20100109120109ch21a

2005 Pearson Education South Asia Pte Ltd

Chapter Objectives

• The nature of electric charge• Interactions of electric charges• Coulomb’s law• The concept of electric field


Chapter Outline

1. Electric Charge

2. Conductors, Insulators, and Induced Charges

3. Coulomb’s Law

4. Electric Field and Electric Forces

5. Electric-Field Calculations

6. Electric Field Lines


21.1 Electric Charge

• Electric charge is a fundamental attribute of particles.

• Electrostatics are defined as the interactions between electric charges that are at rest (or nearly so).

• The figure shows some experiments used to demonstrate electrostatics.



Fig. 21.1


The Triboelectric Series

No! No!

When two of the following materials are rubbed together under ordinary circumstances, the top listed material becomes positively charged and the lower listed material becomes

negatively charged.

MORE POSITIVE rabbit's fur

glass mica nylon wool

cat's fur silk

paper cotton wood

acrylic cellophane tape

polystyrene polyethylene

rubber balloon saran wrap

MORE NEGATIVE

No! No!


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.



• Electrostatics experiments show that there are exactly two kinds of electric charge, negative and positive.

• Two positive charges or two negative charges repel each other. A positive charge and a negative charge attract each other.



Electric Charge and the Structure of Matter• The atomic structure consists of three particles: the

negatively charged electron, the positively charged proton, and the uncharged neutron.

• Protons and neutrons make up the nucleus while electrons orbit it from a distance.

• The figure shows how changes in the atomic structure of lithium determines its net electric charge.



Electric Charge and the Structure of Matter

Fig. 21.4



Electric Charge and the Structure of Matter• Atomic number is defined as the number of

protons or electrons in a neutral atom of an element.

• A positive ion is formed by removing one or more electrons from an atom; a negative ion is one that has gained one or more electrons. This process is called ionization.



Electric Charge and the Structure of Matter• When the total number of protons equals the total

number of electrons in a macroscopic body, its total charge is zero and the body as a whole is electrically neutral.

• When we speak of the charge of a body, we always mean its net charge.



Electric Charge and the Structure of Matter• The Principle of Conservation of Charge: The

algebraic sum of all the electric charges in any closed system is constant.

• In any charging process, charge is not created or destroyed but merely transferred from one body to another.



Electric Charge and the Structure of Matter• The magnitude of charge of the electron or

proton is a natural unit of charge.

• Every observable amount of electric charge on any macroscopic body is always either zero or an integer multiple (positive or negative) of this basic unit, the electron charge – quantization of charge.


21.2 Conductors, Insulators, and Induced Charges

• Conductors of electricity are materials that permit electric charge to move easily through them; Insulators do not.

• Most metals are good conductors while most non-metals are insulators. Semiconductors are intermediate in their properties between good conductors and good insulators.

• The figure shows the use of copper as a good conductor, and glass and nylon as good insulators.



• Charging by induction is the process in which a charged body can give another body a charge of opposite sign without losing any of its own charge.

• The figure shows the charging of a metal sphere by induction.



Fig. 21.5



Fig. 21.6



• Excess charges that develop in the region of a body during electrical induction are called induced charges.

• The earth is a conductor, and it is so large that it can act as an infinite source of extra electrons or sink of unwanted electrons. The charge it acquires via induction will be equal and opposite to the charge remaining on the electrically induced body.


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 rod and wire are then removed simultaneously. 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.


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)


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 thesame 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.



• In a metallic conductor, the mobile charges are always negative electrons.

• In ionic solutions and ionized gases, both positive and negative charges are mobile.



• A charged body can exert forces even on objects that are not charged themselves – induced-charge effect.

• This is due to polarization, in which a charged object of either sign exerts an attractive force on an uncharged (neutral) insulator.


• Coulomb’s Law states that:

The magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• The directions of the forces the two charges exert on each other are always along the line joining them, as shown in the figure.

21.3 Coulomb’s Law



Fig. 21.9



• Coulomb’s Law is usually written as:

where

229

0

22120

/100.94

1

/10854.8

CmN

mNC



• The most fundamental unit of charge is the magnitude of the charge of an electron or proton, denoted by e, where

e = 1.602176462(63) x 10-19 C


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.


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.


Example 21.1 Electric force versus gravitational force

An particle (“alpha”) is the nucleus of a helium atom. It has a mass of m = 6.66 x 10-27 kg and a charge q = +2e = 3.2 x 10-19 C. Compare the force of the electric repulsion between two particles with the force of gravitational attraction between them.


Example 21.1 (SOLN)

Identify and Set Up

The magnitude Fe of the electric force is given by Eq. (21.2),

The magnitude Fg of the gravitational force is given by Eq. (12.1),

We compare these two magnitudes by calculating their ratio.

2

2

041

r

qFe

2

2

r

mGFg


Example 21.1 (SOLN)

Execute

The ratio of the electric force to the gravitational force is

35

227

219

2211

229

2

2

0

101.3

)1064.6(

)102.3(

/1067.6

/100.94

1

kg

C

kgmN

CmN

m

qGF

F

g

e


Example 21.1 (SOLN)

Evaluate

This astonishingly large number shows that the gravitational force in this situation is completely negligible in comparison to the electric force. This is always true for interactions of atomic and subatomic particles. (Notice that this result doesn’t depend on the distance r between the two particles.) But within objects the size of a person or a planet, the positive and negative charges are nearly equal in magnitude, and the net electric force is usually much smaller than the gravitational force.


Example 21.2 Force between two point charges

Two point charges, q1 = +25 nC and q2 = -75 nC, are separated by a distance of 3.0 cm (Fig. 21.10a). Find the magnitude and direction of a) the electric force that q1 exerts on q2; b) the electric force that q2 exerts on q1.


Example 21.2 (SOLN)

Identify and Set Up

We use Coulomb’s law, Eq. (21.2), to calculate the magnitude of the force that each particle exerts on the other. The problem asks us for the force on each particle due to the other particle, so we use Newton’s third law.


Example 21.2 (SOLN)

Execute

a) Converting charge to coulombs and distance to meters, the magnitude of the force that q1 exerts on q2 is

N

m

CCCmN

r

qqF on

019.0

)030.0(

|)1075)(1025(|)/100.9(

||4

1

2

99229

221

021


Example 21.2 (SOLN)

Since the two charges have opposite signs, the force is attractive; that is, the force that acts on q2 is directed toward q1 along the line joining the two charges, as shown in Fig. 21.10b.

Fig. 21.10


Example 21.2 (SOLN)

b) Remember that Newton’s third law applies to the electric force. Even though the charges have different magnitudes, the magnitude of the force that q2 exerts on q1 is the same as the magnitude of the force that q1 exerts on q2:

Newton’s third law also states that the direction of the force that q2 exerts on q1 is exactly opposite the direction of the force that q1 exerts on q2 ; this is shown in Fig. 21.10c.

NF on 019.012


Example 21.2 (SOLN)

Evaluate

Note that the force on q1 is directed toward q2, as it must be, since charges of opposite sign attract each other.


Example 21.3 Vector addition of electric forces on a line

Two point charges are located on the positive x-axis of a coordinate system (Fig. 21.11a). Charge q1 = 1.0 nC is 2.0 cm from the origin, and charge q2 = -3.0 nC is 4.0 cm from the origin. What is the total force exerted by these two charges on a charge q3 = 5.0 nC located at the origin? Gravitational forces are negligible.


Example 21.3 (SOLN)

Identify

Here there are two electric forces acting on the charge q3, and we must add these forces to find the total force.


Example 21.3 (SOLN)

Set Up

Figure 21.11a shows the coordinate system. Our target variable is the net electric force exerted on charge q3 by the other two charges. This is the vector sum if the forces due to q1 and q2 individually. Fig. 21.11


Example 21.3 (SOLN)

Execute

Figure 21.11b is a free-body diagram for charge q3. Note that q3 is repelled by q1 (which has the same sign) and attracted to q2 (which has the opposite sign).


Example 21.3 (SOLN)

Execute

Converting charge to coulombs and distance to meters, we use Eq. (21.2) to find the magnitude F1 on 3 of the force of q1 on q3:

This force has a negative x-component because q3 is repelled (that is, pushed in the negative x-direction) by q1.

NN

m

CCCmN

r

qqF on

1121012.1

)020.0(

|)100.5)(100.1(|)/100.9(

||4

1

4

2

99229

231

031


Example 21.3 (SOLN)

Execute

The magnitude F2 on 3 of the force of q2 on q3 is

This force has a positive x-component because q3 is attracted (that is, pulled in the positive x-direction) by q2.

NN

m

CCCmN

r

qqF on

84104.8

)040.0(

|)100.5)(100.3(|)/100.9(

||4

1

5

2

99229

232

032


Example 21.3 (SOLN)

Execute

The sum of the x-components is

There are no y- or z- components. Thus the total force on q3 is directed to the left, with magnitude 28 N = 2.8 x 10-5 N.

NNNFx 2884112


Example 21.3 (SOLN)

Evaluate

To check the magnitudes of the individual forces, note that q2 has three times as much charge (in magnitude) as q1 but is twice as far from q3. From

Eq. (21.2) this means that F2 on 3 must be 3/22 = as

large as F1 on 3. Indeed, our results show that this ratio is (84 N)/(112 N) = 0.75. The direction of the net force also makes sense: is opposite to and has a larger magnitude than , so the net force is in the direction of .

43

31onF

32onF

31onF


Example 21.4 Vector addition of electric forces in a plane

In Fig. 21.12, two equal positive point charges q1 = q2 = 2.0 C interact with a third point charge Q = 4.0 C. Find the magnitude and direction of the total (net) force on Q.

Fig. 21.12


Example 21.4 (SOLN)

Identify and Set Up

As in Example 21.3, we have to compute the force each charge exerts on Q and then find the vector sum of the forces. The easiest way to do this is to use components.


Example 21.4 (SOLN)

Execute

Figure 21.12 shows the force on Q due to the upper charge q1. From Coulomb’s law the magnitude F of this force is

Nm

CCCmNF Qon

29.050.0

)100.2)(100.4()/100.9(

2

66229

1


Example 21.4 (SOLN)

Execute

The angle is below the x-axis, so the components of this force are given by

Nmm

NFF

Nmm

NFF

QonyQon

QonxQon

17.050.030.0

)29.0(sin)()(

23.050.040.0

)29.0(cos)()(

11

11


Example 21.4 (SOLN)

Execute

The lower charge q2 exerts a force with the same magnitude but at an angle above the x-axis. From symmetry we see that its xcomponent is the same as that due to the upper charge, but its ycomponent has the opposite sign. So the components of the total force on Q are

The total force on Q is in the +x-direction, with magnitude 0.46 N.

F

017.017.0

46.023.023.0

NNF

NNNF

y

x


Example 21.4 (SOLN)

Evaluate

The total force on Q is in a direction that points neither directly away from q1 nor directly away from q2. Rather, this direction is a compromise that points away from the system of charges q1 and q2. Can you see that the total force would not be in the +x-direction if q1 and q2 were not equal or if the geometrical arrangement of the charges were not so symmetrical?

20100109120109ch21a

Documents

Transcript of 20100109120109ch21a