phy 712 electrodynamics 10-10:50 am mwf olin 107 plan for lecture 35:
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PHY 712 Electrodynamics 10-10:50 AM MWF Olin 107 Plan for Lecture 35: Comments and problem solving advice: Comment about PHY 712 final General review. Monday 4/28/2014. Wednesday 4/30/2014. Final exam for PHY 712 Available: Friday, May 2, 2014 Due: Monday, May 12, 2014. - PowerPoint PPT PresentationTRANSCRIPT
PHY 712 Spring 2014 -- Lecture 35 1
PHY 712 Electrodynamics10-10:50 AM MWF Olin 107
Plan for Lecture 35:
Comments and problem solving advice:
Comment about PHY 712 final
General review
04/25/2014
PHY 712 Spring 2014 -- Lecture 35 204/25/2014
PHY 712 Spring 2014 -- Lecture 35 304/25/2014
PHY 712 Spring 2014 -- Lecture 35 404/25/2014
Time Presenter Name
Presenter Title
10-10:20 AM
Sam Flynn “Group Theory and Electromagnetism”
10:25-10:40 AM
Ahmad ?????????????????????????
Time Presenter Name
Presenter Title
9:30-9:50 AM
Calvin Arter “Electrodynamics and the interaction potential”
9:55-10:20 AM
Ryan Melvin “Effects of electric fields on small strands of human RNA”
10:25-10:40 AM
Drew Onken “The Electromagnetic Theory Behind the Free Electron Laser”
Monday4/28/2014
Wednesday4/30/2014
PHY 712 Spring 2014 -- Lecture 35 504/25/2014
Final exam for PHY 712 Available: Friday, May 2, 2014 Due: Monday, May 12, 2014
PHY 712 Spring 2014 -- Lecture 35 604/25/2014
Maxwell’s equations
0
02
SI units; Microscopic or vacuum form ( 0; 0):
Coulomb's law: /
1Ampere-Maxwell's law:
Faraday's law: 0
No magnetic monopoles:
c t
t
P M
E
EB J
BE
2
0 0
0
1 c
B
PHY 712 Spring 2014 -- Lecture 35 704/25/2014
Maxwell’s equations
0
0
0
1SI units; Macroscopic form ( 0; = ):
Coulomb's law:
Ampere-Maxwell's law:
Faraday's law: 0
No magnetic monopol
free
freet
t
D E P H B M
D
DH J
BE
es: 0 B
PHY 712 Spring 2014 -- Lecture 35 804/25/2014
Maxwell’s equations
Gaussian units; Macroscopic form ( 4 0; = 4 ):
Coulomb's law: 4
1 4Ampere-Maxwell's law:
1Faraday's law: 0
No magn
free
freec t c
c t
D E P H B M
D
DH J
BE
etic monopoles: 0 B
PHY 712 Spring 2014 -- Lecture 35 904/25/2014
Energy and power (SI units)
1Electromagnetic energy density:
2Poynting vector:
u
E D H B
S E H
tititi )e,()e,()e,(,t)( rErErErE *~~
2
1~
:fields harmonic for time Equations
*
avg
1
2t,t ( , ) ( , ) S r E r H r
* *
avg
1
4tu ,t ( , ) ( , ) ( , ) ( , ) r E r D B rHr r
PHY 712 Spring 2014 -- Lecture 35 1004/25/2014
0 02
Solution of Maxwell's equations:
1 /
0 0
c t
t
EE B J
BE B
Introduction of vector and scalar potentials:
0
0 0
or
t t
t t
B B A
B AE E
A AE E
PHY 712 Spring 2014 -- Lecture 35 1104/25/2014
0
20
02
2
02 2
Scalar and vector potentials continued:
/ :
/
1
1
t
c t
c t t
E
A
EB J
AA J
PHY 712 Spring 2014 -- Lecture 35 1204/25/2014
JA
A
A
JA
A
A
02
2
22
02
2
22
2
02
2
2
02
1
/1
01
require -- form gauge Lorentz
1
/
:equations potential vector andscalar theof Analysis
tc
tc
tc
ttc
t
LL
LL
LL
PHY 712 Spring 2014 -- Lecture 35 1304/25/2014
22
02 2
22
02 2
Solution methods for scalar and vector potentials
and their electrostatic and magnetostatic analogs:
1/
1
LL
LL
c t
c t
A
A J
In your “bag” of tricks: Direct (analytic or numerical) solution of
differential equations Solution by expanding in appropriate
orthogonal functions Green’s function techniques
PHY 712 Spring 2014 -- Lecture 35 1404/25/2014
How to choose most effective solution method -- In general, Green’s functions methods work well when
source is contained in a finite region of space
2
2
3
0
0
3
2
( , ) 4 ( )
1( )
Con
( ) ( , )4
1ˆ ( , ) (
sider the electrostatic problem:
/
Define:
) ( ) ( , ) .4
' '
L V
S
L
G
d r G
d r G G
r r
r r r r
r r r r r r r
r r
PHY 712 Spring 2014 -- Lecture 35 1504/25/2014
lm
*lmlml
l
,φθYθ,φYr
r
l''
12
4
'
11
rr
( ) is contained in a small
1 region of
For electrostat
space a
ic problems
nd , ( , )'
where
S G
r rr r
r
PHY 712 Spring 2014 -- Lecture 35 1604/25/2014
Electromagnetic waves from time harmonic sources
0,~
,~ 0,,
:condition continuity that theNote
,~
, :densityCurrent
,~, :density Charge
rJrrJr
rJrJ
rr
itt
t
et
etti
ti
'
( ) and ( ) are
contained in a small region of space and
For dynamic problems
,
wh
( , ', )
e , ,
'
re
ic
S
eG
r r
Jr
r r
r
r r
PHY 712 Spring 2014 -- Lecture 35 1704/25/2014
Electromagnetic waves from time harmonic sources – continued:
,'~'
'4
1,
~,
~
) gauge, (Lorentz potentialscalar For
'3
00
rrr
rrrr
ike
rd
ck
,'~
''
4,
~,
~
) gauge, (Lorentz potential For vector
'30
0
rJrr
rArArr
ike
rd
ck
PHY 712 Spring 2014 -- Lecture 35 1804/25/2014
Electromagnetic waves from time harmonic sources – continued:
:function Hankel Spherical
:function Bessel Spherical
'ˆˆ'4
:expansion Useful
*'
krinkrjkrh
krj
YYkrhkrjike
lll
l
lmlmllm
l
ik
rrrr
rr
'ˆ,'~',~
ˆ,~
,~
,~
*3
0
0
rr
rrr
lmlllm
lmlm
lm
Ykrhkrjrdik
r
Yr
PHY 712 Spring 2014 -- Lecture 35 1904/25/2014
Model of dielectric properties of matter:
iii
ti
ti
ti
eim
im
qe
mmeqm
rrpP
PEED
Erp
Errr
rrEr
3
0
220
02
220
000
200
:fieldnt Displaceme
1
:dipole Induced
1 ,For
http://img.tfd.com/ggse/d6/gsed_0001_0012_0_img2972.png
Drude model Vibrations of charged particles near equilibrium:
dr
PHY 712 Spring 2014 -- Lecture 35 2004/25/2014
rrEr 200 mmeqm ti
Drude model: Vibration of particle of charge q and mass m near equilibrium:
dr http://img.tfd.com/ggse/d6/gsed_0001_0012_0_img2972.png
dipoles typeoffraction
umedipole/volnumber
:fieldnt Displaceme
3
0
i f
N
fN
i
iii
iii
prrpP
PEED
PHY 712 Spring 2014 -- Lecture 35 2104/25/2014
Drude model dielectric function:
i ii
i
i
ii
I
i ii
i
i
ii
R
IR
i iii
ii
m
qfN
m
qfN
i
im
qfN
222220
2
0
22222
22
0
2
0
00
220
2
0
1
11
PHY 712 Spring 2014 -- Lecture 35 2204/25/2014
Kramers-Kronig transform – for use in dielectric analysis
z-α
f(z)dz
-αz
)f(zdz
πi
z-α
f(z)dz
πif
restR
RR
includes
2
1
2
1
Re(z)
Im(z)
a
=0
f-αz
)f(zdzP
πi
-αz
)f(zdz
πi f
R
RR
R
RR )(
2
1
2
1
2
1
PHY 712 Spring 2014 -- Lecture 35 2304/25/2014
Kramers-Kronig transform – for dielectric function:
IIRR
RI
IR
-dP
-dP
;with
'
1 1
''
1
'
1
''
11
00
00
Further comments on analytic behavior of dielectric function
00
0
0
1
, ,,
:fields and between iprelationsh Causal""
ieGd
tGdtt rErErD
DE