:30 -- Ryan Godwin Drude Oscillator Model9:30 - 9:45 -- David Harrison Charges on a sphere9:45 - 10:00 -- (Evan Welchman) (Ewald Summation)
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 4
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 5
Vector and scalar potentials in vacuum
JA
AA
A
AE
AB
ctc
tc
tc
tc
41
1
41:equationsSource
1
:unitsGaussian CGS
2
2
22
2
JA
AA
A
AE
AB
02
2
2
22
02
1
1
/
:equationsSource
:unitsSI
tc
tc
t
t
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 6
Polarization and Magnetization
cn
ck
HMHBEPED
44
:unitsGaussian CGS
cn
ck
00
0
0
:unitsSI
HMHBEPED
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 7
Some identities useful for spherical geometries:
0
*1
01 'ˆˆ'ˆˆ
'1
llm
l
lmlml
l
lll
l
YYrrP
rr rrrr
rr
0
*'
'ˆˆ4' l
lm
l
lmlmll
ik
YYkrhkrjike rrrr
rr
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 8
Some significant results: Ewald summation formula
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 9
Some significant results: Magnetic dipoles in atoms and hyperfine Hamiltonian
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 10
Some significant results: Reflection and refraction of plane polarized
electromagnetic waves
’ ’
k’ki kRi R
q
z
x
s-polarization – E field “polarized” perpendicular to plane of incidence
sin'cos': thatNote
cos''
cos
cos2'
cos''
cos
cos''
cos
222
0
0
0
0
innn
nin
inEE
nin
nin
EE
i
i
R
q
q
q
q
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 11
Some significant results: Reflection and refraction of plane polarized
electromagnetic waves
’ ’
k’ki kRi R
q
z
x
p-polarization – E field “polarized” parallel to plane of incidence
sin'cos': thatNote
coscos''
cos2'
coscos''
coscos''
222
0
0
0
0
innn
nin
inEE
nin
nin
EE
i
i
R
q
q
q
q
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 12
Some significant results: Drude model of dielectric function
i ii
i
i
ii
I
i ii
i
i
ii
R
IR
i iii
ii
mqfN
mqfN
i
imqfN
222220
2
0
22222
22
0
2
0
00
220
2
0
1
11
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 13
Some significant results: Kramers-Kronig transform of dielectric function
IIRR
RI
IR
-dP
-dP
;with '11''1
'1''11
00
00
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 14
Some significant results: Radiation from dipole source; example:
RrRr eRi
JeJ /0/0 cos,~ˆ,~
rzrJ
''cos,~
''ˆ,~
10
1/'2
0
0
00
0/'2
00
krjkrhedrrRkJ
krjkrhedrrikJ
Rr
Rr
r
zrA
Rk
Rkri
rekJ
RkR
reJ
Rr
ikr
ikr
222
3
0
0
222
3
00
121cos,~
12ˆ,~
:for Evaluation
r
zrA
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 15
Some significant results: Lorentz transformation of electromagnetic fields
Field strength tensor AAF
00
00
xyz
xzy
yzx
zyx
BBEBBE
BBEEEE
F
0'''''
'0''''''''0''''''0
100001000000
':tionTransforma
xzvyvyvzv
xyvzvzvyv
zvyvyvzvx
yvzvzvyvx
vvv
vvv
vvv
BEBBEBEBBE
EBEBEBEBEE
F
FF
LLL
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 16
Some significant results: Liénard-Wiechert potentials
04/26/2013 PHY 712 Spring 2013 -- Lecture 36 17
Some significant results: Power radiated from accelerating charge q:
223
222
6
22
2
6
2
2
22
sin4
ˆˆ4
1:limiticrelativist-nonIn the
ˆ1
ˆˆ
4ˆ
ˆ1
ˆˆˆ
4,ˆ
4,
vβRR
Rβ
ββRRRS
Rβ
ββRRRrERrS
cq
cq
ddP
cqR
ddP
cRqtct