Transcript Chapter 12

No area of
UNIT
physicsTHREE
has had
aElectricity
greater impact
on the way we
and
live than the
Magnetism
study of
electricity and
magnetism.
Chapter 12
Electrostatic
Phenomena
Lecture PowerPoint
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What does
lightning
have in
common...
... with hair
on a dry
winter day?
Effects of Electric
Charge
 Hair seems to have a mind of its own when
combed on a dry winter day.
 What causes the hairs to repel one another?
Why does a piece of
plastic refuse to leave your
hand after you peeled it off
a package?
Why do you get a slight
shock after walking across
carpet and touching a light
switch?
 All these phenomena involve different materials rubbing
against one another.

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Electrostatic effects can be demonstrated by rubbing plastic or glass
rods with different furs or fabrics.
Small wads of dry, paperlike material called pith balls are light
enough to be strongly influenced by electrostatic forces.
When a plastic rod, vigorously rubbed with cat fur, is brought near
the pith balls, at first the pith balls are attracted to the rod like bits of
iron to a magnet.
After contacting the rod, the pith balls
dance away from the rod.
They are now repelled by the rod and
also by each other.
 A repulsive force must be acting between the two pith balls
after they have been in contact with the rod.



Perhaps the balls have received something (call it electric charge)
from the rod that is responsible for the force we observe.
This charge was somehow generated by rubbing the rod with the cat
fur.
The force that is exerted by one stationary charge on another is
called the electrostatic force.
 Experiments with different materials indicate that there are
two types of charge.
 An electroscope consists of two metallic-foil leaves
suspended from a metal post inside a glass-walled
container.





If the foil leaves are uncharged, they will hang straight down.
If a charged rod is brought in contact with the metal ball on top, the
leaves immediately spread apart and stay apart, even if the rod is
removed.
If an object of the same charge as the
original rod is later brought near the
metal ball, the leaves will spread
farther apart.
An object with the opposite charge will
make the leaves come closer together.
A larger charge produces a larger
effect.
Like charges repel each other,
and unlike charges attract
each other.
 Benjamin Franklin introduced the names positive and
negative for the two types of charge.
 He also proposed that a single
fluid was being transferred
from one object to another
during charging.


A positive charge resulted from
a surplus of the fluid, and a
negative charge resulted from
a shortage of the fluid.
Franklin arbitrarily proposed
that the charge on a glass rod
when rubbed with silk be called
positive.
Like charges repel each other,
and unlike charges attract
each other.
 Franklin’s model comes surprisingly close to our modern
view.
 When objects are rubbed together, electrons may be
transferred from one object
to the other.
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
Electrons are small, negatively
charged particles present in all
atoms and, therefore, in all
materials.
A negatively charged object has
a surplus of electrons, and a
positively charged object has a
shortage of electrons.
The atomic or chemical properties
of materials dictate which way the
electrons flow when objects are
rubbed together.
Like charges repel each other,
and unlike charges attract
each other.
Conductors and
Insulators
 Different materials behave differently in the
presence of electrostatic forces.

Charge can readily flow through conductors:


Materials that do not ordinarily permit charge to
flow are insulators:
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
metals, like copper, silver, iron, gold; our bodies
plastic; glass; ceramics; other nonmetallic materials
Charge flows much more readily through several
miles of copper wire than through the few inches
of insulating ceramic material.
Semiconductors are intermediate between a
good conductor and a good insulator.

Their importance to modern technology is enormous.
Can you charge an object without
actually touching it with another
charged object?
 Charging by induction
involves the conducting
property of metals:



Charge a plastic rod with
cat fur and bring the rod
near a metal ball mounted
on an insulating post.
The electrons in the metal
ball are repelled by the
negative rod.
There is a negative charge
buildup on the side opposite
the rod, and a positive
charge on the near side.
Can you charge an object without
actually touching it with another
charged object?
 To charge the ball by
induction, now touch the
ball with your finger on the
side opposite the rod.


The negative charge flows
from the ball to your body,
since it is still repelled by
the negative rod.
If you now remove your
finger and then the rod, a
net positive charge is left on
the ball.
 Charging by induction illustrates the mobility of
charges on a conducting object such as the metal
ball.
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

The process will not work with a glass ball.
Charging by induction is an important process in
machines used for generating electrostatic charges, and
in many other practical devices.
It also explains some of the phenomena associated with
lightning storms.
Why are insulators attracted to
charged objects?
 Recall that the pith balls
were attracted to the
charged rod before they
were charged themselves.
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Electrons are not free to move
in the insulating material of the
pith balls.
However, within each atom or
molecule, charges can move.
Each atom becomes an
electric dipole: the center of
the negative charge is slightly
displaced from the center of
the positive charge.
The material is polarized.
 Since the negatively charged surface is closer to
the rod than the positively charged surface, it
experiences a stronger electrostatic force.



The overall effect is that the pith ball is attracted to the
charged rod, even though the net (total) charge on the
pith ball is zero.
After the ball comes in contact with the charged rod,
some of the charge on the
rod is transferred to the
pith ball.
The pith ball is then
positively charged like the
rod, and so is repelled by
the rod.
 Polarization explains why small bits of paper or
styrofoam are attracted to a charged object such
as a sweater rubbed against some other material.
 Electrostatic precipitators used to remove particles
from smoke in industrial smoke stacks use this
property.

Polarized particles are attracted to charged plates in the
precipitator, removing them from the emitted gases.
The Electrostatic Force:
Coulomb’s Law
 Coulomb measured how the
electrostatic force varies with
distance and quantity of
charge.
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Since the electrostatic force is
so weak, he had to develop
special techniques, involving a
torsion balance.
The degree of twist of the wire
measures the repulsive force
between the two charges.
 Determining the amount of
charge on the balls was
more difficult.
 Although he could not measure absolute quantities
of charge on the balls, Coulomb was able to
measure the effects due to different relative
amounts of charge.
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
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By bringing two identical metal balls into contact, one
charged and the other initially uncharged, Coulomb knew
he had equal amounts of charge on both balls.
By repeating the process, he could get a ball with exactly
half that charge, or one-fourth, etc.
He could then measure
how the strength of the
electrostatic force varied
when the amount of
charge was doubled,
quadrupled, etc., in
addition to how the force
varied with distance
between the balls.
Coulomb’s Law
 The electrostatic force between two charged
objects is proportional to the quantity of each
of the charges and inversely proportional to
the square of each distance between the
charges.
kq1q2
F 2
q in units of coulombs (C)
r
Coulomb' s constant k  9 109 N  m 2 / C 2
Two positive charges, one 2 C and the
other 7 C, are separated by a distance
of 20 cm. What is the magnitude of the
electrostatic force that each charge
exerts upon the other?
a)
b)
c)
d)
e)
0.32 N
0.63 N
0.70 N
2.02 N
3.15 N
e) q1 . 2 C
F
q2  7 C
r  20 cm  0.2 m
kq1q2
r2
9 10


9
N  m2 /C 2 2 106 C7 106 C
0.2 m
0.126 N  m2

 3.15 N
2
0.04 m
2
 The electrostatic force has the same inverse-square
dependence on distance as Newton’s law of
gravitation.
Gm1m2
Fg 
r2






kq1q2
and Fe  2
r
If we double the distance between the charges, the force
falls to one-fourth of the original.
The gravitational force depends on the masses, and the
electrostatic
force depends on the charges.

Gravity is always attractive; there is no such thing as
negative mass.
Gravity is much weaker than the electrostatic force.
Physicists are still trying to understand the reasons for the
relative strengths of the fundamental forces.
The search for a unified field theory that would explain the
relationships between all of the fundamental forces is a
major area of research in modern theoretical physics.
Three positive charges are located along a line as
shown. What is the magnitude of the force exerted
on the 0.02-C charge by the 0.10-C charge?
b) q1 . 0.02 C
a)
b)
c)
d)
e)
2.25 x 106 N
4.5 x 106 N
9.0 x 106 N
1.8 x 107 N
2.7 x 108 N
F
q2  0.10 C
kq1q2
r2
9 10


9
N  m2 /C 2 0.02 C0.10 C
2 m
2
 4.5 10 6 N (to the right)

r2m
Three positive charges are located along a line as
shown. What is the magnitude of the force exerted
on the 0.02-C charge by the 0.04-C charge?
a)
b)
c)
d)
e)
c) q1 . 0.02 C
1.8 x 106 N
3.6 x 106 N
7.2 x 106 N
1.44 x 107 N
2.88 x 107 N
F
q2  0.04 C
kq1q2
r2
9 10


9
N  m2 /C 2 0.02 C0.04 C
1 m
2
 7.2 10 6 N (to the left)

r 1m
Three positive charges are located along a line as
shown. What is the net force exerted on the 0.02-C
charge by the other two charges?
a)
b)
c)
d)
e)
2.25 x 106 N
4.5 x 106 N
9.0 x 106 N
1.8 x 107 N
2.7 x 106 N
e) F . F1  F2
 7.2 10 6 N  4.5 10 6 N
 2.7 10 6 N (to the left)

The Electric Field
 How do the charges exert forces on each
other, when they are not even touching?


The concept of an electric field describes how
one charge affects the space around it, which then
exerts a force on another charge.
The electric field at a given point in space is the
electric force per unit positive charge that would
be exerted on a charge if it were placed at that
point.
F
E

q
It is a vector having the same direction as the
force on a positive charge placed at that point.
Two point charges, 3 C (left) and 2 C (right),
are separated by a distance of 30 cm. A third
charge q0 =4 C is placed between them as shown.
The force exerted by q1 on q0 is 10.8 N, and the
force exerted by q2 on q0 is 1.8 N.
What is the net electrostatic force acting on q0?
a)
b)
c)
d)
e)
1.8 N to the left
9 N to the right
10.8 N to the right
12.6 N to the right
12.6 N to the left
b) F . F1  F2
 10.8 N 1.8 N
 9 N (to the right)

What is the electric field at the location of the
charge q0 due to the other two charges?
a)
b)
c)
d)
e)
2.25 x 106 N/C left
3.0 x 106 N/C left
4.5 x 106 N/C left
2.25 x 106 N/C right
3.0 x 106 N/C right
d)
. F
E
q0

9N
4 10 -6 C
 2.25 10 6 N/C (to the right)

 We can then use the field to find the force on
any other charge placed at that point:





If the charge q is negative, the minus sign indicates that the
direction of the force on a negative charge is opposite to the
direction of the field.
The direction of the electric field is the direction of the force
exerted on a positive test charge.
We can talk about the field at a point in space even if there is
no charge at that point.
The electric field can exist even in a vacuum.
The field concept can also be used to define a gravitational
field or a magnetic field, as well as others.
 Although Maxwell was the major
contributor to the electric field concept,
Faraday also developed the idea of field
lines as a means of visualizing both the
direction and strength of the field.
The direction of the electric
field lines around a positive
charge can be found by
imagining a positive test
charge q0 placed at various
points around the source
charge.
The field has the same
direction as the force on a
positive test charge.
 Although Maxwell was the major
contributor to the electric field concept,
Faraday also developed the idea of field
lines as a means of visualizing both the
direction and strength of the field.
The electric field lines
associated with a positive
charge are directed radially
outward.
 Although Maxwell was the major
contributor to the electric field concept,
Faraday also developed the idea of field
lines as a means of visualizing both the
direction and strength of the field.
A positive test charge is
attracted to a negative
charge.
The electric field lines
associated with a negative
charge are directed inward,
as indicated by the force on
a positive test charge, q0.
 An electric dipole is two charges of equal
magnitude but opposite sign, separated
by a small distance.

Electric field lines originate on positive
charges and end on negative charges.
The field lines point away
from the positive charge,
and in toward the negative
charge.
Near each charge, the
electric field approximates
the field due to a single point
charge of the same sign.
Two charges, of equal magnitude but opposite sign, lie
along a line as shown. What are the directions of the
electric field at points A, B, C, and D?
a)
b)
c)
d)
e)
A:left, B:left, C:right, D:right
A:left, B:right, C:right, D:right
A:left, B:right, C:right, D:left
A:right, B:left, C:left, D:right
A:right, B:left, C:right, D:right
c)
.
Electric Potential
 The electrostatic force is a conservative force,
which means we can define an electrostatic
potential energy.

We can therefore define electric potential or
voltage.
Two parallel metal plates
containing equal but
opposite charges produce
a uniform electric field
between the plates.
This arrangement is an
example of a capacitor, a
device to store charge.
 A positive test charge placed in the uniform electric
field will experience an electrostatic force in the
direction of the electric field.
 An external force F, equal in magnitude to the
electrostatic force qE, will move the charge q a
distance d in the uniform field.
The external force does work
on the charge and increases the
potential energy of the charge.
The work done by the external
force is qEd, the force times the
distance.
This is equal to the increase in
potential energy of the charge:
PE = qEd.
This is analogous to what
happens when a mass m is lifted
against the gravitational force.
 Electric potential is related to electrostatic potential
energy in much the same way as electric field is
related to electrostatic force.
 The change in electric potential is equal to the change
in electrostatic potential energy per unit of positive test
charge:
V 
PE
q
in units of volts (V)
1 J/C  1 V
PE  qV
 Electric potential and potential energy are closely
related, but they are NOT the same.

If
the charge q is negative, its potential energy will decrease
when it is moved in the direction of increasing electric
potential.
 It is the change in potential energy that is meaningful.
Two plates are oppositely charged so that they have
a uniform electric field of 1000 N/C between them,
as shown. A particle with a charge of +0.005 C is
moved from the bottom (negative) plate to the top
plate. What is the change in potential energy of the
charge?
a)
b)
c)
d)
e)
0.15 J
0.3 J
0.5 J
0.8 J
1.5 J
a) PE
.  W  Fd  qEd
 (0.005 C)(1000 N/C)(0.03m)
 0.15 J
What is the change in electric potential from the
bottom to the top plate?
a)
b)
c)
d)
e)
0.15 V
0.3 V
5V
30 V
150 V
d) V.  PE  0.15 J  30 V
q
0.005 C
 The potential energy of a positive charge
increases when we move it against the field.

For a uniform electric field, there is a simple
relationship between the magnitude of the electric
field and the change in electric potential: V = Ed.
For non-uniform fields, the
relationship is more
complicated, but the electric
potential always increases
most rapidly in the direction
opposite to the electric field.
For a positive point charge,
the electric potential
increases as we move closer
to the charge.
What is lightning?
 Most thunderclouds generate a separation of
charge resulting in a net positive charge near the
top and a net negative charge near the bottom.
 The charge separation produces strong electric
fields in the cloud as well as between the cloud and
earth.
 Since moist earth is a reasonably good conductor, a
positive charge is induced on the surface of the
earth below the cloud.
 The electric field generated can be several thousand volts
per meter; the potential difference between the cloud’s
base and the earth can easily be several million volts!
 This creates an initial flow of charge (the “leader”) along a
path that offers the best conducting properties over the
shortest distance.
The leader ionizes some of the
atoms in the air along that path.
The following strokes all take
place along this same path in
rapid succession.
The heating and ionizing
produce the lightning we see.
The thunder (sound waves) is
produced at the same time, but
takes longer to reach us since
sound travels slower than light.