02/06/2013 PHY 712 Spring 2013 -- Lecture 9 1 PHY 712 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for Lecture 9: Continue reading Chapter 4 Dipolar fields and dielectrics A. Electric field due to a dipole B. Electric polarization P C. Electric displacement D and dielectric functions
14
Embed
PHY 712 Electrodynamics 11-11:50 AM MWF Olin 107 Plan for ...users.wfu.edu/natalie/s13phy712/lecturenote/lecture9/lecture9slides.… · 02/06/2013 PHY 712 Spring 2013 -- Lecture 9
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 1
PHY 712 Electrodynamics11-11:50 AM MWF Olin 107
Plan for Lecture 9:
Continue reading Chapter 4
Dipolar fields and dielectrics
A. Electric field due to a dipole
B. Electric polarization P
C. Electric displacement D and dielectric functions
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 2
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 3
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 4
General results for a multipole analysis of the electrostatic potential due to an isolated charge distribution:
''''''112
11
that Suppose
''12
4''4
1
'''
41
:density chargeisolatedfor ,alueboundary v with potentialticelectrostaofformGeneral
0
121
0
13
0
3
0
rdrrrrdrrr
θ,φYl
θ,φYr
,φθYθ,φYrr
lrd
rd
r
lm
r
r
lllm
lllm
lm
lmlmlm
lm
*lmlml
l
r
r
r
rrrr
r
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 5
Notion of multipole moment:
)ρ(rrrrdQ
x,y,z)(i,jQ
)ρ(rd
)ρ(rdq
q
)ρ(Yrrdq
)ρ(q
ijji
ij
lml
lm
lm
''''3'
:componentsmoment quadrupole thedefine
'''
:moment dipole thedefine
''
:moment monopole thedefine--tion representaCartesian In the
'','''
:on distributicharge(confined) theofmoment thedefine--tion representaharmonicsphericalIn the
23ij
3
3
*3
r
rrp
p
r
r
r
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 6
ji
jiij
lml
lmlm
*lm
l
lml
lm
rrr
Qrr
q
rθ,φY
lq
,φθYrrdrθ,φY
l
r
,53
0
10
31
0
21
41
:expansionCartesian ofIn terms
124
41
'''''12
44
1:ofextent theoutsideFor
rpr
rr
r
General form of electrostatic potential in terms of multipole moments:
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 7
rpprprrE
rpr
r
35
2
0
30
343
41
:fieldticElectrosta4
1:potentialticElectrosta
:ofextent theoutsideFor
rr
r
r
Focus on dipolar contributions:
02/06/2013 PHY 712 Spring 2013 -- Lecture 9 8
Coarse grain representation of macroscopic distribution of dipoles: