Ch. 21

1
Ch. 21

• The Electric Field I Discrete Charge
  Distributions

2
Ch. 21 Overview

• Properties of Charge
• Conductors and Insulators
• Forces between Charges
• Comparison of the Electrostatic and Gravitational
  Forces
• The Electric Field
• Electric Dipoles in Electric Fields

3
Which of the following are fundamental properties
of matter? (CT)

• Mass
• Charge
• Spin
• 1 and 2
• 1,2, and 3

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4
Charge

• If you rub a piece of amber with fur the amber
  will attract bits of paper
• Greek term for amber Elektronos from which we
  derive electron
• If two amber rods are brought together, they will
  repel

5
If charges can attract or repel each other then
what do they exert on each other? (GR)
6
What does it suggest about charges that the force
between them can be both attractive and
repulsive?(GR)How is this different than the
force between masses? (Gravity) (GR)
7
If a piece of fur is rubbed against an amber rod,
the amber rod becomes negatively charged. What
is the sign of the charge of the fur? (TPS)

1. Negative
2. Positive
3. It is uncharged
4. Cannot be determined

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8
If a piece of fur is rubbed against an amber rod,
the amber rod becomes negatively charged. What
is the sign of the charge of the fur? (CT)

1. Negative
2. Positive
3. It is uncharged
4. Cannot be determined

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9
Properties of Charge

• Charges exert forces on each other
• Forces can be repulsive or attractive
• Two Types of Charge called /- due to Franklin
• Like charges repel, opposite charges attract
• Charge is conserved
• Charge is quantized

10
Quantization of Charge

• Basic unit of charge is the charge of an electron
• e -1.602 x 10-19 C
• The charge of a proton is opposite the charge of
  the electron
• p 1.602 x 10-19 C e
• SI (derived) unit of charge is the coulomb, C

11
Quantization of Charge (cont.)

• The charge, q, on any object can be expressed as
  q Ne where N is some integer
• Fundamental SI units 1 C 1 As (ampere second)

12
Ex How many electrons are there in -1 C of
charge?
13
Solutionq NeSolve for NN q/eN -1 C/
-1.602 x 10-19 CN 6.2 x 1018 electrons
14
A student makes the following statement. When I
rub a piece of glass with silk, the glass obtains
17.5 charges and silk has -11.3. What if
anything is wrong with the students statement?
(TPS)

1. The statement contains no errors
2. The statement violates charge conservation
3. The statement violates charge quantization
4. 2 and 3
5. Cannot be determined

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15
A student makes the following statement. When I
rub a piece of glass with silk, the glass obtains
17.5 charges and silk has -11.3. What if
anything is wrong with the students statement?
(TPS)

1. The statement contains no errors
2. The statement violates charge conservation
3. The statement violates charge quantization
4. 2 and 3
5. Cannot be determined

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16
Insulators and Conductors

• What is the difference between an insulator and a
  conductor? (BRST)

17
Insulators and Conductors

• In an Insulator all of the electrons are strongly
  localized around an individual atom
• In a Conductor about one electron per atom is
  shared by the metal as a whole. This electron is
  called a free electron

18
Two uncharged metal spheres are in contact. A
negatively charge amber rod is brought near one
of the spheres. Draw a sketch showing the charge
distribution on the spheres.
19
(No Transcript)
20
The electroscope

• Simple Device Used to indicate charge
• Two metal foil leaves are suspended from the
  bottom of a conducting rod

21
Electroscope Demonstration

• What happens when a charged insulating rod is
  brought near the electroscope?
• What happens when a charge insulating rod is
  rubbed against the electroscope?
• What happens when you bring your hand near the
  electroscope?
• What happens when you touch the charged
  electroscope?

22
A piece of PVC pipe is rubbed with a piece of fur
and then brought near an empty aluminum can lying
on its side. What will happen to the can? (TPS)

1. Nothing
2. It will be repelled from the can
3. It will be attracted to the can
4. It cannot be determined

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23
A piece of PVC pipe is rubbed with a piece of fur
and then brought near an empty aluminum can lying
on its side. What will happen to the can?

1. Nothing
2. It will be repelled from the can
3. It will be attracted to the can
4. It cannot be determined

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24
Insulators vs. Conductors

• An uncharged plastic rod is placed on the bulb of
  an electroscope. A charged plastic rod is
  brought near the other plastic rod but away form
  the electroscope. What will happen?
• A piece of metal is placed on the bulb of an
  electroscope. A charge plastic rod is brought
  near the other plastic rod but away form the
  electroscope. What will happen?

25
A plastic rod is charged and brought near a few
small pieces of paper. What will happen to the
paper?

1. Nothing since the paper is an insulator
2. The paper will be attracted to the rod
3. The paper will be repelled by the rod
4. Cannot be determined

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26
How is it possible that the insulating paper can
be attracted to the rod?
27
Induced Polarization

• Bringing a charge near an insulator can cause a
  slight rearrangement of the electrons around the
  nucleus of the atom
• The insulator can then be slightly attracted to
  charge
• Ex. Rub a balloon on your head and stick it to
  the wall

28
Coulombs Law

• Like charges repel
• Opposite charges attract
• Force depends inversely on the square of the
  distance between the charges

29
Charles Coulomb

• Determined form of force between charges using a
  torsional balance

30
Coulombs Law
q1
31
Coulombs Law

• ke 8.99 x 109 N m2/C2
• e0 8.85 x 10-12 C2/Nm2 (Ch. 19)

32
Two positive charges are separated by a known
distance. The distance is then doubled, how does
this affect the force? (TPS)

1. The force is unchanged
2. The force is doubled
3. The force is halved
4. The force is quadrupled
5. The force is reduced by ¼
6. Cannot be determined

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33
Two positive charges are separated by a known
distance. The distance is then doubled, how does
this affect the force?

1. The force is unchanged
2. The force is doubled
3. The force is halved
4. The force is quadrupled
5. The force is reduced by ¼
6. Cannot be determined

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34
Ex. Find the magnitude and direction of the
force on charge 1 shown below.
35
Solution

• F kq1q2/r2
• 8.99 x 109 Nm2/C2 x 2.5 x 10-6 C x 3.0 x
  10-6C/(.25 m)2
• .27 N
• The direction is down.

36
How will the force on charge 1 compare to the
force on charge 2? (CT)

1. It will be larger
2. It will be the same
3. It will be smaller
4. Cannot be determined without first calculating
   the answer

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37
A student measures the force on each of two
charged objects due to the other. She finds the
forces to be the same in magnitude and opposite
in direction. Which of the following is true
about the charges? (CT)

1. The charges must be identical
2. The charges are equal in magnitude and of
   opposite sign
3. The charges must have the same sign but can have
   different magnitudes
4. The charges must have opposite signs but can have
   different magnitudes
5. Cannot be determined

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38
In what ways is Coulombs Law similar to Newtons
Law of Gravity?What is a significant difference
Coulombs Law and Newtons Law of Gravity
39
Comparison of Newtons Law of Gravity and
Coulombs Law
Inverse Square Law
Strength is proportional to product of source terms
Gravity is always attractive Electrostatic Force can be both attractive and repulsive
40
Ex. Find the ratio of the electrostatic force
between two protons and the gravitational force
between them if they are separated by .25 m.
41
Solution
42
1.24 x 1036

• The electrostatic force is much stronger
• Protons are like charges and thus in a nucleus of
  an atom will repel each other
• Gravity is not strong enough to hold the nucleus
  together
• Nucleus is held together by short range force
  called the Strong Force

43
The Electric Field

• Theres a core question about long range forces
  such as the electrostatic force or the
  gravitational force.
• If two charges are separated by a distance, then
  how do they know there is a force between them.

44
The Electric Field

• Newtons answer for gravity was that they just do
  Action at a distance.
• Michael Faraday borrowed an idea from magnetism
  and introduced tubes of force

45
Definition of the Electric Field

• Consider a small positive charge called a test
  charge, q0 brought near a positive charge, Q

Q
q0
46
Which of the following is the correct force
vector on the test charge q0?

5. None of the above is correct

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47
Suppose the test charge was moved further away
from the charge Q, how will the force vector
change?

1. It will be larger
2. It will be smaller
3. It will not change
4. Cannot be determined

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48
Suppose the test charge was moved closer to the
charge Q, how will the force vector change?

1. It will be larger
2. It will be smaller
3. It will not change
4. Cannot be determined

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49
Definition of the Electric Field

• The test charge will feel a force anywhere it is
  placed
• The source charge affects the space around it
• The effect on the space around it is the electric
  field
• We test the electric field with the test charge,
  but the electric field is due to the source charge

50
Definition of the Electric Field
51
Definition of the Electric Field

• Electric field is force per charge
• The electric field is defined so that the test
  charge is positive
• Units N/C

52
Ex. A force 0f .25 N is exerted to the left on a
test charge of magnitude q0 2 µC. a) Sketch
the situation. b) What is the magnitude and
direction of the electric field at the location
of the test charge?
53
Ex. A test charge of magnitude is located in an
electric field of magnitude 200 N/C directed to
the right. a) Sketch the situation. b) Find
the magnitude and direction of the force on the
test charge.
54
The Electric Field due to a Point Charge

• We can use coulombs law to find the electric
  field due to a point charge, Q

q0
Q
r
55
The Electric Field due to a Point Charge

• Force on the test charge (by definition positive)
  is given by

56
The Electric Field due to a Point Charge

• Electric field is defined as
• E F/q0
• So

57
The Electric Field due to a Point Charge

• This result is also usually known as Coulombs law

58
If the source charge Q is positive, what is the
direction of the electric field at the location
of the test charge? (CT)

1. To the right
2. To the left
3. Up
4. Down
5. Cannot be determined

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59
If instead the source charge Q is negative, what
is the direction of the electric field at the
location of the test charge? (CT)

1. To the right
2. To the left
3. Up
4. Down
5. Cannot be determined

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60
Ex. A point P is 3.0 cm north of a charged
point particle with charge Q 3.5 pC. a)
Sketch the situation. b) Find the magnitude and
direction of the electric field at the point P.
61
Superposition

• The electric field at a point due to several
  charges is the sum of the field due to the
  individual charges
• Since the electric field is a vector, vector
  algebra must be used to find the sum

62
FPE Exercise on Electric Fields
63
Electric Fields in Conductors in Electrostatic
equilibrium

• A piece of metal is placed in a constant electric
  field. Sketch a picture of what happens to the
  charge in the metal
• When does the charge separation stop?

64
Electric Fields in Conductors in Electrostatic
equilibrium

• A conductor in electrostatic equilibrium has an
  electric field of 0 inside the conductor