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PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
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PHYSICS 272
Electric & Magnetic Interactions
Lecture 4
Charged Objects; Polarization of Atoms;
Induced Dipoles
[EMI 15.1-15.4]
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 1
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Dipole Moment
x:
y, z:

E1 

E2 
1 2qs
p
,0
,0,0
,0
33
40 rr
r>>s
 1 qs
p
,,00,,00
33
40 r
The electric field of a dipole is proportional to the
Dipole moment: p = qs

p  qs, direction from –q to +q
Dipole moment is a vector pointing
from negative to positive charge
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 2
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
 Dipole

F  qE
in a Uniform Field
Forces on +q and –q have the same
magnitude but opposite direction



Fnet  qE  qE  0
It would experience a torque about its
center of mass.
What is the equilibrium position?
Electric dipole can be used to measure
the direction of electric field.
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 3
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Choice of System
Multiparticle systems: Split into objects to include into system
and objects to be considered as external.
To use field concept instead of Coulomb’s law we split the
Universe into two parts:
• the charges that are the sources of the field
• the charge that is affected by that field
Example: Oscilloscope
Charges on metal plates are the
sources of an uniform E field
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 4
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Question 1
What is the direction of the electric field at location X,
due to the dipole?
+
C
B
D
A
E
X
iClicker Frequency Code: “AB” (before each lecture)
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 5
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Question 2
Locations 1 and 2 are equidistant from the center of the
dipole. At which location is the magnitude of the electric
field larger?
d
+
1
d
A. at location 1
B. at location 2
2
C. magnitudes are the same
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 6
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Chapter 15
Matter and Electric
Fields
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 7
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Net Charge
Matter is made out of atoms.
Atom contains charged particles: electrons (-e), protons (+e)
Neutral atom: number of electrons and protons is equal:
Example: Hydrogen atom: 1 proton, 1 electron
net charge = (+e) + (-e)=0
Sodium atom: 11 protons, 11 electrons
Sodium atom (Na) can lose an electron:
Sodium ion (Na+): (+11e) + (-10e) = +e
Ordinary matter is electrically neutral.
However, can be charged by adding/removing charged particles
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 8
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Conservation of Charge
The net charge of a system and
its surroundings cannot change
If one object gets charged positively, there must be an object
which gets charged negatively.
The net electric charge is conserved in any physical process.
Charge can be transferred from one object to another.
Annihilation : e  e    
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 9
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
The Structure of an Atom
Hydrogen
10-10 m (1 Å)
Nucleus, ~10-15 m
Charge of electron cloud equals that of nucleus  neutral atom.
If the electron cloud is centered on the nucleus  electric field
produced by electrons exactly cancels the field produced by
nucleus.
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 10
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Polarization of Atoms
E
+
-
+
Force due to E created by positive charge shifts electron
cloud and nucleus in opposite directions: electric dipole.
An atom is said to be polarized when its electron cloud has
been shifted by the influence of an external charge so that
the electron cloud is not centered on the nucleus.
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 11
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Induced Dipole
An applied electric field creates induced dipoles!
E
• it is not a permanent dipole
• an induced dipole is created when a neutral object is polarized
by an applied electric field
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 12
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Polarization
Amount of polarization p in most materials is proportional to the
magnitude of the applied electric field:


p  E
 - “polarizability” of a material
In an induced dipole, is the distance between the charges fixed?
The distance is proportional to the strength of the applied field.
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 13
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge
1. Charge q1 creates field E1 at the location of the atom

E1 
1
q1
rˆ
2
40 r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 15
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge

1 q1
E

1) 1 4 r 2 rˆ
0
2. Field E1 polarizes the atom creating a dipole


p  E1 
1 q1
rˆ
2
40 r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 16
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge

1 q1
1) E1  4 r 2 rˆ
0

1 q1
p

rˆ
2)
2
40 r
3. Dipole creates field E2 at the location of q1
2
r
1 2p
1 2 r  1  2 q1
E2 

E1  
r̂
3
3
5

4 0 r
4 0 r
 4 0  r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 17
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge

1 q1
1) E1  4 r 2 rˆ
0
2
3)
  1  2q1

E2  
rˆ
5
 40  r

1 q1
p

rˆ
2)
2
40 r
4. Induced dipole exerts force F1 on the charge:
2

  1  2q12

F1  q1E2  
rˆ
5
 40  r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 18
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge

1 q1
1) E1  4 r 2 rˆ
0
2

1 q1
p

rˆ
2)
2
40 r
3)
  1  2q1

E2  
rˆ
5
 40  r
4)
  1  2q12

F1  
rˆ
5
4

r
0 

2
5. The charge q1 exerts force F2 on the dipole (reciprocity):
2


 1  2q12

F2   F1  
rˆ
5
 40  r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 19
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Neutral Atom and a Point Charge

1 q1
1) E1  4 r 2 rˆ
0

1 q1
p

rˆ
2)
2
40 r
2
3)
  1  2q1

E2  
rˆ
5
 40  r
4)
  1  2q12

F1  
rˆ
5
4

r
0 

5)

 1  2q12

F2  
rˆ
5
 40  r
2
2
Neutral atoms are attracted by charges!
Interaction strength ~ 1/r5
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 20
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Exercise
Atom A is easier to polarize than atom B. Which atom would
experience a greater attraction to a point charge a distance r away?
A
B
-
FA
+
-
+
FB
2
  1  2q12

F2  
~
5
 40  r
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 21
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Electric Field Through Intervening Matter
F
F
The field appears to be weaker in presence of intervening object
Superposition principle: the presence of matter does not affect
the electric field produced by a charged object.
Intervening matter does not “block” the E field
The resulting field is a superposition of two fields:
Field of the other charge plus the field of induced dipoles.
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 22
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
(with ions)
(in your body, batteries…)
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 23
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 24
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
 

E  Eapplied  Edipoles
Relatively small
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 25
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Model of a Metal
Metal lattice
Positive atomic cores
and mobile-electron sea
Electrons are not completely free – they are bound to the
metal as a whole.
There is no net interaction between mobile electrons
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 26