### Coulomb`s Law

```Unit 14: Electrostatics
Units of Chapter 16
• Static Electricity; Electric Charge and Its
Conservation
• Electric Charge in the Atom
• Insulators and Conductors
• Induced Charge; the Electroscope
• Coulomb’s Law
• Solving Problems Involving Coulomb’s Law and
Vectors
• The Electric Field
Units of Chapter 16
• Field Lines
• Electric Fields and Conductors
Do Now
1. How do protons and electrons differ in their
electrical charge?
2. Is an electron in a hydrogen atom the same as
an electron in a uranium atom?
3. Which has more mass – a proton or an
electron?
4. In a normal atom, how many electrons are
there compared to protons?
Do Now
1. How do protons and electrons differ in their
electrical charge?
Same magnitude, but opposite charge.
2. Is an electron in a hydrogen atom the same as
an electron in a uranium atom?
Yes.
3. Which has more mass – a proton or an
electron?
Proton
4. In a normal atom, how many electrons are
there compared to protons?
Same number, no net charge.
Atomic Structure
16.1 Static Electricity; Electric Charge
and Its Conservation
Objects can be charged by rubbing
Triboelectric Series
• Friction can cause electrons to transfer
from one material to another
• Different materials have a different degree
of attraction for electrons
• The triboelectric series determines which
materials have a greater attraction.
• When two materials are rubbed together,
the one with the higher attraction will end
up getting some of the electrons from the
other material
Triboelectric Series
If two materials are rubbed together, the one that is higher in
the series will give up electrons and become more positive.
MORE POSITIVE
Human Hands (if very dry)
Leather
Rabbit Fur
Glass
Human Hair
Nylon
Wool
Fur
Silk
Aluminum
Paper
Cotton
Steel (neutral)
Wood
Amber
Hard Rubber
Nickel, Copper
Brass, Silver
Gold, Platinum
Polyester
Styrene (Styrofoam)
Saran Wrap
Polyurethane
Polyethylene (scotch tape)
Polypropylene Vinyl (PVC)
Silicon
Teflon
MORE NEGATIVE
Question
• If fur is rubbed on glass, will the glass
become positively charged or negatively
charged?
• Glass – positive
• Fur -negative
16.1 Static Electricity;
Electric Charge and Its
Conservation
Charge comes in two
types, positive and
negative; like charges
repel and opposite
charges attract
Interaction Between Charged
and Neutral Objects
• Any charged object - whether positively
charged or negatively charged - will have
an attractive interaction with a neutral
object.
16.1 Static Electricity; Electric Charge
and Its Conservation
Electric charge is conserved – the
arithmetic sum of the total charge cannot
change in any interaction.
16.2 Electric Charge in the Atom
Atom:
Nucleus (small,
massive, positive
charge)
Electron cloud (large,
very low density,
negative charge)
16.2 Electric Charge in the Atom
Atom is electrically neutral.
Rubbing charges objects by moving electrons
from one to the other.
16.2 Electric Charge in the Atom
Polar molecule: neutral overall, but charge not
evenly distributed
16.3 Insulators and Conductors
Conductor:
Insulator:
Charge flows freely
Almost no charge flows
Metals
Most other materials
Some materials are semiconductors.
How Charge Is Transferred
• Objects can be charged by rubbing
• Metal objects can be charged by
conduction
• Metal objects can be charged by
• induction
16.4 Induced Charge; the Electroscope
Metal objects can be charged by conduction:
Charging by Induction
• When an object gets charged by induction, a
charge is created by the influence of a
charged object but not by contact with a
charged object. The word induction means to
influence without contact.
• If a rubber balloon is charged negatively
(perhaps by rubbing it with animal fur) and
brought near (without touching) the spheres,
electrons within the two-sphere system will be
induced to move away from the balloon.
Charging By Induction
With Negatively Charged Object
In step iii, why is the charge on the right sphere
almost uniformly distributed?
Charging By Induction
With Negatively Charged Object
What was the source of positive charge
that ended up on sphere B?
Source of charge in induction
• In induction, the source of charge that is
on the final object is not the result of
movement from the charged object to the
neutral object.
Ground
• An infinite source or sink for
charge
16.4 Induced Charge; the Electroscope
They can also be charged by induction:
16.4 Induced Charge; the Electroscope
The electroscope
can be used for
detecting charge:
16.4 Induced Charge; the Electroscope
The electroscope can be charged either by
conduction or by induction.
16.4 Induced Charge; the Electroscope
The charged electroscope can then be used to
determine the sign of an unknown charge.
16.4 Induced Charge; the Electroscope
Nonconductors won’t become charged by
conduction or induction, but will experience
charge rearrangement. The atoms or molecules
become polarized.
:
16.4 Induced Charge; the Electroscope
Nonconductors won’t become charged by
conduction or induction, but will experience
charge separation:
Do Now
True or False? Explain your reasoning.
1. An object that is positively charged contains
all protons and no electrons.
False
Positively charged objects have electrons; they
simply possess more protons than electrons.
2. An object that is electrically neutral contains
only neutrons.
False
Electrically neutral atoms simply possess the
same number of electrons as protons.
Do Now
True or False? Explain your reasoning.
1. An object that is positively charged
contains all protons and no electrons.
2. An object that is electrically neutral
contains only neutrons.
Coulomb’s Law
• The French physicist Charles Coulomb (1736 –
1806) investigated electric forces in the 1780s
using a torsion balance.
16.5 Coulomb’s Law
Experiment shows that the electric force
between two charges is proportional to the
product of the charges and inversely
proportional to the distance between them.
Coulomb’s Law
1. If two point charges Q 1 and Q 2 are a
distance r apart, the charges exert forces on
each object of magnitude:


Q1
F1 on 2  F 2 on 1  k
Q2
r
2
These forces are an action/reaction pair,
equal in magnitude but opposite in direction.
16.5 Coulomb’s Law
2. The forces are along the line connecting the
charges, and is attractive if the charges are
opposite, and repulsive if they are the same.
16.5 Coulomb’s Law
Unit of charge: coulomb, C
The proportionality constant in Coulomb’s
law is then:
When we only need two significant figures:
k  9 . 0  10 N  m / C
9
2
2
Charges produced by rubbing are
typically around a microcoulomb:
16.5 Coulomb’s Law
Charge on the electron:
Electric charge is quantized in units
of the electron charge.
This is the smallest charge in nature –
fundamental or elementary charge.
The net charge of any object must be a multiple
of that charge.
16.5 Coulomb’s Law
The proportionality constant k can also be
written in terms of
, the permittivity of free
space:
(16-2)
16.5 Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces
on each charge from every other charge can be
calculated and then added as vectors.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
The net force on a charge is the vector
sum of all the forces acting on it.
16.6 Solving Problems Involving
Coulomb’s Law and Vectors
Example 1
Suppose that two point charges, each with a
charge of +1.00 Coulomb are separated by
a distance of 1.00 meter. Determine the
magnitude of the electrical force of repulsion
between them.
Given:
Find: F - ?
IQI I= 1.00 C
Q2 I= 1.00 C
r = 1.00 m
Solve:
F k
Q1 Q 2
r
2
( 9 . 0  10 )(1)(1)
9
F 
1
2
 9 . 0  10 N
9
The force of repulsion of two +1.00
Coulomb charges held 1.00 meter apart is
9 billion Newton. This is an incredibly large
force that compares in magnitude to the
weight of more than 2000 jetliners.
Example 2
Determine the magnitude and direction of
the electric force on the electron of a
hydrogen atom exerted by the single proton
that is the atom’s nucleus. Assume the
average distance between the revolving
 10
electron an the proton r  0 . 53  10 m
Given:
Find: F-?
Q 1  Q 2  1 . 6  10
r  0 . 53  10
 10
 19
m
C
Solution:
F k
Q1 Q 2
r
2
( 9 . 0  10 N  m / C )(1 . 6  10
9

2
2
( 0 . 53  10
 10
 19
m)
2
C )(1 . 6  10
 19
C)
 8 . 2  10
8
N
Problem 1
A balloon with a charge of 4 . 0  10  5 C is held a
distance of 0.10m from a second balloon
having the same charge. Calculate the
magnitude of the electrical force between
the charges. Draw a diagram.
F k
Q1 Q 2
r
2
( 9 . 0  10 N  m / C )( 4 . 0  10
9

2
2
( 0 . 10 m )
2
5
C )( 4 . 0  10
5
C)
 14400  10
1
 1440 N
Problem 2
• Calculate the electrical force exerted
between a 22-gram balloon with a charge
of -2.6μC and a wool sweater with a
charge of +3.8μC; the separation
distance is 75cm. (Note: 1 C  1  10 C )
6
F k
Q1 Q 2
r
2
( 9 . 0  10 N  m / C )( 2 . 6  10
9

2
2
( 0 . 75 m )
2
6
C )( 2 . 6  10
6
C)
 158 . 08  10
3
N  0 . 158 N
Neutral vs. Charged Objects
• if an atom contains equal numbers of protons
and electrons, the atom is described as being
electrically neutral.
• if an atom has an unequal number of protons
and electrons, then the atom is electrically
charged and referred to as an ion.
• Any particle, whether an atom, molecule or
ion, that contains less electrons than protons
is said to be positively charged.
• Conversely, any particle that contains more
electrons than protons is said to be negatively
charged.
Charged Objects as an Imbalance of
Protons and Electrons
• Electrons can move to the electrons’ shells of
other atoms of different materials.
• For electrons to make a move from the atoms
of one material to the atoms of another
material, there must be an energy source and
a low-resistance pathway.
• rubbing your feet on carpet
• clothes tumble in the dryer
Charged Objects as an Imbalance of
Protons and Electrons
• The principle stated earlier for atoms can be
applied to objects.
• Objects with more electrons than protons are
charged negatively; objects with fewer
electrons than protons are charged positively.
True or False?
1. An object that is positively charged contains all
protons and no electrons.
False
Positively charged objects have electrons; they
simply possess more protons than electrons.
2. An object that is electrically neutral contains only
neutrons.
False
Electrically neutral atoms simply possess the same
number of electrons as protons.
Do Now
Suppose you rub a glass rod with a silk cloth and
a second glass rod with rabbit fur. The silk cloth
will acquire a __________ (+ , -) charge; the
rabbit fur will acquire a __________ (+ , -)
charge.
The rabbit fur and the silk cloth will then be
observed to ______________________ (attract,
repel, not
interact with) each other.
Three Ways to Charge an Object
1.
Friction (by rubbing)
2. Conduction(with contact)
3. Induction(without contact)
Ground
An infinite source or sink for charge
• Charge always distributes itself
evenly around a conducting
sphere
• We can think of ground as a
conductor that is so large that it
can always accept more charge
(or provide more charge).
Symbol
Charging by Conduction
• When charging something by
contact it is important to note
the following properties
• The objects must actually
touch and transfer some
electrons.
• The objects become charged
alike.
• The original charged object
becomes less charged because
it actually lost some charge.
The Electroscope
The electroscope
can be used for
detecting charge:
Electroscope Can be Charged by
Induction
Electroscope Can be Charged by
Conduction
• Once the contact of the rod to the
electroscope is made, the electrons move
from the electroscope to the rod. The
electroscope is positively charged.
Nonconductors
Nonconductors won’t
become charged by
conduction or induction, but
will experience charge
rearrangement. The atoms or
molecules become polarized.
Do Now
• Object A is rubbed with object B. Object C is rubbed
with
• object D. Objects A and D are observed to repel each
other.
• Object B is observed to repel a negatively charged
balloon.
• This is conclusive evidence that …
• … object A acquired a __________ (+ , -) charge.
• … object B acquired a __________ (+ , -) charge.
• … object C acquired a __________ (+ , -) charge.
• … object D acquired a __________ (+ , -) charge.
Law of Universal Gravitation Analogy
• Coulomb’s Law
F k
q1 q 2
d
2
• Law of Universal
Gravitation
F G
m1m 2
d
2
Questions:
1. Two charged objects have a repulsive force of
.080 N. If the charge of one of the objects is
doubled, then what is the new force?
2. Two charged objects have a repulsive force of
.080 N. If the distance separating the objects is
doubled, then what is the new force?
Do Now
•
•
•
•
Object A is rubbed with object B.
Object C is rubbed with object D.
Objects A and D are observed to repel each other.
Object B is observed to repel a negatively charged
balloon.
This is conclusive evidence that …
… object A acquired a __________ (+ , -) charge.
… object B acquired a __________ (+ , -) charge.
… object C acquired a __________ (+ , -) charge.
… object D acquired a __________ (+ , -) charge.
Six Flags Trip
1. Meet in the auditorium after Pd.2.
2. 1PM Check in at buffet in Old Country Picnic
Grove.
3. 5 PM Meet at fountain.
4. Cell phone.
5. Sunscreen.
Do Now
• Find the force exerted on the test charge.
Indicate the direction of that force
(Hint: Calculate individual forces on the test
charge and add them as vectors.)
qA= +2nC
1m
qtest=-1C
1m
qB=+3nC
Solution
F AonT  k
Q AQT
r
2
( 9  10 )( 2  10
9

(1)
9
)(1)
2
 18 N
to the left
F BonT  k
Q B QT
r
2
( 9  10 )( 3  10
9

F net  27 N  18 N  9 N
(1)
9
2
to the right
)(1)
 27 N
to the right
Gravitational Force
• Objects near surface of
Earth
Force
• Gravitational force
always directed towards
the center of Earth.
GMm
F  mg 
r
r
g 
GM
r
2
2
Gravitational Force
Force depends on mass of
object.


F  mg
Gravitational force always
directed towards center of
earth.
Even when there is no mass
nearby the earth, we can
gravitational field near the
earth- pointing towards
earth.
Electric Field
• Space around Earth and every mass is filled
with gravitational field.
• Space around every electric charge is filled
with electric field.
Strength of Electric Field
• An electric field is a vector. It has both
magnitude and direction.
• Its magnitude can be measured by its effect
on a small positive test charge q placed in it.
• The greater the force acting on the charge, the
stronger the electric field.
• E – strength of electric field
E 
F electric
q
Units – N/C
16.7 The Electric Field
The electric field is the force
on a small (point) charge,
divided by the charge:
• If you know the
direction
and magnitude of the
electric field, you can
determine the direction of
the force.
• Negatively charged
particles will have
opposite direction of force.
The Electric Field
E  F /q
F 
kqQ
r
F
q

q- test charge
2
Q – source charge
kQ
r
2
General Expression for point charge: E  k
Q
r
2
Gravitational Field Analogy
• Strength of electric
field:
E 
F electric
q
• Strength of gravitational
field:
F=mg
g 
F gravitatio
m
nal
Example 1
Jack pulls his wool sweater over his head, which
charges his cotton t-shirt as the sweater rubs
against it.
a) What is the magnitude and direction of the
 19

1
.
60

10
C
electric field at a location where a
-piece of lint experiences a force of
9
3 . 2  10 N as it floats near Jack?
Given: q  1 . 60  10  19 C
F  3 . 2  10
9
N
• Solution:
E 
F
q

3 . 2  10
1 . 60  10
9
N
 19
C
 2 . 0  10
10
N /C
Example 2
Charge Q acts as a point charge to create an
electric field. Its strength, measured a distance
of 30 cm away, is 40 N/C. What would be the
electric field strength ...
a)30 cm away from a source with charge 2Q?
b)60 cm away from a source with charge Q?
a) 80N/c
Q
E k 2
b) 10N/C
r
Example 3
What is the magnitude and direction of the
electric field 0.25 meters away from a source
charge with -5.0 μC. Draw a diagram.
E 
kQ
r
2
( 9  10 )( 5 . 0  10
9

( 0 . 25 )
2
6 )
 7 . 2  10 N / C
5
16.7 The Electric Field
Force on a point charge in an electric field:
(16-5)
Superposition principle for electric fields:
16.7 The Electric Field
Problem solving in electrostatics: electric
forces and electric fields
1. Draw a diagram; show all charges, with
signs, and electric fields and forces with
directions
2. Calculate forces using Coulomb’s law
3. Add forces vectorially to get result
16.8 Field Lines
The electric field can be represented by field
lines. These lines start on a positive charge
and end on a negative charge.
16.8 Field Lines
The number of field lines starting (ending)
on a positive (negative) charge is
proportional to the magnitude of the charge.
The electric field is stronger where the field
lines are closer together.
16.8 Field Lines
Electric dipole: two equal charges, opposite in
sign:
16.8 Field Lines
The electric field between
two closely spaced,
oppositely charged parallel
plates is constant.
16.8 Field Lines
Summary of field lines:
1. Field lines indicate the direction of the
field; the field is tangent to the line.
2. The magnitude of the field is proportional
to the density of the lines.
3. Field lines start on positive charges and
end on negative charges; the number is
proportional to the magnitude of the
charge.
16.9 Electric Fields and Conductors
The static electric field inside a conductor is
zero – if it were not, the charges would move.
The net charge on a conductor is on its
surface.
A conducting box used for shielding delicate
instruments from unwanted external electric
fields.
16.9 Electric Fields and Conductors
The electric field is
perpendicular to the
surface of a conductor –
again, if it were not,
charges would move.
16.12 Photocopy Machines and
Computer Printers Use Electrostatics
Laser printer is similar, except a computer
controls the laser intensity to form the image
on the drum
Summary of Chapter 16
• Two kinds of electric charge – positive and
negative
• Charge is conserved
• Charge on electron:
• Conductors: electrons free to move
• Insulators: nonconductors
Summary of Chapter 16
• Charge is quantized in units of e
• Objects can be charged by conduction or
induction
• Coulomb’s law:
• Electric field is force per unit charge:
Summary of Chapter 16
• Electric field of a point charge: E 
kQ
r
2
• Electric field can be represented by electric
field lines
• Static electric field inside conductor is zero;
surface field is perpendicular to surface
Chapter 17
Electric Potential
Units of Chapter 17
• Electric Potential Energy and Potential
Difference
•Relation between Electric Potential and
Electric Field
•Equipotential Lines
•Capacitance
17.1 Electrostatic Potential Energy and
Potential Difference
The electrostatic force is
conservative – potential
energy can be defined
Change in electric potential
energy is negative of work
done by electric force:
(17-1)
Electric Potential
ElectricPo tential 
Electrical PotentialE nergy
Ch arg e
1volt  1
joule
coulomb
17.1 Electrostatic Potential Energy and
Potential Difference
Electric potential is defined as potential
energy per unit charge:
(17-2a)
Unit of electric potential: the volt (V).
1 V = I J/C.
17.1 Electrostatic Potential Energy and
Potential Difference
Only changes in potential can be measured,
allowing free assignment of V = 0.
(17-2b)
Example 4
What is the potential difference between the
terminals of a battery if 60.J of work are
done when 3.0 C are pushed trough a wire
from one terminal to the other?
Given:
W=60J
q= 3.0C
Find: V-?
Solution:
V 
W
q

60 . J
3 .0 C
 20 .V
17.1 Electrostatic Potential Energy and
Potential Difference
Analogy between gravitational and electrical
potential energy:
Electrical Potential Energy
• Work is done when you move an object in the
direction of the force.
• When you raise an object, you move it against
gravitational field, you increase its potential
energy.
• When you move electric charge against
electric field, you increase its potential energy.
Diagram B.
Diagram A.
• Work would not be
• Moving a positive test charge
required to move an
against the direction of an
object from a high
electric field is like moving a
potential energy
mass upward within Earth's
location to a low
gravitational field.
potential energy
• Both movements would be like
location.
going against nature and
would require work by an
external force.
17.2 Relation between Electric Potential
and Electric Field
Work is charge multiplied by potential:
Work is also force multiplied by
distance:
17.2 Relation between Electric Potential
and Electric Field
Solving for the field,
(17-4b)
If the field is not uniform, it can be
calculated at multiple points:
17.3 Equipotential Lines
An equipotential is a line or
surface over which the
potential is constant.
Electric field lines are
perpendicular to
equipotentials.
The surface of a conductor is
an equipotential.
Equipotential Lines
• Equipotential lines are like contour lines on a
map which trace lines of equal altitude. In this
case the "altitude" is electric potential or
voltage.
• Equipotential lines are always perpendicular
to the electric field.
• Movement along an equipotential line
requires no work because such movement is
always perpendicular to the electric field.
17.3 Equipotential Lines
Equipotential Lines
• Dashed lines are equipotential lines
• Solid lines are electric field lines
Summary of Chapter 17
• Electric potential energy:
• Electric potential difference: work done to
move charge from one point to another
• Relationship between potential difference
and field:
Summary of Chapter 17
• Equipotential: line or surface along which
potential is the same
•
```