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PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
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PHYSICS 272
Electric & Magnetic Interactions
Lecture 3
Superposition of electric field;
Dipoles
Note: for iclickers to work: 1) must be turned on prior to answering
question, 2) set proper frequency “AB” – hold down power button for
~2 sec, then press “A” and “B”
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/
The Superposition Principle
The net electric field at a location in space is a vector sum
of the individual electric fields contributed by all charged
particles located elsewhere.
The electric field contributed by a charged particle is
unaffected by the presence of other charged particles.
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/
The Superposition Principle
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/
The E of a Uniformly Charged Sphere
Can calculate using principle of superposition:

1 Q
Esphere 
rˆ
2
40 r

Esphere  0
for r>R (outside)
for r<R (inside)
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/
The Superposition Principle
The electric field of a dipole:
Electric dipole:
Two equally but oppositely charged
point-like objects
s
-q
+q
Example of electric dipole: HCl molecule
What is the E field far from the dipole (r>s)?
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/
Calculating Electric Field
Choice of the origin
y
s
-q
+q
x
z
Choice of origin: use symmetry
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/
1. E along the x-axis
E1, x  E , x  E , x 
E1, x 
E1, x 
1
q
4 0 r  s 2 
2

1
q
4 0 r  s 2 2
1 qr 2  qrs  qs 2 / 4  qr 2  qrs  qs 2 / 4
4 0
1
r  s 2  r  s 2
2
2
2qrs
4 0 r  s 2 2 r  s 2 2
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/
Approximation: Far from the Dipole
E1, x 
1
2 srq
2
2
40 
s 
s
r

r


 

2 
2

2
2
s 
s

if r>>s, then  r     r    r 2
2 
2

E1, x
1 2 sq

40 r 3

E1 
1 2sq
,0,0
3
40 r
While the electric field of a point charge is proportional to 1/r2,
the electric field created by several charges may have a different
distance dependence.
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/
2. E along the y-axis

E


s
s
r  0, y ,0  ,0,0   , y ,0 
2
2

  r  r 

s
s
r  0, y ,0   ,0,0  , y ,0 

2
2
s
y2   
2
2

E 

E 
1
q
40
s
y2   
2
1
q
40
s
y2   
2
1
q
rˆ
2
40 r
s
y2   
2
2
s
 , y ,0
2
2
s
y2   
2
2
s
, y ,0
2
2
s
y2   
2
2
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/
2. E along the y-axis

E 
1
q
40
s
y  
2
2
s
 , y ,0
2
2
s
y2   
2
2



1
E2  E   E  
40
s
y2   
2
2

E 
1
q
40
s
y  
2
2
qs
q
33
2 2
 2 s
y   
2

s
 , y ,0
2
2
s
y  
2
2
2
 1s,0,0



1 qs
,0,0
if r>>s, then E2 
3
4 0 r
at <0,r,0>
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/
3. E along the z-axis

E1 

E2 
 1 qs
,0,0
3
40 r
1 2sq
,0,0
3
40 r
at <r,0,0>
at <0,r,0>
or <0,0,r>
Due to the symmetry E along the z-axis must
be the same as E along the y-axis!
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/
Other Locations
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/
The Electric Field
Point Charge:

E1 
1
q1
rˆ
2
40 r
Dipole:
for r>>s :
y
+q
z
1 2qs
E
,0,0
3
4 0 r
x
-
at <r,0,0>
1 qs
,0,0
3
4 0 r
at <0,r,0>
1 qs
E
,0,0
3
4 0 r
at <0,0,r>
E
s
-q
+
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/
Example
Problem
A dipole is located at the origin, and is composed of particles with
y
E=?
charges e and –e, separated by a distance 210-10 m along the xaxis. Calculate the magnitude of the E field at <0,210-8,0> m.
sq
Since r>>s:
40 r 3
2 
10
19 


Nm
2

10
m

1.6

10
C
9
E1, x   9  10


3
2 
8
C  


2  10 m
N
E1, x  7.2  104
C
E1, x 
200Å
1

x
2Å

Using exact solution:
4 N
E1, x  7.1999973  10
C
Fall 2010 Prof. Yong Chen ([email protected]) Prof. Michael Manfra ([email protected]) Lecture 2 Slide 14
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Question 1 (Chap. 14)
What is the direction of the electric field at location X,
due to the dipole?
+
C
B
D
A
E
X
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/
Question 2 (Chap. 14)
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 16
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Interaction of a Point Charge and
a Dipole

Edipole

F

F


F  QEdipole  Q
 1 2qs
,0,0
3
40 d
• Direction makes sense?
- negative end of dipole is closer, so its net contribution is larger
• What is the force exerted on the dipole by the point charge?
- Newton’s third law: equal but opposite sign
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/
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 18
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
Dipole
in
a
Uniform
Field


F  qE
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 19
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 20
PHYS 272: Matter and Interactions II -- Electric And Magnetic Interactions
http://www.physics.purdue.edu/academic_programs/courses/phys272/
A Fundamental Rationale
• Convenience: know E at some
r location – know the electric
force on any charge: F  qE
• Can describe the electric properties of matter in terms of
electric field – independent of how this field was produced.
Example: if E>3106 N/C air becomes conductor
• Limitations to Coulomb’s law
Nothing can move faster than light c
c = 300,000 km/s = 30 cm/ns
Coulomb’s law is not completely correct – it does not
contain time t nor speed of light c.

F
1 q1q2
rˆ
2
40 r

E
1
q
rˆ
2
40 r
v<<c !!!
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/
Chapter 15
Matter and Electric
Fields
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/
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 23
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 24