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Homework

Reading: Chap. 25 and Chap. 26

Suggested exercises: 25.1, 25.2, 25.6, 25.7,

25.10, 25.13, 25.14, 25.15, 25.17, 25.18,

25.19, 25.20, 25.21, 25.22, 25.24, 25.26, 25.27

Problems: 25.29, 25.31, 25.33, 25.36, 25.39,

25.43, 25.49, 25.51, 25.55, 25.58, (due:

Mon., Sept. 28)

Chapter 26. Electric Charges and Forces

The electric force is one of

the fundamental forces of

nature. Controlled electricity

is the cornerstone of our

modern, technological

society.

Chapter Goal: To develop

a basic understanding of

electric phenomena in terms

of charges, forces, and

fields.

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Chapter 26. Basic Concepts

• Electric charge and their interactions

• Coulomb’s law

• Conductor, insulator, semiconductor

• Electric field

Forces

What kinds of forces we have learnt so far?

Gravitational force (G)

Tension (EM)

Spring (elastic force) (EM)

Friction (EM)

Normal (support) (EM)

The Electromagnetic Force (EM)

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Charge Model

10-10 m 1012 m

Attraction between the positively charged nucleus and the negatively charged electrons

Charge Model

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Atoms and Electricity

• An atom consists of a very small and dense

nucleus surrounded by much less massive orbiting electrons.

• The nucleus is a composite structure consisting

of protons, positively charged particles, and neutral

neutrons.

• The atom is held together by the attractive electric

force between the positive nucleus and the negative

electrons.

• Electrons and protons have charges of opposite sign

but exactly equal magnitude, they carry the smallest unit of

charge.

• This atomic-level unit of charge, called the

fundamental unit of charge, is represented by the symbol e.

Charge Quantization

e = 1.60×10-19 C

where Np and Ne are the number of protons and electrons contained in

the object

• A macroscopic object has net charge

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Electric Charge

• A fundamental property of matter

• Charge is of two types: positive + and negative –

• Like charges repel; unlike charges attract

Unlike charges attract

Like charged repel

Electric Charges

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Material Properties

Conductors

Insulators

Semiconductors

Superconductors

Insulators

Insulators

--

--

Charges are isolated in insulators.

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

- +

+

+

+

-

-

-

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Insulators

• The electrons in the insulator are

all tightly bound to the positive

nuclei and not free to move around.

• Charging an insulator by friction

leaves patches of molecular ions on

the surface, but these patches

are immobile.

--

-

--

--

insulator

The Electric Dipole

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The Electric Dipole

Conductors

--

--

-

-

-+

+

+

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

Charges move about easily in conductors.

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Conductors

• In metals, the outer atomic electrons

are only weakly bound to the nuclei.

• These outer electrons

become detached from their

parent nuclei and are free to

wander about through the entire solid.

• The solid as a whole

remains electrically neutral, but

the electrons are now like a negatively

charged liquid permeating an array

of positively charged ion cores.

Charges Transfer in Conductor

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Charges Transfer in Conductor

Transfer Charges to A Metal Ball

Before touching a solid ball Before touching a hallow ball

- --

-

-

--

-

--

-

-

-

-

-

-

-

-

--

-

-

After touching a solid ball

----

-----

---

-

---

--

-- -

--

-

After touching a hallow ball

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Thought Quiz:

How can a charged balloon stick to an uncharged wall?

-

-

-

-

-

-

+

++

Induction

-

--

Charge Polarization

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Charge Polarization

Electrostatic force

𝐹 =𝑞1𝑞2

4𝜋𝜀0𝑟2 𝑟

𝑞1

𝑞2

𝑟 𝑟

𝑭

Source charge

Test charge

• A vector Unit: Newton

• Determined by both source charge and test charge

• If 𝑞1𝑞2 > 0, the direction is 𝑟; if 𝑞1𝑞2 < 0, direction

is − 𝑟.

𝜀0 = 8.85 × 10−12𝐶2/𝑁 ∙ 𝑚2

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The Force Analysis for a Charged Car

+ -+

q1 q2q3

The Equilibrium Position for a Charged Car

+ ++

q1 q2q3

2L

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The Motion of a Charged Car

+ ++

Q q Q

2L

In-class Activity #1

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After removing the conducting wire, what happens to the

charge distribution of the metal ball? How about after removing

the charged rod?

In-Class Activity #2

In-class Activity #3

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In-class Activity #4

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In the figure, two tiny conducting balls of

identical mass m and identical charge q hand

from nonconducting threads of length L.

Assume that is so small that tan can be

replaced by its approximate equal, sin.

Show that, for equilibrium,

3/1

0

2

2

mg

Lqx

Example #3

The figure shows a long, nonconducting, massless rod of length L,

pivoted at its center and balanced with a block of weight W at a

distance x from the left end. At the left and right ends of the rod are

attached small conducting spheres with positive charges q and 2q,

respectively. A distance h directly beneath each of these sphere is a

fixed sphere with positive charge Q. (a) Find the distance x when

the rod is horizontal and balanced. (b) What value should h have so

that the rod exerts no vertical force on the bearing when the rod is

horizontal and balanced?

Example #4

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The Electric Field

rF ˆ4 2

0

21

r

qq

q1

Source

charge

r̂

Pq2

Test

charge

The magnitude of the electrostatic

force is proportional to the test charge

2qF

There is a fundamental quantity that can represent this kind of

interaction: It should only depend on the source and distance:

Electric field: E

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The Electric Field

Superposition principle:

P

q1 q2 q3 qm

E = E1 + E2 + … + Em

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Electric Field of a Positive Point Charge

• The picture shows the electric field vector at

several points.

Visualization: Electric Field Lines

• Electric field lines show the direction of E at any point (tangent).

• The magnitude of E is proportional to the density of electric field lines.

• Electric field lines originate on positive charges and terminate on negative charges, unless they extend to infinity.

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Electric Field Lines for a Negative Point Charge

Electric Field Lines of Two Charged Particles

Act#1

& 2

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Electric Field Lines for a Infinitely large, nonconducting sheet

++

+ +

++

Problems to find electric fields

Use Coulomb's law to find the field

Superposition principle

Important: electric field is a vector, it

has magnitude and direction.

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The Electric Field

We begin our investigation of electric fields by postulating

a field model that describes how charges interact:

1.Some charges, which we will call the source

charges, alter the space around them by creating an

electric field.

2.A separate charge in the electric field experiences a

force exerted by the field.

Suppose probe charge q experiences an electric force Fon q

due to other charges.

The units of the electric field are N/C. The magnitude E of

the electric field is called the electric field strength.

The Electric Field of a Point Charge

The electric field at distance r from a point charge q is

where the unit vector for r points away from the charge to

the point at which we want to know the field.

This unit vector expresses the idea “away from q”.

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EXAMPLE 26.8 The electric field of a proton

QUESTIONS:

EXAMPLE 26.8 The electric field of a proton

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EXAMPLE 26.8 The electric field of a proton

In-class Activity #5

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In-class Activity #6

Chapter 26. Summary Slides

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General Principles

Important Concepts

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Important Concepts

Important Concepts

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Important Concepts

Chapter 26. Clicker Questions

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A. see if the object attracts a charged plastic rod.

B. see if the object repels a charged glass rod.

C. Both A and B.

D. Either A or B.

To determine if an object has “glass

charge,” you need to

To determine if an object has “glass

charge,” you need to

A. see if the object attracts a charged plastic rod.

B. see if the object repels a charged glass rod.

C. Both A and B.

D. Either A or B.

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A. qa = qb > qe > qc > qd

B. qa > qe > qd > qc > qb

C. qe > qa > qd > qb > qc

D. qd > qc > qe > qa = qb

E. qd > qc > qe > qa > qb

Rank in order, from most positive to most

negative, the charges qa to qe of these five

systems.

Rank in order, from most positive to most

negative, the charges qa to qe of these five

systems.

A. qa = qb > qe > qc > qd

B. qa > qe > qd > qc > qb

C. qe > qa > qd > qb > qc

D. qd > qc > qe > qa = qb

E. qd > qc > qe > qa > qb

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A.The leaves get closer together.

B. The leaves spread further apart.

C. The leaves don’t move.

D.One leaf moves higher, the other lower.

An electroscope is positively charged by

touching it with a positive glass rod. The

electroscope leaves spread apart and the

glass rod is removed. Then a negatively

charged plastic rod is brought close to the

top of the electroscope, but it doesn’t

touch. What happens to the leaves?

An electroscope is positively charged by

touching it with a positive glass rod. The

electroscope leaves spread apart and the

glass rod is removed. Then a negatively

charged plastic rod is brought close to the

top of the electroscope, but it doesn’t

touch. What happens to the leaves?

A.The leaves get closer together.

B. The leaves spread further apart.

C. The leaves don’t move.

D.One leaf moves higher, the other lower.

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A. FA on B > FB on A

B. FA on B < FB on A

C. FA on B = FB on A

Charges A and B exert repulsive forces on

each other. qA = 4qB. Which statement is

true?

Charges A and B exert repulsive forces on

each other. qA = 4qB. Which statement is

true?

A. FA on B > FB on A

B. FA on B < FB on A

C. FA on B = FB on A

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A.to the right.

B.to the left.

C.zero.

D.There’s not enough information to tell.

An electron is

placed at the

position marked

by the dot. The

force on the

electron is

An electron is

placed at the

position marked

by the dot. The

force on the

electron is

A.to the right.

B.to the left.

C.zero.

D.There’s not enough information to tell.

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Rank in order, from largest to smallest,

the electric field strengths E1 to E4 at

points 1 to 4.

A. E2 > E4 > E1 > E3

B. E1 = E2 > E3 = E4

C. E2 > E1 = E4 > E3

D. E2 > E1 > E4 > E3

E. E1 > E2 > E3 > E4

A. E2 > E4 > E1 > E3

B. E1 = E2 > E3 = E4

C. E2 > E1 = E4 > E3

D. E2 > E1 > E4 > E3

E. E1 > E2 > E3 > E4

Rank in order, from largest to smallest,

the electric field strengths E1 to E4 at

points 1 to 4.

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Chapter 26. Reading Quizzes

What is the SI unit of charge?

A. Coulomb

B. Faraday

C. Ampere

D. Ohm

E. Volt

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What is the SI unit of charge?

A. Coulomb

B. Faraday

C. Ampere

D. Ohm

E. Volt

A charge alters the space around it.

What is this alteration of space called?

A. Charged plasma

B. Charge sphere

C. Electric ether

D. Electric field

E. Electrophoresys

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A charge alters the space around it.

What is this alteration of space called?

A. Charged plasma

B. Charge sphere

C. Electric ether

D. Electric field

E. Electrophoresys

Topics:

• Developing a Charge Model

• Charge

• Insulators and Conductors

• Coulomb’s Law

• The Field Model

Chapter 26. Electric Charges and Forces

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If a negative charged rod is held near a

neutral metal ball, the ball is attracted to

the rod. This happens

A. because of magnetic effects.

B. because the ball tries to pull the

rod’s electrons over to it.

C. because the rod polarizes the metal.

D. because the rod and the ball

have opposite charges.

If a negative charged rod is held near a

neutral metal ball, the ball is attracted to

the rod. This happens

A. because of magnetic effects.

B. because the ball tries to pull the

rod’s electrons over to it.

C. because the rod polarizes the metal.

D. because the rod and the ball

have opposite charges.

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The electric field of a charge is defined

by the force on

A. an electron.

B. a proton.

C. a source charge.

D. a test charge.

The electric field of a charge is defined

by the force on

A. an electron.

B. a proton.

C. a source charge.

D. a test charge.