Transcript Electrostatic PowerPoint

Electrostatics
Essential Knowledge

1.B.2: There are only two kinds of electric charge. Neutral objects or systems contain
equal quantities of positive and negative charge, with the exception of some
fundamental particles that have no electric charge.

Like-charged objects and systems repel and unlike-charged objects and systems attract.

Charged objects or systems may attract neutral systems by changing the distributions of
charge in neutral systems.

1.B.3: The smallest observed unit of charge that can be isolated is the electron charge,
also known as the elementary charge.

The magnitude of the elementary charge is equal to1.6 x1 10-19 Coulombs.

Electrons have a negative elementary charge of equal magnitude, although the mass of
the proton is much larger than the mass of an electron.

3.C.2: Electric force results from the interaction of one object that has an electric
charge with another object that has an electric charge.

Electric force dominates the properties of the objects in our everyday experiences.
However, the large number of particles interaction that occur make it more convenient
to treat everyday forces, such as normal force, friction, and tension.

Electric force may be attractive or repulsive, depending upon the charges on the
objects involved.

5.A.1: A system is an object or collection of objects. The objects are treated as having
no internal structure.
Learning Objectives

1.B.2.1: The students is able to construct and explanation of the two charge
models of electric charge based on evidence produced through scientific
practices.

1.B.3.1: The student is able to challenge the claim that an electric charge
smaller than elementary charge has been isolated.

3.C.2.1: The students is able to use Coulomb’s law qualitatively and
quantitatively to make predictions about the interaction between two
electric point charges (interaction between collections of electric point
charges are not covered in Physics 1 and instead are restricted to Physics 2)

3.C.2.2: The student is able to connect concepts of gravitational forces and
electric force to compare similarities and differences between the forces.
Science Practices

1.5: The student can re-express key elements of natural phenomena across multiple
representations in the domain.

2.2: The student can apply mathematical routines to quantities that describe natural
phenomena.

6.1: The student can justify claims with evidence.

6.2: The students can construct explanations of phenomena based on evidence
produced through scientific practices.

6.4: The student can make claims and predictions about natural phenomena based on
scientific theories and models.

7.2: The students can connect concepts in and across domain(s) to generalize or
extrapolate in and/or across enduring understanding and/or big ideas.
Electric Charges
1. Two kinds of charges: Positive and Negative
2. Like charges repel, unlike charges attract
3. Charge is conserved
4. Charge is quantized
LINK
Law of Conservation of Charge
The total charge in a closed system remains constant.
Charges are transferred.
The total charge in a closed system remains constant.
 Neutral objects have equal amounts of positive and negative charge.
 Only electrons are transferred in solids.
 Single charges may not be created nor destroyed.
 Pairs of opposite charges may be created or destroyed.
Examples: Charge separation by friction
Chemical equations
Beta Decay
Pair production / pair annihilation
SI Unit for Charge

Coulomb [C] is the SI unit for charge.

Coulomb is a derived unit based on the fundamental unit for current, Ampere.

Coulomb is a humongous amount of charge.
Natural unit for charge
On the atomic level, the unit of charge is the
elementary charge, e.

+e is the charge of a proton

-e is the charge of an electron

+2e is the charge of an alpha particle
Balloon Charge Tester
Item
Attract
Repel
Natural unit for charge
On the sub-atomic level, fractional charges
exist.
Quarks have
+ (1/3) e
or + (2/3) e
Charge is Quantized
In 1909 Robert Millikan confirmed that electric charge always
occurs in integral multiples of the fundamental unit of charge, e.
q is the standard symbol for charge (units - Coulombs)
QT  N  q
Total
Charge
Number of
fundamental
charges
Elementary
Charge
1.6 x 10-19 C
Money is quantized, the
smallest unit of US
currency is the penny!
Fundamental particle properties
Particle
Mass
electron 9.11 x 10 -31 kg
proton
1.672 x 10 -27 kg
neutron 1.674 x 10 -27 kg
Charge
-1.6 x 10 -19 C
-1e
+1.6 x 10 -19 C
+1e
0
An object has a net charge of +3 Coulombs
1. How many more protons than electrons are on the object?
2. Can you determine the total number of protons on the
object?
QT  N  qe
Ex: Find the total charge on the object in each case
Object
# of Excess
Protons/Electrons
Quantity of Charge (Q)
in Coulombs (C)
A
1 x 106 excess
electrons
- 1.6 x 10-13 C
B
2 x 108 excess protons
+ 3.2 x 10-11C
C
2 x 1010 excess
electrons
- 3.2 x 10-9 C
QT  N  qe  (1106 )  (1.6 1019 )C  1.6 1013 C
QT  N  qe  (2 108 )  (1.6 1019 )C  3.2 1011 C
Conductors and Insulators
Good conductors
have many “free”
electrons
EX: Metals
Insulators have few
“free” electrons
Ex: Rubber, wood
Insulators and Conductors
Electrical Conductibility
Insulators
Semi-conductors
No movement of
charges within the
object
Limited number
of free carriers
Wood, plastics, glass
Silicon, Germanium
Conductors
Free movement
of charges
Metals (Cu, Ag, Al)
Grounding: The “Earth” is considered an infinite sink of charges
Ground (Earthing)

Grounding: The “Earth” is considered an infinite source or
sink for excess charge.

Grounding prevents charge from building up on the
chassis of appliances.

Mutual grounding provides a common reference point.
Coulomb’s Law
In 1785 Charles Coulomb established a law of electric force
between two stationary charged particles.
1.
2.
3.
4.
5.
Force inversely proportional to square of distance
Force along the line joining the particles
Force proportional to the product of the charges
Force attractive between opposite sign charges.
Force repulsive between charges of the same sign
k = Coulomb constant
= 8.99 x 109 Nm2/C2
Direction of the Coulomb Force
1. Force can be attractive or repulsive
2. Equal in magnitude
3. Opposite in direction
Ex: If q1 =-3uC, q2 = +4uC, and d = 2 m,
find the electric force between the charges.
F21
+
d
q2
F12
q1q2
F k 2
r
-
q1
6
6
(

3

10
C
)(4

10
C)
9
2
2
 (8.99 10 N  m / C ) 
2
(2m)
 .027N
q1q2
F k 2
r
Coulomb Force is
proportional to 1/r2
Hyperbolic relationship between force and distance
1
F 2
d
link
Analogy to Gravitational Force
Coulomb Force
Gravitational Force
q1q2
Fe  k 2
d
m1m2
Fg  G 2
d
The gravitational force can only be attractive.
Example: Compare the
gravitational force in the hydrogen
atom to the Coulomb (electric)
force. Which is stronger?
Atomic Radius: 10-10 meters
Nuclear Diameter: 10-15 meters
Mass of electron: me = 9.11 x 10-31 kg

Mass
of proton: mp = 1.67 x 10-27 kg
Compare the gravitational
force in the hydrogen atom
to the Coulomb (electric)
force. Which is stronger?
How much stronger?
m1m2
r2
(6.67 x1011 N  m 2 / kg 2 )(1.67 X 1027 kg )(9.11x1031 kg )

(1010 m) 2

FG  G
k q1q2 (9 x109 N  m2 C 2 )(1.6 x1019 C ) 2
FE 

2
r
(1010 m) 2
 4.6 x1018 N
Difference and Similarities between Electricity and Gravity

Coulomb Law and Law of Gravitation similarities

Gravitation is always attractive

Electrical force can be attractive or repulsive

Electric force dominates the atomic world

Gravitational forces dominates the macroscopic scale: people, planets,
galaxies

Electric forces are stronger !!!
A metal sphere is charged by losing 5.18 x 1013 electrons
while a second sphere is charged by losing 15.54 x 1013
electrons. The two spheres are 25 cm apart. Determine
the force between the two spheres.
1. Two charged objects have a repulsive force of .080 N. If the
charge of one is doubled, and the distance separating them is
doubled what is the new force?
2. Two charged objects have a repulsive force of .080 N. If the
charge of both of the objects is doubled and the distance
separating the objects is doubled what is the new force?
3. Two charged objects have an attractive force of .080 N. If the
charge of one of the objects is quadrupled, and the distance
separating the objects is doubled what is the new force?
4.
Two charged objects have an
attractive force of .080 N. If the
charge of one is tripled and the
distance separating the objects
is tripled what is the new force?
Two uniformly charged spheres are firmly fastened to and
electrically insulated from a table. The charge on sphere 2 is three
times the charge on sphere 1. Which diagram correctly shows the
magnitude and direction of the electrostatic forces:
Alternate Form of Coulomb’s law
Coulomb’s constant k is often written in terms of the
permittivity of free space e0
q1q2
F k 2
r
0
1
4 k
 8.85 10 C /N  m
-12
2
2
Coulomb’s Law can then be written as:
q1q2
F
2
4 0 d
1
Superposition Principle
When more than two charges are present, the resultant
force on any one of them is equal to the vector sum of the
forces exerted by each of the individual charges.
FT  F12  F13  F14 
Three point charges located at corners of triangle as shown. Find
The resultant force on q3
q1 = q3 = 5 C
q2 = -2 C
a = .1 m
F31
F32
Solution:
450
 Note the direction of forces
 Resolve F32 and F31 into their x and y components
 Add the x and y components of F32 and F31 to find x and y
components of F3
 Find the magnitude and direction of F3
450
Two 2 gram balloons are suspended by strings that are 60 cm long. The
two balloons establish equilibrium with an angle between the two strings
of 250. Determine the charge on each balloon. Assume the same amount
of charge is on each.
Methods of Charging
1. Friction - Transfer of electrons between neutral objects.
2. Induction - A neutral object becomes charges without
ever contacting the charged object.
3. Conduction - A charged body comes in contact with
another body and charge is transferred between them.
1. Friction
- When two neutral objects are rubbed together.
One gives up its negative charges to the other. One becomes positively
charged while the other becomes equally negative.
Hair gives up
electrons to the
balloon.
Frictional charging is a result of transfer of electrons
Some materials are greedy and steal electrons, they have a high
electroconductivity, while others are willing to give them up.
2. Induction - When an object is charged by the influence of
a charged object near, but not in contact with it. The word
induction means to influence without contact.
1. Positively charged object brought near,
does not touch the electroscope.
2. Ground’s attached and electrons are
drawn up.
3. Ground is removed trapping electrons
on the electroscope.
4. Electroscope ends up oppositely
charged to the object brought near.
Temporary polarization by induction
Electrons pushed by negative
object toward the bottom of the
electroscope. The foil leaves at
the bottom have a negative
charge so they repel each other.
Electrons attracted by the positive
object toward the top of the
electroscope. The foil leaves at the
bottom have a positive charge so
they repel each other.
Electrostatic Induction occurs only in conductors.
Ground - Is an infinite source or sink for electrons.
Induction
Induction
Polarization and Induction
Induction

A negatively charged rubber rod is brought near an
uncharged sphere

The charges in the sphere are redistributed.

After the sphere is grounded they leave the sphere

The positive charge on the sphere is evenly distributed

Charging by induction requires no contact with the
object inducing the charge
3. Conduction – Charging by contact
When charging something by contact:
1. A charged objects must touch and transfer some electrons.
2. The objects become charged alike.
3. The original charged object becomes less charged.
Conduction

A charged object (the rod) is placed in
contact with another object (the sphere)

Some electrons on the rod can move to the
sphere

When the rod is removed, the sphere is left
with a charge

The object being charged is always left
with a charge having the same sign as the
object doing the charging
Grounding neutralizes a charged object
Polarization and charging by contact
Polarization-Induced Attractions


Attraction is more common than repulsion
Charged objects can attract uncharged ones
 A charged rod attracts a neutral metal ball

It redistributes the charge  separation of charge in the
uncharged object. The attractive force is then greater.
Water faucet
comb demo
Conduction or Induction?
After rubbing the balloon, why does balloon stick to wall?
How do you know that this force is stronger than gravity?
Negatively charged paint adheres
to positively charged metal.
Van def Graff generator and charging by contact
Charge Distributions

The excess charge on a conductor resides on the
outer surface concentrating on rough edges and
corners.

Automobiles are a safe haven from lightening.

Lightening rods and point discharge
Gravitational Fields
•Surround anything with mass
•Vector fields (have magnitude and direction)
•Weaken as you move away from a single mass
•Magnitude of field can be calculated by:
FG
w
g

m
m
Electric Fields
•Surround charged objects
•Vector fields (magnitude and direction)
•Direction depends on the charge
•Weaken as you move away from isolated one
charge
•Magnitude of field calculated by:
F
E=
q0
Unit : N/C
 q0 is the test charge
 Q is the charged object in the area
 E is the electric field experienced by
q0 due to Q
Electric Field Strength
The Electric Field Strength at a point in an
Electric Field is the Force per unit positive
test charge exerted on a charge at that
point.
E = F/q
*Vector Quantity
*[N/C]
Field of an isolated point charge
q1q2
F k 2
r
F
E=
q0
Unit : N/C
q1q2
F
2
4 0 d
1
F
E=
q0
Unit : N/C
q1
Ek 2
d
q1
1
E
4o d 2
q1q2
F k 2
r
Coulomb Force is
proportional to 1/r2
Hyperbolic relationship between force and distance
1
F 2
d
Calculate the force exerted by E = 4 N/C to the
right(→) on each of the following:

q1 = +1 C

q2 = +4 C

q3 = - 4 C

q4 = + 1.5 C

q5 = - 1.5 C

q6 = 6 μC

q7 = p +

q8 = e-

q9 = 2e-
1. What is the strength of the electric field 2 cm fron a +3uC charge?
6
Q
(3

10
C)
9
2
2
E  k 2  (8.99 10 N  m / C )
r
(.02m)2
2. If you double the distance from the charge what will be the new electric field strength
at that point?
 6.74 10 N / C
7
Ans: ¼ the original strength
1
 (6.74 107 N / C )  1.68 107 N / C
4
 The number of lines per unit area through the surface is
proportional to the magnitude of the electric field
 The closer the lines the stronger the field, ‘E’.
Drawing Electric Field Lines
 Lines begin on positive and end on negative charges.
 No two field lines can cross.
 Number of field lines leaving is proportional to the charge.
 Strength of the field is proportional to the density of lines.


Electric field lines are proportional to magnitude of the charge
Electric field is tangent at any point
If charges are not equal in magnitude the greater charge will
have more field lines
Twice the charge, twice the field lines
Double the charge means double the field lines
Field the same strength at every point
along the circle
The diagram below is a representation of the electric field
arising from?
a. a single negative charge
b. two unlike charges
c. a single positive charge
d. a pair of positive charges
e. a pair of negative charges
Must Know what the electric fields looks like
around
1.
2.
3.
4.
5.
6.
7.
A positive point charge
A negative point charge
A positive and negative point charge
Two positive point charges
Two negative point charges
Around and inside a conducting sphere
Between 2 parallel plates
NOTE: Point Charges have no dimensions
Positive Point Charge
+
+
1.
2.
3.
4.
Field emanates from positive charge
Perpendicular to the surface
Field lines never cross
Field weakens as 1/r2
Negative Point Charge
1. Field terminates on it
2. Field perpendicular to
the surface
3. Field lines never cross
4. Field weakens as the
distance increases
Positive Point Charge
1. Inverse square law: 1/r2
2. Double the distance the field is a ¼ the original strength.
3. Less field lines per unit area.
One Positive and one
Negative Point Charge
1. Out of the positive
and into the negative
2. Strongest between the
charges
3. Field lines are
perpendicular to the
surface
4. Field lines never
cross
Two Positive Point Charges
1. Field zero between
the charges
2. Field lines diverge
3. Field lines never
cross
4. Field lines
perpendicular to
surface
Two Negative Point Charges
Same as positive charge diagram except field lines go into
the charges
1. Field 0 between
the charges
2. Field lines
diverge
3. Field lines never
cross
4. Field lines
perpendicular to
surface
Negatively Charged
Conducting Sphere
_
_
_
_
_
E=0
_
_
_
It’s NOT
dimensionless
1. Field ends on the
charge
2. Field ZERO inside
the sphere
3. All excess charge is
on the surface
4. More charge equals
more field lines
Field lines perpendicular
to surface
Double the
distance, field is ¼
original strength.
E=0
Everywhere
inside
Inverse square law
Positively Charged
Conducting Sphere
1. Field begins on the
charge
2. Field ZERO inside
the sphere
3. All excess charge is
on the surface
4. More charge equals
more field lines
Edge effects- Electric field lines bulge out slightly around
the edges of Parallel Plates – Field weaker
All fields are vectors:
1. Magnitude - The force on a charge placed in the field divided by
the charge itself.
F
N
E

q
C
2. Direction - The direction that the force would be on a positive test
charge placed at that point.
The field lines for a large positively charged plate. The field lines
flow away from the plate on both sides. (Note: this is a small
section near the center of a large plate. This is why the field lines
are not coming from the outside rim of the plate.)
A uniform electric field is created between two parallel
metal plates if the plates are connected to a battery.
The way the terminals are connected
determines the direction of the field
Field around and between charged parallel plates
1. Field comes out of the
positive plate goes into
the negative plate
2. Field is UNIFORM,
same strength
everywhere
3. Field above and below
the plates is zero.
Positive
plate
Parallel Plate Capacitor
+ + + + + + + + + + + + + + + + + +
E =const.
Uniform field
- - - - - - - - - - - - - - - - - - - - - - - - -
Everywhere outside the
plates the field is zero
Negative
Plate
A charged particle
introduced perpendicular
to the electric field will
follow a parabolic path
Like a projectile in a
gravitational field