Ch. 21 The Electric Field I: Discrete Charge Distributions

Ch. 21 Ch. 21

The Electric Field I: The Electric Field I: Discrete Charge Discrete Charge

DistributionsDistributions

Ch. 21 OverviewCh. 21 Overview

Properties of ChargeProperties of Charge Conductors and InsulatorsConductors and Insulators Forces between ChargesForces between Charges Comparison of the Electrostatic and Comparison of the Electrostatic and

Gravitational ForcesGravitational Forces The Electric FieldThe Electric Field Electric Dipoles in Electric FieldsElectric Dipoles in Electric Fields

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

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0% 0% 0%0%0%

1.1. MassMass

2.2. ChargeCharge

3.3. SpinSpin

4.4. 1 and 21 and 2

5.5. 1,2, and 31,2, and 3

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ChargeCharge If you rub a piece of If you rub a piece of

amber with fur the amber with fur the amber will attract bits amber will attract bits of paperof paper

Greek term for amber – Greek term for amber – Elektronos from which Elektronos from which we derive electronwe derive electron

If two amber rods are If two amber rods are brought together, they brought together, they will repelwill repel

If charges can attract or repel If charges can attract or repel each other then what do they each other then what do they exert on each other? exert on each other? (GR)(GR)

What does it suggest about What does it suggest about charges that the force between charges that the force between them can be both attractive and them can be both attractive and repulsive?repulsive?(GR)(GR)

How is this different than the How is this different than the force between masses? force between masses? (Gravity) (Gravity) (GR)(GR)

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

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0% 0%0%0%

1.1. NegativeNegative

2.2. PositivePositive

3.3. It is unchargedIt is uncharged

4.4. Cannot be Cannot be determineddetermined

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

1 2 3 4

0% 0%0%0%

1.1. NegativeNegative

2.2. PositivePositive

3.3. It is unchargedIt is uncharged

4.4. Cannot be determinedCannot be determined

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Properties of ChargeProperties of Charge

Charges exert forces on each otherCharges exert forces on each other Forces can be repulsive or attractiveForces can be repulsive or attractive Two Types of Charge called +/- due Two Types of Charge called +/- due

to Franklinto Franklin Like charges repel, opposite charges Like charges repel, opposite charges

attractattract Charge is conservedCharge is conserved Charge is quantizedCharge is quantized

Quantization of ChargeQuantization of Charge

Basic unit of charge is the charge of an Basic unit of charge is the charge of an electronelectron

e = -1.602 x 10e = -1.602 x 10-19-19 C C The charge of a proton is opposite the The charge of a proton is opposite the

charge of the electron charge of the electron

p = 1.602 x 10p = 1.602 x 10-19-19 C = |e| C = |e| SI (derived) unit of charge is the coulomb, SI (derived) unit of charge is the coulomb,

CC

Quantization of Charge (cont.)Quantization of Charge (cont.)

The charge, q, on any object can be The charge, q, on any object can be expressed as q = Ne where N is expressed as q = Ne where N is some integersome integer

Fundamental SI units 1 C = 1 As Fundamental SI units 1 C = 1 As (ampere second)(ampere second)

Ex: How many electrons are Ex: How many electrons are there in -1 C of charge? there in -1 C of charge?

Solution:Solution:q = Neq = NeSolve for NSolve for N

N = q/eN = q/eN = -1 C/ -1.602 x 10N = -1 C/ -1.602 x 10-19 -19 CC

N = 6.2 x 10N = 6.2 x 101818 electrons electrons

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

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0% 0% 0%0%0%

1.1. TheThe statement contains no errors statement contains no errors

2.2. The statement violates charge The statement violates charge conservationconservation

3.3. The statement violates charge The statement violates charge quantizationquantization

4.4. 2 and 32 and 3

5.5. Cannot be determinedCannot be determined

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

students statement? students statement? (TPS)(TPS)

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0% 0% 0%0%0%

1.1. The statement contains no errorsThe statement contains no errors

2.2. The statement violates charge The statement violates charge conservationconservation

3.3. The statement violates charge The statement violates charge quantizationquantization

4.4. 2 and 32 and 3

5.5. Cannot be determinedCannot be determined

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Insulators and ConductorsInsulators and Conductors

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

Insulators and ConductorsInsulators and Conductors

In an In an InsulatorInsulator all of the electrons are all of the electrons are strongly localized around an strongly localized around an individual atomindividual atom

In a In a ConductorConductor about one electron about one electron per atom is shared by the metal as a per atom is shared by the metal as a whole. This electron is called a whole. This electron is called a free free electronelectron

Two uncharged metal Two uncharged metal spheres are in contact. A spheres are in contact. A negatively charge amber rod negatively charge amber rod is brought near one of the is brought near one of the spheres. Draw a sketch spheres. Draw a sketch showing the charge showing the charge distribution on the spheres.distribution on the spheres.

++

--

The electroscopeThe electroscope

Simple Device Simple Device Used to indicate Used to indicate chargecharge

Two metal foil Two metal foil leaves are leaves are suspended from suspended from the bottom of a the bottom of a conducting rodconducting rod

Electroscope DemonstrationElectroscope Demonstration

What happens when a charged What happens when a charged insulating rod is brought near the insulating rod is brought near the electroscope?electroscope?

What happens when a charge insulating What happens when a charge insulating rod is rubbed against the electroscope?rod is rubbed against the electroscope?

What happens when you bring your What happens when you bring your hand near the electroscope?hand near the electroscope?

What happens when you touch the What happens when you touch the charged electroscope?charged electroscope?

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

(TPS)(TPS)

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1.1. NothingNothing

2.2. It will be repelled It will be repelled from the canfrom the can

3.3. It will be attracted It will be attracted to the canto the can

4.4. It cannot be It cannot be determineddetermined

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

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0% 0%0%0%

1.1. NothingNothing

2.2. It will be repelled It will be repelled from the canfrom the can

3.3. It will be attracted It will be attracted to the canto the can

4.4. It cannot be It cannot be determineddetermined

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Insulators vs. ConductorsInsulators vs. Conductors

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

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

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

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1.1. Nothing since the paper is an Nothing since the paper is an insulatorinsulator

2.2. The paper will be attracted to The paper will be attracted to the rodthe rod

3.3. The paper will be repelled by The paper will be repelled by the rodthe rod

4.4. Cannot be determinedCannot be determined

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How is it possible that the How is it possible that the insulating paper can be insulating paper can be

attracted to the rod?attracted to the rod?

Induced PolarizationInduced Polarization

Bringing a charge near Bringing a charge near an insulator can cause an insulator can cause a slight a slight rearrangement of the rearrangement of the electrons around the electrons around the nucleus of the atomnucleus of the atom

The insulator can then The insulator can then be slightly attracted to be slightly attracted to chargecharge

Ex. Rub a balloon on Ex. Rub a balloon on your head and stick it your head and stick it to the wallto the wall

Coulomb’s LawCoulomb’s Law

Like charges repelLike charges repel Opposite charges Opposite charges

attractattract Force depends Force depends

inversely on the inversely on the square of the square of the distance between distance between the chargesthe charges

Charles CoulombCharles Coulomb

Determined form Determined form of force between of force between charges using a charges using a torsional balancetorsional balance

Coulomb’s LawCoulomb’s Law

rr

qqkF e ˆ

221

q2

rq1

Coulomb’s LawCoulomb’s Law

kkee = 8.99 x 10 = 8.99 x 1099 N m N m22/C/C22

εε00 = 8.85 x 10 = 8.85 x 10-12-12 C C22/Nm/Nm22 (Ch. 19) (Ch. 19)

04

1

ek

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

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1.1. The force is unchangedThe force is unchanged

2.2. The force is doubledThe force is doubled

3.3. The force is halvedThe force is halved

4.4. The force is quadrupledThe force is quadrupled

5.5. The force is reduced by ¼The force is reduced by ¼

6.6. Cannot be determinedCannot be determined

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Two positive charges are separated by a Two positive charges are separated by a known distance. The distance is then known distance. The distance is then

doubled, how does this affect the force?doubled, how does this affect the force?

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0% 0% 0%0%0%0%

1.1. The force is unchangedThe force is unchanged

2.2. The force is doubledThe force is doubled

3.3. The force is halvedThe force is halved

4.4. The force is quadrupledThe force is quadrupled

5.5. The force is reduced by ¼The force is reduced by ¼

6.6. Cannot be determinedCannot be determined

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Ex. Find the magnitude and Ex. Find the magnitude and direction of the force on charge direction of the force on charge

1 shown below.1 shown below.

.25 m

q1 = 2.5 µC

q2 = -3.0 μC

SolutionSolution

F = kqF = kq11qq22/r/r22

= = 8.99 x 108.99 x 1099 Nm Nm22/C/C22 x 2.5 x 10 x 2.5 x 10-6-6 C x 3.0 x 10 C x 3.0 x 10-6-6C/(.25 C/(.25 m)m)22

= .27 N= .27 N

The direction is down.The direction is down.

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

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1.1. It will be largerIt will be larger

2.2. It will be the sameIt will be the same

3.3. It will be smallerIt will be smaller

4.4. Cannot be determined Cannot be determined without first calculating the without first calculating the answeranswer

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

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1.1. The charges must be identicalThe charges must be identical

2.2. The charges are equal in magnitude and The charges are equal in magnitude and of opposite signof opposite sign

3.3. The charges must have the same sign The charges must have the same sign but can have different magnitudesbut can have different magnitudes

4.4. The charges must have opposite signs The charges must have opposite signs but can have different magnitudesbut can have different magnitudes

5.5. Cannot be determinedCannot be determined

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In what ways is Coulomb’s In what ways is Coulomb’s Law similar to Newton’s Law Law similar to Newton’s Law

of Gravity?of Gravity?

What is a significant What is a significant difference Coulomb’s Law difference Coulomb’s Law

and Newton’s Law of Gravityand Newton’s Law of Gravity

Comparison of Newton’s Law of Comparison of Newton’s Law of Gravity and Coulomb’s LawGravity and Coulomb’s Law

rr

qqkF e ˆ

221

rr

mmGF ˆ

221

Inverse Square LawInverse Square Law

Strength is Strength is proportional to proportional to product of “source” product of “source” terms terms

Gravity is always Gravity is always attractiveattractive

Electrostatic Force Electrostatic Force can be both can be both attractive and attractive and repulsiverepulsive

Ex. Find the ratio of the Ex. Find the ratio of the electrostatic force between electrostatic force between

two protons and the two protons and the gravitational force between gravitational force between

them if they are separated by them if they are separated by .25 m..25 m.

SolutionSolution

kgkgkg

mN

CCC

mN

mGm

qqk

mGm

r

r

qqkr

mmG

r

qqk

F

F

e

e

e

g

e

27272

211

19192

29

21

21

21

2

221

221

221

1067.11067.11067.6

10602.110602.11099.8

= 1.24 x 10= 1.24 x 103636

The electrostatic force is much The electrostatic force is much strongerstronger

Protons are like charges and thus in a Protons are like charges and thus in a nucleus of an atom will repel each nucleus of an atom will repel each otherother

Gravity is not strong enough to hold Gravity is not strong enough to hold the nucleus togetherthe nucleus together

Nucleus is held together by short Nucleus is held together by short range force called the “Strong Force”range force called the “Strong Force”

The Electric FieldThe Electric FieldThere’s a core question about There’s a core question about long range forces such as the long range forces such as the electrostatic force or the electrostatic force or the gravitational force.gravitational force.

If two charges are separated by a If two charges are separated by a distance, then how do they distance, then how do they “know” there is a force between “know” there is a force between them.them.

The Electric FieldThe Electric Field

Newton’s answer for Newton’s answer for gravity was that they gravity was that they just do – “Action at a just do – “Action at a distance.”distance.”

Michael Faraday Michael Faraday borrowed an idea from borrowed an idea from magnetism and magnetism and introduced tubes of introduced tubes of forceforce

Definition of the Electric FieldDefinition of the Electric Field

Consider a small positive charge Consider a small positive charge called a called a test charge, test charge, qq00 brought near brought near a positive charge, Qa positive charge, Q

Q q0

Which of the following is the correct force Which of the following is the correct force vector on the test charge qvector on the test charge q00??

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1.1.

2.2.

3.3.

4.4.

5.5. None of the above is correctNone of the above is correct

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

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0% 0%0%0%

1.1. It will be largerIt will be larger

2.2. It will be smallerIt will be smaller

3.3. It will not changeIt will not change

4.4. Cannot be Cannot be determineddetermined

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

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0% 0%0%0%

1.1. It will be largerIt will be larger

2.2. It will be smallerIt will be smaller

3.3. It will not changeIt will not change

4.4. Cannot be Cannot be determineddetermined

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Definition of the Electric FieldDefinition of the Electric Field

The test charge will feel a force The test charge will feel a force anywhere it is placedanywhere it is placed

The “source” charge affects the The “source” charge affects the space around itspace around it

The effect on the space around it is The effect on the space around it is the electric fieldthe electric field

We test the electric field with the test We test the electric field with the test charge, but the electric field is due to charge, but the electric field is due to the source chargethe source charge

Definition of the Electric FieldDefinition of the Electric Field

000

limq

FE

q

Definition of the Electric FieldDefinition of the Electric Field

Electric field is force per chargeElectric field is force per charge The electric field is defined so that The electric field is defined so that

the test charge is positivethe test charge is positive Units – N/CUnits – N/C

Ex. A force 0f .25 N is exerted Ex. A force 0f .25 N is exerted to the left on a test charge of to the left on a test charge of magnitude qmagnitude q00 = 2 = 2 μμC. a) C. a)

Sketch the situation. b) What is Sketch the situation. b) What is the magnitude and direction of the magnitude and direction of the electric field at the location the electric field at the location of the test charge?of the test charge?

Ex. A test charge of magnitude is Ex. A test charge of magnitude is located in an electric field of located in an electric field of magnitude 200 N/C directed to the magnitude 200 N/C directed to the right. a) Sketch the situation. b) right. a) Sketch the situation. b) Find the magnitude and direction of Find the magnitude and direction of the force on the test charge. the force on the test charge.

The Electric Field due to a Point The Electric Field due to a Point ChargeCharge

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

Qq0

r

The Electric Field due to a Point The Electric Field due to a Point ChargeCharge

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

20

r

QqkF

The Electric Field due to a Point The Electric Field due to a Point ChargeCharge

Electric field is Electric field is defined as defined as

E = F/qE = F/q00

So So

2

02

0 1

r

Qk

qr

QqkE

The Electric Field due to a Point The Electric Field due to a Point ChargeCharge

This result is also usually known as This result is also usually known as Coulomb’s lawCoulomb’s law

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

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1.1. To the rightTo the right

2.2. To the leftTo the left

3.3. UpUp

4.4. DownDown

5.5. Cannot be determinedCannot be determined

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

1 2 3 4 5

0% 0% 0%0%0%

1.1. To the rightTo the right

2.2. To the leftTo the left

3.3. UpUp

4.4. DownDown

5.5. Cannot be determinedCannot be determined

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

SuperpositionSuperposition

The electric field at a point due to The electric field at a point due to several charges is the sum of the several charges is the sum of the field due to the individual chargesfield due to the individual charges

Since the electric field is a vector, Since the electric field is a vector, vector algebra must be used to find vector algebra must be used to find the sumthe sum

FPE Exercise on Electric FieldsFPE Exercise on Electric Fields

Electric Fields in Conductors in Electric Fields in Conductors in Electrostatic equilibriumElectrostatic equilibrium

A piece of metal is placed in a A piece of metal is placed in a constant electric field. Sketch a constant electric field. Sketch a picture of what happens to the picture of what happens to the charge in the metalcharge in the metal

When does the charge separation When does the charge separation stop?stop?

Electric Fields in Conductors in Electric Fields in Conductors in Electrostatic equilibriumElectrostatic equilibrium

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