Ch 18 Electric Fields

Chapter 18

Electric Forces &

Electric Fields

AP Learning Objectives

ELECTRICITY AND MAGNETISM Electrostatics

• Charge and Coulomb’s Law

• Students should understand the concept of electric charge, so they can:

• Describe the types of charge and the attraction and repulsion of charges.

• Describe polarization and induced charges.

• Students should understand Coulomb’s Law and the principle of superposition, so they can:

• Calculate the magnitude and direction of the force on a positive or negative charge due to other specified point charges.

• Analyze the motion of a particle of specified charge and mass under the influence of an electrostatic force.

AP Learning Objectives

ELECTRICITY AND MAGNETISM Electric field and electric potential (including point charges)

• Students should understand the concept of electric field, so they can:

• Define it in terms of the force on a test charge.

• Describe and calculate the electric field of a single point charge.

• Calculate the magnitude and direction of the electric field produced by two or more point charges.

• Calculate the magnitude and direction of the force on a positive or negative charge placed in a specified field.

• Interpret an electric field diagram.

• Analyze the motion of a particle of specified charge and mass in a uniform electric field.

Table of Contents

1. The Origin of Electricity

2. Charged Objects and the Electric Force

3. Conductors & Insulators

4. Charging by Contact and by Induction

5. Coulomb’s Law

6. The Electric Field

7. Electric Field Lines

8. The Electric Field Inside a Conductor: Shielding

9. Gauss’ Law (Not AP B)

10. Copiers & Computer Printers (AP?)

Ch 18: Electric Fields

Section 1

The Origin of Electricity

The electrical nature of matter is inherentin atomic structure.

kg10673.1 27pm

kg10675.1 27nm

kg1011.9 31em

C1060.1 19ecoulombs



In nature, atoms are normally found with equal numbers of protons and electrons, so they are electrically neutral.

By adding or removing electrons from matter it will acquire a net electric charge with magnitude equal to e times the number of electrons added or removed, N.

Neq

Example 1 A Lot of Electrons

How many electrons are there in one coulomb of negative charge?

Neq

e

qN

C101.60

C 00.119-

181025.6

18.1.1. A brass key has a net positive charge of +1.92 1016 C. Approximately, how many electrons must be added to the key to make it electrically neutral?

a) 770

b) 960

c) 1200

d) 1800

e) 2100

18.1.2. Can an object carry a charge of 2.4 × 1019 C?

a) Yes, if the object is a conductor.

b) Yes, if the object has electrons or protons.

c) Yes, if the object is an insulator.

d) No, because objects do not have charge.

e) No, because charge is quantized.

18.1.3. The smallest charge on a single particle has been measured to be 1.60 × 1019 C. What can we conclude from the fact that no smaller charges have been measured?

a) Charge is quantized.

b) Electrons are conserved.

c) Charge is conserved.

d) Electrons have the smallest unit of charge.

e) Charge is the same as mass.


Section 2:

Charged Objects and

The Electric Force

Charged Objects

It is possible to transfer electric charge from one object to another?

The body that loses electrons has an excess of positive charge, while the body that gains electrons has an excess of negative charge.

Law of Conservation of Electric Charge

During any process, the net electric charge of an isolated system remains constant (is conserved).

The Electric Force

Like charges repel

Unlike charges attract each other.

Applications: eReaders

18.2.1. Complete the following statement: When a glass rod is rubbed with silk cloth, the rod becomes positively charged as

a) negative charges are transferred from the rod to the silk.

b) negative charges are transferred from the silk to the rod.

c) positive charges are created on the surface of the rod.

d) positive charges are transferred from the silk to the rod.

e) positive charges are transferred from the rod to the silk.

18.2.2. Glass is a very good electrical insulator. How is then possible that a glass rod can be charged by rubbing it with cloth?

a) When the rod is rubbed, it becomes an electrical conductor.

b) Although the rod is an insulator, any excess charge will slowly be conducted away.

c) When the rod is rubbed, the part of the rod that is in contact with the cloth becomes electrically conductive.

d) Because the rod is an insulator, the charge that is transferred to the surface of the rod has difficulty moving.

e) None of the above answers are correct.


Section 3:

Conductors & Insulators

Not only can electric charge exist on an object, but it can also move through and object.

Substances that readily conduct electric charge are called electrical conductors.

Materials that conduct electric charge poorly are called electrical insulators.

Conductors and Insulators


Section 4:

Charging by Contact &

Induction

Charging by contact

Electrons repel on another, so they spread out evenly in a conducting material

Charging by Induction

Bring charged object near a neutral conductor. Opposite charges are attracted, like charges repel Attach grounding wire to far side

• Repelled charge will spread out into the wire Disconnect wire, then remove charged object

Static Cling

The negatively charged rod induces a slight positive surface charge on the plastic or insulators.

Charge can remain on surface and effect other objects

18.4.1. An initially electrically neutral conducting sphere is placed on an insulating stand. A negatively-charged glass rod is brought near, but does not touch the sphere. Without moving the rod, a wire is then attached to the sphere that connects it to earth ground. The wire, then the rod are removed. What is the final charge on the sphere?

a) negative

b) positive

c) neutral

d) It has a fifty percent chance of having a positive charge and a fifty percent chance of having a negative charge.

18.4.2. An initially electrically neutral conducting sphere is placed on an insulating stand. A positively-charged glass rod is brought near, but does not touch the sphere. Without moving the rod, a wire is then attached to the sphere that connects it to earth ground. The wire, then the rod are removed. The sphere is subsequently found to have a negative charge. From the outcome and results of this experiment, what can we conclude about the charging process?

a) Positive charges move freely from the sphere to the ground.

b) Negative charges move freely from the ground to the sphere.

c) Both positive charges and negative charges are moving freely.

d) More experimentation needs to be done before the sign of moving charges can be determined.

18.4.3. Three identical conducting spheres on individual insulating stands are initially electrically neutral. The three spheres are arranged so that they are in a line and touching as shown. A negatively-charged conducting rod is brought into contact with sphere A. Subsequently, someone takes sphere C away. Then, someone takes sphere B away. Finally, the rod is taken away. What is the sign of the final charge, if any, of the three spheres?

A B Ca) + +

b) + +

c) + 0

d) + 0

e)

18.4.4. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere A at the end of the sequence?

a) +Q

b) + Q/2

c) + Q/3

d) + Q/4

e) + Q/8

18.4.5. Consider the conducting spheres labeled A, B, and C shown in the drawing. The spheres are initially charged as shown on the left, then wires are connected and disconnected in a sequence shown moving toward the right. What is the final charge on sphere C at the end of the sequence?

a) +Q

b) + Q/2

c) + Q/3

d) +2Q

e) +3Q


Section 5:

Coulomb’s Law

Coulomb’s Law

2

21

r

qqkF

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2212 mNC1085.8

Coulomb’s Law

The magnitude of the electrostatic force exerted by one point charge on another point charge is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them.

2

21

r

qqF

o called the permittivity of free space

Example 3 A Model of the Hydrogen Atom

In the Bohr model of the hydrogen atom, the electron is in orbit about thenuclear proton at a radius of 5.29x10-11m. Determine the speed of the electron, assuming the orbit to be circular.

2

21

r

qqkF

211

219229

m1029.5

C1060.1CmN1099.8

cmaF

mFrv

N1022.8 8

rmv2

kg109.11

m1029.5N1022.831-

118

sm1018.2 6

Example 4 Three Charges on a Line

Determine the magnitude and direction of the net force on q1.

221

12 r

qqkF

2

3113 r

qqkF

1312 FFF

2

66229

m20.0

C100.4C100.3CmN1099.8 N7.2

2

66229

m15.0

C100.7C100.3CmN1099.8 N4.8

N4.8N7.2 5.7N

18.5.1. Three insulating balls are hung from a wooden rod using thread. The three balls are then individually charged via induction. Subsequently, balls A and B are observed to attract each other, while ball C is repelled by ball B. Which one of the following statements concerning this situation is correct?

a) A and B are charged with charges of opposite signs; and C is charged with charge that has the same sign as B.

b) A and B are charged with charges of the same sign; and C is electrically neutral.

c) A is electrically neutral; and C is charged with charge that has the same sign as B.

d) B is electrically neutral; and C is charged with charge that has the same sign as A.

e) Choices a and c are both possible configurations.

18.5.2. Two objects separated by a distance r are each carrying a charge q. The magnitude of the force exerted on the second object by the first is F. If the first object is removed and replaced with an identical object that carries a charge +4q, what is the magnitude of the electric force on the second object?

a) 4F

b) 2F

c) F

d) F/2

e) F/4

18.5.3. Two objects, A with charge +Q and B with charge +4Q, are separated by a distance r. The magnitude of the force exerted on the second object by the first is F. If the first object is moved to a distance 2r from the second object, what is the magnitude of the electric force on the second object?

a) zero newtons

b) 2F

c) F

d) F/2

e) F/4

18.5.4. Consider the two charges shown in the drawing. Which of the following statements correctly describes the direction of the electric force acting on the two charges?

a) The force on q1 points to the left and the force on q2 points to the left.

b) The force on q1 points to the right and the force on q2 points to the left.

c) The force on q1 points to the left and the force on q2 points to the right.

d) The force on q1 points to the right and the force on q2 points to the right.

18.5.5. Consider the two charges shown in the drawing. Which of the following statements correctly describes the magnitude of the electric force acting on the two charges?

a) The force on q1 has a magnitude that is twice that of the force on q2.

b) The force on q2 has a magnitude that is twice that of the force on q1.

c) The force on q1 has the same magnitude as that of the force on q2.

d) The force on q2 has a magnitude that is four times that of the force on q1.

e) The force on q1 has a magnitude that is four times that of the force on q2.

18.5.6. Two point charges are stationary and separated by a distance R. Which one of the following pairs of charges would result in the largest repulsive force?

a) –2q and +4q

b) –3q and 2q

c) +3q and 2q

d) +2q and +4q

e) –3q and q

18.5.7. A charged particle is located at the center of a uniformly charged hollow sphere. What is the net electrostatic force on the charged particle?

a) The net electrostatic force on the particle will be zero newtons because all of the charges on the sphere are either repelled or attracted to the particle, so they exert no force on it.

b) The net electrostatic force on the particle will be zero newtons because the vector sum of all of the forces on it due to the charges on the sphere is zero, so they exert no force on it.

c) The net electrostatic force on the particle will be the least at the center, but its magnitude will be greater than zero newtons.

d) The net electrostatic force on the particle will be positive if the particle and sphere have opposite signs and negative if they have the same sign.

e) The net electrostatic force on the particle will be negative if the particle and sphere have opposite signs and positive if they have the same sign.

18.5.8. A charged particle is located at a distance R/2 from the center of a uniformly charged hollow sphere of radius R. What is the net electrostatic force on the charged particle?

a) The net electrostatic force on the particle will be zero newtons because the vector sum of all of the forces on it due to the charges on the sphere is zero, so they exert no force on it.

b) The net electrostatic force on the particle will be larger than that which would be exerted if the particle was at the center of the sphere.

c) The net electrostatic force on the particle will be smaller than that which would be exerted if the particle was at the center of the sphere.

d) The net electrostatic force on the particle will be positive if the particle and sphere have opposite signs and negative if they have the same sign.

e) The net electrostatic force on the particle will be negative if the particle and sphere have opposite signs and positive if they have the same sign.

18.5.9. Three plates may be charged positively or negatively or be electrically neutral. In the drawing shown, plate A is attracted by both plates B and C. What occurs if plates B and C are brought close together?

a) B and C would be attracted to one another.

b) B and C would be repelled by one another.

c) B and C would exert no force on each other.

d) There is too little information given to make a conclusion.

18.5.10. Three plates may be charged positively or negatively or be electrically neutral. In the drawing shown, plate A is repelled by both plates B and C. What occurs if plates B and C are brought close together?

a) B and C would be attracted to one another.

b) B and C would be repelled by one another.

c) B and C would exert no force on each other.

d) There is too little information given to make a conclusion.

18.5.11. As shown in the drawing, a positively charged particle remains stationary between particles A and B. The positively charged particle is one-quarter the distance between the two other particles, as shown. What can be concluded from the situation?

a) The charge on A must be four times as large as the charge on B.

b) The charge on A must be sixteen times as large as the charge on B.

c) The charge on A must be one-half as large as the charge on B.

d) The charge on A must be one-fourth as large as the charge on B.

e) The charge on A must be one-sixteenth as large as the charge on B.

18.5.12. Two particles are separated by a distance d. Particle A has a charge +Q and particle B has a charge +3Q. At what distance from particle A along the line connecting particles A and B would you place a third charged particle such that no net electrostatic force acts on it?

a) d/3

b) d/2

c) d/4

d) d/6

e) d/9


Section 6:

The Electric Field

Electric Fields

It is often easier to think of natural forces as acting on an object, than analyzing the force itself

Gravity

• We use F = mg much more that we use F = Gm1m2 /r2

The same is true for Electric forces We often look out how Coulomb’s law effects a small charge

• Just as with gravity we look at how a planet effects a small mass

We call the effect of a charge of a group of charges the Electric Field

We look at the effect of the electric forces present on a small positive charge

The positive charge experiences a force which is the vector sum of the forces exerted by the charges on the rod and the two spheres.

This test charge should have a small magnitude so it doesn’t affect the other charge.

Electric Fields

Example 6 A Test Charge

The positive test charge has a magnitude of 3.0x10-8C and experiences a force of 6.0x10-8N.

(a) Find the force per coulomb that the test chargeexperiences.

(b) Predict the force that a charge of +12x10-8Cwould experience if it replaced the test charge.

oq

F(a)

(b) C100.12CN0.2 8F

C100.3

N100.68

8

CN0.2

N1024 8

The electric field that exists at a point is the electrostatic force experiencedby a small test charge placed at that point divided by the charge itself:

oq

FE

SI Units of Electric Field: newton per coulomb (N/C)

Definition of Electric Field

It is the surrounding charges that create the electric field at a given point.

Example 7 An Electric Field Leads to a Force

The charges on the two metal spheres and the ebonite rod create an electricfield at the spot indicated. The field has a magnitude of 2.0 N/C. Determinethe force on the charges in (a) and (b)

EqF o(a)

(b) EqF o

C100.18CN0.2 8 N1036 8

C100.24CN0.2 8 N1048 8

Electric fields from different sourcesadd as vectors.

Electric Force in 2D

Example 10 The Electric Field of a Point Charge

The isolated point charge of q=+15μC isin a vacuum. The test charge is 0.20m to the right and has a charge qo=+15μC.

Determine the electric field at point P.

2

21

r

qqkF

2

66229

m20.0

C1015C1080.0CmN1099.8 F

oq

FE

N7.2

C100.80

N 7.26-

CN104.3 6

2r

qkE

The electric field does not depend on the test charge.

o

o

qr

qqk

12

Point charge qo:

The Electric Field Equation

oq

FE Test charge

Example 11 The Electric Fields from Separate Charges May Cancel

Two positive point charges, q1=+16μC and q2=+4.0μC are separated in avacuum by a distance of 3.0m. Find the spot on the line between the chargeswhere the net electric field is zero.

2r

qkE

2

6

2

6

m0.3

C100.4C1016

dk

dk

21 EE

22m0.30.2 dd

m 0.2d

Conceptual Example 12 Symmetry and the Electric Field

Point charges are fixes to the corners of a rectangle in twodifferent ways. The charges have the same magnitudesbut different signs.

Consider the net electric field at the center of the rectanglein each case. Which field is stronger?

Parallel platecapacitor A

qE

o

2212 mNC1085.8

charge density

The Parallel Plate Capacitor

o

18.6.1. A positively-charged object is released from rest in a region containing a uniform electric field. Which one of the following statements concerning the subsequent motion of the object is correct?

a) The object will remain motionless.

b) The object will accelerate to some constant speed and move in the direction of the electric field.

c) The object will accelerate to some constant speed and move in the direction opposite that of the electric field.

d) The object will experience a constant acceleration and move in the direction of the electric field.

e) The object will experience a constant acceleration and move in the direction opposite that of the electric field.

18.6.2. Two negatively-charged objects are located on the x axis, equally distant from the origin as shown. Consider the electric field at the point P1. How will that electric field change if a third object with a charge +q is placed at point P2? Note: the point P2 is the same distance from the origin as the point P1 and the magnitude of each of the charges is the same.

a) The magnitude of the electric field will decrease by 25%.

b) The magnitude of the electric field will increase by 25%.

c) The magnitude of the electric field will decrease by 50%.

d) The magnitude of the electric field will increase by 50%.

e) The magnitude of the electric field will increase by 100%.

18.6.3. At a distance of one centimeter from an electron, the electric field strength has a value E. At what distance is the electric field strength equal to E/2?

a) 0.5 cm

b) 1.4 cm

c) 2.0 cm

d) 3.2 cm

e) 4.0 cm


Section 7:

Electric Field Lines

Electric field lines or lines of force provide a map of the electric field in the space surrounding electric charges.


They show where a test charge (+) would be pushed.

Electric field lines are always directed away from positive charges andtoward negative charges.


-

Electric field lines always begin on a positive charge and end on a negative charge and do not stop in midspace.


The number of lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.


+ -


+ +

Conceptual Example 13 Drawing ElectricField Lines

There are three things wrong with part (a) of the drawing. What are they?

Number of field lines should be

proportional to the charge:

• 2q should have double the

lines of each of the q’s

Field lines cannot cross

Field lines will almost never be

parallel lines for point charges

18.7.1. Consider the drawing, where the solid lines with arrows represent the electric field due to the charged object. An electron is placed at the point P and released at rest. Which of the following vectors represents the direction of the force, if any, on the electron?

18.7.2. The plates of a parallel plate capacitor are connected to a battery. Each plate has an area A. One plate has a net charge of +q. What is the magnitude of the electric field outside the capacitor? Note: ignore end effects at the edges of the capacitor.

a)

b)

c) Aq

d) q

e) zero N/C

A

q 0

0A

q

18.7.3. An electron traveling horizontally to the right enters a region where a uniform electric field is directed downward. What is the direction of the force exerted on the electron once it has entered the field?

a) upward

b) downward

c) to the right

d) to the left

e) The force is zero newtons.

18.7.4. Consider the electric field lines shown in the drawing. Which of the following statements correctly describes this situation?

a) The electric field is due to a positively charged particle.

b) The electric field is due to a negatively charged particle.

c) The electric field is due to a positively charged particle and a negatively charged particle.

d) The electric field is due to particles that are both charged either positively or negatively.

18.7.5. Consider the electric field lines shown in the drawing. Which of the following statements correctly describes this situation?

a) A and B are both positively charged particles.

b) A and B are both negatively charged particles.

c) A is a positively charged particle and B is a negatively charged particle.

d) B is a positively charged particle and A is a negatively charged particle.

18.7.6. Four charges are located on the corners of a square as shown in the drawing. What is the direction of the net electric field at the point labeled P?

a) toward the upper left corner of the square

b) toward the middle of the right side of the square

c) toward the middle of the bottom side of the square

d) toward the lower right corner of the square

e) There is no direction. The electric field at P is zero N/C.

P

18.7.7. Four charges are located on the corners of a square as shown in the drawing. What is the direction of the net electric field at the point labeled P?

a) toward the upper left corner of the square

b) toward the middle of the right side of the square (directly right)

c) toward the middle of the bottom side of the square (directly down)

d) toward the lower right corner of the square

e) There is no direction. The electric field at P is zero N/C.

P

18.7.8. A positively charged object is located to the left of a negatively charged object as shown. Electric field lines are shown connecting the two objects. The five points on the electric field lines are labeled A, B, C, D, and E. At which one of these points would a test charge experience the largest force?

a) A

b) B

c) C

d) D

e) E

18.7.9. A positively charged object is located to the left of a negatively charged object as shown. Electric field lines are shown connecting the two objects. The five points on the electric field lines are labeled A, B, C, D, and E. At which one of these points would a test charge experience the smallest force?

a) A

b) B

c) C

d) D

e) E

18.7.10. A positively charged object is located to the left of a negatively charged object as shown. Electric field lines are shown connecting the two objects. The five points on the electric field lines are labeled A, B, C, D, and E. At which one of these points would a test charge experience the largest force?

a) A

b) B

c) C

d) D

e) E

18.7.11. A positively charged object is located to the left of a negatively charged object as shown. Electric field lines are shown connecting the two objects. The five points on the electric field lines are labeled A, B, C, D, and E. At which one of these points would a test charge experience the smallest force?

a) A

b) B

c) C

d) D

e) E


Section 8:

The Electric Field Inside

a Conductor: Shielding

Charges Inside a Conductor

Electrons will repel each other equally.

At equilibrium under electrostatic

conditions, any excess charge resides

on the surface of a conductor.

At equilibrium under electrostatic

conditions, the electric field is zero at any

point within a conducting material.

The conductor shields any charge within

it from electric fields created outside the

conductor.

The electric field just outside the surface of a conductor is perpendicular to the surface at equilibrium under electrostatic conditions.

Field Lines Approaching a Conductor

Conceptual Example 14 A Conductor in an Electric Field

A charge is suspended at the center ofa hollow, electrically neutral, spherical conductor. Show that this charge induces

(a) a charge of –q on the interior surface and

(b) a charge of +q on the exterior surface of the conductor.

18.8.1. The drawing shows a hollow conducting sphere with a net positive charge uniformly distributed over its surface. A small negatively-charged object has been brought near the sphere as shown. What is the direction of the electric field at the center of the sphere?

a) There is no electric field at the center of the sphere.

b) to the left

c) to the right

d) upward

e) downward


Section 9:

Gauss’ Law

Not AP B

22 4 rqrkqE o

oAqE

o

qEA

EAE flux, Electric

Gauss’ Law

AEE cos

Gauss’ Law

GAUSS’ LAW

The electric flux through a Gaussiansurface is equal to the net charge enclosed in that surface divided bythe permittivity of free space:

o

QAE

cos

SI Units of Electric Flux: N·m2/C

Example 15 The Electric Field of a Charged Thin Spherical Shell

A positive charge is spread uniformly over the shell. Find the magnitude of the electric field at any point (a) outside the shell and (b) inside theshell.

o

QAE

cos

24

0coscos

rEAE

AEAEE

o

QrE

24

o

QrE

24

(a) Outside the shell, the Gaussian surface encloses all of the charge.

or

qE

24

(b) Inside the shell, the Gaussian surface encloses no charge.

0E

Example 15 cont’d

18.9.1. Gauss’ law may be written:

Which of the following statements concerning the charge q is true?

a) The charge q is the sum of all charges.

b) The charge q is the sum of all charges on the Gaussian surface.

c) The charge q is the sum of all charges inside the Gaussian surface.

d) The electric field due to q is zero inside the Gaussian surface.

0 q

AEE )cos(

18.9.2. When you calculate the electric flux through a Gaussian surface, of what are you determining the flow through the surface?

a) charge

b) electric current

c) electric energy

d) electric field

e) None of the above answers are correct.

18.9.3. Consider the five situations shown. Each one contains either a charge q or a charge 2q. A Gaussian surface surrounds the charged particle in each case. Considering the electric flux through each of the Gaussian surfaces, which of the following comparative statements is correct?

a)

b)

c)

d)

e)

2 4 1 3

1 3 2 4

2 1 4 3

3 4 2 1

4 3 2 1

18.9.4. When a particle with a charge Q is surrounded by a spherical Gaussian surface, the electric flux through the surface is S. Consider what would happen if the particle was surrounded by a cylindrical Gaussian surface or a Gaussian cube. How would the fluxes through the cylindrical Cyl and cubic Cubic surfaces compare to S?

a)

b)

c)

d)

e)

S Cubic Cyl

S Cyl Cubic

S Cyl Cubic

S Cubic Cyl

S Cubic Cyl

18.9.5. A spherical Gaussian surface of radius R is surrounding a particle with a net charge q. If the spherical Gaussian surface is replaced by a cube, under what conditions would the electric flux through the sides of the cube be the same as through the spherical surface?

a) under all conditions

b) if the sides of the cube are of length R

c) if the sides of the cube are of length 2R

d) if the diagonals of the cube are of length 2R

e) under no conditions


Section 10:

Copiers & Computer Printers

Ch 18 Electric Fields

Education

Transcript of Ch 18 Electric Fields