Transcript P212C22

Chapter 22: Electric Charge and Electric Field
Electric Charge
Ancient Greeks ~ 600 BC
Static electricity: electric charge via friction
(Attempted) pith ball demonstration:
2 kinds of properties
2 objects with same property repel each other
2 objects with different properties attract each other
both properties are always created together
Benjamin Franklin:
kinds of charges are positive and negative
by convention, negative charge associated with amber
Conservation of Charge: The algebraic sum of all the electric
charges in any closed system is constant.
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Conductors and Insulators
(Objects are usually “charged” by moving electric charge
around, rather than creating or destroying charge.)
Conductor:
charge passes easily through the material
=> conductors contain charges which are free to move
Insulator:
charge cannot move (easily) through material
Semiconductor:
transition between insulator and conductor, usually of
interest because of exotic electrical properties
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Charging by induction.
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Quantization and Conservation of Charge
Microscopic structure of matter: Atoms
Nucleus
most of mass
positive charge
composed of protons (each has charge = +e) and
neutrons (no electric charge)
“orbiting” electrons (each has charge = -e)
Atoms tend to be charge neutral
charge quantized: e = 1.6x10-19 C
Charge transfer usually in the form of addition or removal of
electrons.
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Coulomb’s Law
A description of the interaction between two (point) charges
The magnitude of the Force exerted by one charge on the
other
is proportional to the magnitude of each of the charges
is inversely proportional to the square of the distance
between the charges
acts along a line connecting the charges
Qq
F k 2
r
2
2
N

m
N

m
9
k
 8.988 109

9

10
4 0
C2
C2
1
Unit of charge is the Coulomb, a new type of quantity.
How big is 1 coulomb?
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Another form of Coulomb’s Law
the force exerted by Q (“source charge”) on q (“test charge”)

Qq
F  k 2 rˆ
r

F  Force on q
rˆ  unit vecto r,
from Q to q
r  distance,
from Q to q
q
Q
rˆ

F
r
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Electric Charge and Electric Field (cont’d)
Coulomb’s Law: the force exerted by Q on q
q

Qq
F  k 2 rˆ
r
Q
For several Sources
  
F  F1 + F2 + 
k
Q1q
Q2 q
r
+
k
r +
ˆ
2 1
2 ˆ2
r1
r2
Qi q
 i k 2 rˆi
ri
rˆ
r

F

F

F2
q
Q1
r1
r2

F1
rˆ2 Q2
rˆ1
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•Analyze geometry/draw diagram
•calculate magnitude of each contribution Fi  k
•calculate components of each contribution
Qi q
ri 2
•add contributions as vectors (add component by component)
A charge q = 5.0 nC is at the origin. A charge Q1 = 2.0 nC is located 2cm to the right on
the x axis and and Q2 = -3.0 nC is located 4 cm to the right on the x axis. What is the
net force on q?
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Q1 = 2.0 µC
Geometry
.3m
q = 4.0 µC
.4m
Magnitudes
.3m
Q2 = 2.0 µC
Components
Net Force
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Example: Compare the electric repulsion of two electrons to their
gravitational attraction
Qq
F k 2
r
2
2
N

m
Mm
N

m
-11
k  9 109
F

G
G

6
.
67

10
C2
r2
kg 2
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Electric Field and Electric forces
Electric field is a “disturbance” in space resulting from the
presence of (source) charge, which exerts a force on a (test)
charge.
q

P
F
Q
rˆ
Q
r
rˆ
Force of interaction
r
Source charge creates a disturbance in space

E (at P ) 

F (at P ) / q
q
Q
rˆ
r

F ( on q ) 

qE (at q )
Test charge “senses” the disturbance in space
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
Q
E  k 2 rˆ
r

E  Field at P
rˆ  unit vecto r,
from Q to P
P
Q
rˆ

E
r
r  distance,
from Q to P
Q
Ek 2
r
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For several Sources
  
E  E1 + E2 + 
Q1
Q2
 k 2 rˆ1 + k 2 rˆ2 + 
r1
r2

E

E2

E1
Q1
r1
r2
rˆ2 Q2
rˆ1
Qi
 i k 2 rˆi
ri
Force Law: F = qE
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Elementary Electric Field Examples:
•What is the electric field 30 cm from a +4nC charge?
•When a 100 volt battery is connected across two parallel conducting plates 1 cm
apart, the resulting charge configuration produces a nearly uniform electric field
of magnitude E = 1.00 E4 N/C.
•Compare the electric force on an electron in this field with its weight.
What is the acceleration of the electron?
The electron is released from rest at the top plate.
What is the final speed of the electron as it hits the second plate?
How long does it take the electron to travel this distance?
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Electric Field Calculations
•Analyze geometry/draw diagram
Electric Field Contributions are directed away from positive charges, toward
negative charges
•calculate magnitude of each contribution
•calculate components of each contribution
Ei  k
Qi
ri 2
•add contributions as vectors (add component by component)
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Electric Dipole: two equal size(Q), opposite sign charges separated by a distance (l = 2a).
Determine the electric field on the x-axis
Geometry
+Q
a
Magnitudes
x
a
Components
-Q
Net Force
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Field of an electric dipole
Ex  0
E y  -k
 -k
+Q
a
x
x
2aQ
2
2
+ a2 
p
32
+a

2 32
p

 -k 3
x  a
x
x
a
-Q
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Line of charge: uniform line of charge (charge Q, l = 2a oriented along y-axis).
Determine the electric field on the x-axis
Geometry
dQ=ldy
a
y
x
Magnitudes
a
Components
dQ dy
Q

l
Q 2a
2a
y
x
sin  
cos  
r
r
r  x2 + y2

dQ
l dy
dE  k 2  k 2
r
x + y2

dE x  dE cos 
k
l dy
x2 + y2
x
x2 + y2
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Add Components
 dE
Ex 
x
all charge
y a

 k x
y - a
l dy
2
+y

2 32
2kl a
kQ


2
2
x x +a
x x2 + a2
Q
Ex  k 2 ,
x  a
x
2kl
Ex 
, x  a
x
infinite line of charge : Er 
2kl
r
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Next: infinite sheet of charge is composed of of a series of
infinite lines of charges
Look carefully at related textbook examples of a ring of charge, and a disk of charge.
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Electric Field due to an infinite sheet of charge
sheet of charge composed of a
series of infinite lines of charge
s = charge per area
l  s dz
Geometry
z
y
sin  
cos  
r
r
r  z2 + y2

Magnitudes
y
 2kl 2ks dz
dE 
 2
r
z + y2
z

dE y  dE cos 
Components

2ks dz
z2 + y2
y
z2 + y2
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Add Components
Ey 
 dE

y
all charge
z 
2ksydz
  2
2
z
+
y
z  -
y
z

1
z
 2ks y arctan
y
y z  -
 - 
 2ks    2ks
2 2 

s
1 
 k 


2 0
4 0 

uniform electric field!!
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Interaction of an electric dipole with an electric field
dipole in a uniform electric field

 Fi  0
F=qE
l
y
torque about center of dipole


 
   i   ri  Fi
RHR!
-q

x
p
-q
z
F = F = qE
F=- qE
l
l
 z  F sin  + F sin 
2
2
 lqE sin 
 pE sin 
 
  p E

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Work done rotating dipole in an electric field
watch directions of ,  an d
y
l
dW   d  - pE sin  d
2
 d
x
p
z
W   - pE sin  d
1
 pE cos 2 - pE cos1  -U
U ( )  - pE cos
 
 -pE
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“Lines of Force”
Electric Field Lines: a means of visualizing the electric field
=A line in space always tangent to the electric field at each point in space
concentration give indication of field strength
direction give direction of electric field
•start on positive charges, end on negative charges
•electric field lines never cross
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+ + + + + + + + + + + + + +
- - - - - - - - - - - - - -
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