Solution Manual for Physics for Scientists & Engineers with Modern Physics, Global
Edition (Pearson, 2024) Volume 2, 5th edition Isbn: 9781292440354 Douglas C. Giancoli
Chapters 21 - 35
,CHAPTER 21: Electric Charge and Electric Field
Responses to Questions
1. Suspend a plastic ruler by a thread and then rub it with a cloth. As shown in Fig. 21–2a, the ruler is
negatively charged. Now bring the charged comb close to the ruler. If the ruler is repelled by the
comb, then the comb is negatively charged. If the ruler is attracted by the comb, then the comb is
positively charged.
2. The shirt or blouse becomes charged as a result of being tossed about in the dryer and rubbing
against the dryer sides and other clothes. When you put on the charged object (shirt), it causes
charge separation within the molecules of your skin (see Fig. 21–9), which results in attraction
between the shirt and your skin.
3. Fog or rain droplets tend to form around ions because water is a polar molecule, with a positive
region and a negative region. The charge centers on the water molecule will be attracted to the ions
or electrons, since opposite charges attract.
4. See also Fig. 21–9 in the text. The negatively
charged electrons in the paper are attracted to
the positively charged rod and move towards
it within their molecules. The attraction occurs
because the negative charges in the paper are
closer to the positive rod than are the positive
charges in the paper, and therefore the
attraction between the unlike charges is
greater than the repulsion between the like charges.
5. A plastic ruler that has been rubbed with a cloth is charged. When brought near small pieces of
paper, it will cause separation of charge (polarization) in the bits of paper, which will cause the
paper to be attracted to the ruler. A small amount of charge is able to create enough electric force to
be stronger than gravity. Thus the paper can be lifted.
On a humid day this is more difficult because the water molecules in the air are polar. Those polar
water molecules will be attracted to the ruler and to the separated charge on the bits of paper,
partially neutralizing the charges and thus reducing the attraction.
6. The net charge on a conductor is the sum of all of the positive and negative charges in the conductor.
If a neutral conductor has extra electrons added to it, then the net charge is negative. If a neutral
conductor has electrons removed from it, then the net charge is positive. If a neutral conductor has
the same amount of positive and negative charge, then the net charge is zero.
The “free charges” in a conductor are electrons that can move about freely within the material
because they are only loosely bound to their atoms. The “free electrons” are also referred to as
“conduction electrons.” A conductor may have a zero net charge but still have substantial free
charges.
,Chapter 21 Electric Charge and Electric Field
7. Most of the electrons are strongly bound to nuclei in the metal ions. Only a few electrons per atom
(usually one or two) are free to move about throughout the metal. These are called the “conduction
electrons.” The rest are bound more tightly to the nucleus and are not free to move. Furthermore, in
the cases shown in Figs. 21–7 and 21–8, not all of the conduction electrons will move. In Fig. 21–7,
electrons will move until the attractive force on the remaining conduction electrons due to the
incoming charged rod is balanced by the repulsive force from electrons that have already gathered at
the left end of the neutral rod. In Fig. 21–8, conduction electrons will be repelled by the incoming
rod and will leave the stationary rod through the ground connection until the repulsive force on the
remaining conduction electrons due to the incoming charged rod is balanced by the attractive force
from the net positive charge on the stationary rod.
8. The electroscope leaves are connected together at the top. That connection can be
modeled as a tension force. The horizontal component of this tension force
balances the electric force of repulsion. The vertical component of the tension
force balances the weight of the leaves.
9. The balloon has been charged. The excess charge on the balloon is able to polarize the water
molecules in the stream of water, similar to Fig. 21–9. This polarization results in a net attraction of
the water towards the balloon, so the water stream curves towards the balloon.
10. (a) When the leaves are charged by induction, no additional charge is added to the leaves. If the
charged rod is near the top of the electroscope it repels charge onto the leaves causing them to
separate as in Fig. 21–11(a). When the rod is removed the charge returns to its initial
equilibrium position and the leaves come back together.
(b) When the leaves are charged by conduction, positive charge is placed onto the electroscope
from the rod causing the leaves to separate. When the rod is removed, the charge remains on
the electroscope and the leaves remain separated. If not all of the excess charge leaves the rod,
then when the rod is removed, the leaves might come back together slightly from their
maximum deflection.
(c) Yes. The electroscope has a negative charge on the top sphere and on the leaves. Therefore the
electroscope has a total net negative charge, so it must have been charged by conduction.
11. Coulomb’s law and Newton’s law are very similar in form. When expressed in SI units, the
magnitude of the constant in Newton’s law is very small, while the magnitude of the constant in
Coulomb’s law is quite large. Newton’s law says the gravitational force is proportional to the
product of the two masses, while Coulomb’s law says the electrical force is proportional to the
product of the two charges. Newton’s law only produces attractive forces, since there is only one
kind of gravitational mass. Coulomb’s law produces both attractive and repulsive forces, since there
are two kinds of electrical charge.
12. The gravitational force between everyday objects on the surface of the Earth is extremely small.
(Recall the value of G: 6.67 1011 N m2 kg2 . ) Consider two objects sitting on the floor near each
other. They are attracted to each other, but the maximum force of static friction for each is much
greater than the gravitational force each experiences from the other, and so they don’t move. Even in
an absolutely frictionless environment, the acceleration resulting from the gravitational force would
be so small that it would not be noticeable in a short time frame. We are aware of the gravitational
force between objects if at least one of them is very massive, as in the case of the Earth and satellites
or the Earth and you.
, Physics for Scientists & Engineers wͅith Modern Physics, 5e, Global Edition Instructor Solutions Manual
The electric force between two objects is typically zero or very close to zero because ordinary
objects are typically neutral or very close to neutral. We are aware of electric forces between objects
when the objects are charged. An example is the electrostatic force (static cling) between pieces of
clothing when you pull the clothes out of the dryer.
13. Coulomb observed experimentally that the force between two charged objects is directly
proportional to the charge on each one. For example, if the charge on either object is tripled, then the
force is tripled. This is not in agreement with a force that is proportional to the sum of the charges
instead of to the product of the charges. Secondly, if two equal but opposite charges are placed near
to each other, they produce an attractive force. But the “sum” version would say the net force is 0 in
such a case. Also, a charged object is not attracted to or repelled from a neutral insulating object. If
the numerator in Coulomb’s law were proportional to the sum of the charges, then there would be a
force between a neutral object and a charged object, because the their total charge would not be 0.
14. Assume that the charged plastic ruler has a negative charge residing on its surface. That charge
polarizes the charge in the neutral paper, producing a net attractive force. When the piece of paper
then touches the ruler, the paper can get charged by contact with the ruler, gaining a net negative
charge. Then, since like charges repel, the paper is repelled by the comb.
15. The test charge creates its own electric field. The measured electric field is the sum of the original
electric field plus the field of the test charge. By making the test charge small, the field that it causes
is small. Therefore the actual measured electric field is not much different than the original field.
Also, if the test charges are large, their fields might significantly re-distribute the charges causing the
original field, and then the measurement would not represent the field of the original configuration of
charges.
16. When determining an electric field, it is best, but not required, to use a positive test charge. A
negative test charge would be fine for determining the magnitude of the field. But the direction of the
electrostatic force on a negative test charge will be opposite to the direction of the electric field. The
electrostatic force on a positive test charge will be in the same direction as the electric field. In order
to avoid confusion, it is better to use a positive test charge. If we used a negative test charge but
wanted to have the same result for the electric field, we would have to define E F q, q 0.
17. See Fig. 21–35(b). A diagram of the electric field lines around two negative charges would be just
like this diagram except that the arrows on the field lines would point towards the charges instead of
away from them. The distance between the charges is l.
l
18. The electric field will be strongest to the right of the positive charge (between the two charges) and
weakest to the left of the positive charge. To the right of the positive charge, the contributions to the
field from the two charges point in exactly the same direction, and therefore add. To the left of the
positive charge, the contributions to the field from the two charges point in exactly opposite
directions, and therefore subtract. Note that this should be confirmed by the density of field lines in
Fig. 21–35a.
Edition (Pearson, 2024) Volume 2, 5th edition Isbn: 9781292440354 Douglas C. Giancoli
Chapters 21 - 35
,CHAPTER 21: Electric Charge and Electric Field
Responses to Questions
1. Suspend a plastic ruler by a thread and then rub it with a cloth. As shown in Fig. 21–2a, the ruler is
negatively charged. Now bring the charged comb close to the ruler. If the ruler is repelled by the
comb, then the comb is negatively charged. If the ruler is attracted by the comb, then the comb is
positively charged.
2. The shirt or blouse becomes charged as a result of being tossed about in the dryer and rubbing
against the dryer sides and other clothes. When you put on the charged object (shirt), it causes
charge separation within the molecules of your skin (see Fig. 21–9), which results in attraction
between the shirt and your skin.
3. Fog or rain droplets tend to form around ions because water is a polar molecule, with a positive
region and a negative region. The charge centers on the water molecule will be attracted to the ions
or electrons, since opposite charges attract.
4. See also Fig. 21–9 in the text. The negatively
charged electrons in the paper are attracted to
the positively charged rod and move towards
it within their molecules. The attraction occurs
because the negative charges in the paper are
closer to the positive rod than are the positive
charges in the paper, and therefore the
attraction between the unlike charges is
greater than the repulsion between the like charges.
5. A plastic ruler that has been rubbed with a cloth is charged. When brought near small pieces of
paper, it will cause separation of charge (polarization) in the bits of paper, which will cause the
paper to be attracted to the ruler. A small amount of charge is able to create enough electric force to
be stronger than gravity. Thus the paper can be lifted.
On a humid day this is more difficult because the water molecules in the air are polar. Those polar
water molecules will be attracted to the ruler and to the separated charge on the bits of paper,
partially neutralizing the charges and thus reducing the attraction.
6. The net charge on a conductor is the sum of all of the positive and negative charges in the conductor.
If a neutral conductor has extra electrons added to it, then the net charge is negative. If a neutral
conductor has electrons removed from it, then the net charge is positive. If a neutral conductor has
the same amount of positive and negative charge, then the net charge is zero.
The “free charges” in a conductor are electrons that can move about freely within the material
because they are only loosely bound to their atoms. The “free electrons” are also referred to as
“conduction electrons.” A conductor may have a zero net charge but still have substantial free
charges.
,Chapter 21 Electric Charge and Electric Field
7. Most of the electrons are strongly bound to nuclei in the metal ions. Only a few electrons per atom
(usually one or two) are free to move about throughout the metal. These are called the “conduction
electrons.” The rest are bound more tightly to the nucleus and are not free to move. Furthermore, in
the cases shown in Figs. 21–7 and 21–8, not all of the conduction electrons will move. In Fig. 21–7,
electrons will move until the attractive force on the remaining conduction electrons due to the
incoming charged rod is balanced by the repulsive force from electrons that have already gathered at
the left end of the neutral rod. In Fig. 21–8, conduction electrons will be repelled by the incoming
rod and will leave the stationary rod through the ground connection until the repulsive force on the
remaining conduction electrons due to the incoming charged rod is balanced by the attractive force
from the net positive charge on the stationary rod.
8. The electroscope leaves are connected together at the top. That connection can be
modeled as a tension force. The horizontal component of this tension force
balances the electric force of repulsion. The vertical component of the tension
force balances the weight of the leaves.
9. The balloon has been charged. The excess charge on the balloon is able to polarize the water
molecules in the stream of water, similar to Fig. 21–9. This polarization results in a net attraction of
the water towards the balloon, so the water stream curves towards the balloon.
10. (a) When the leaves are charged by induction, no additional charge is added to the leaves. If the
charged rod is near the top of the electroscope it repels charge onto the leaves causing them to
separate as in Fig. 21–11(a). When the rod is removed the charge returns to its initial
equilibrium position and the leaves come back together.
(b) When the leaves are charged by conduction, positive charge is placed onto the electroscope
from the rod causing the leaves to separate. When the rod is removed, the charge remains on
the electroscope and the leaves remain separated. If not all of the excess charge leaves the rod,
then when the rod is removed, the leaves might come back together slightly from their
maximum deflection.
(c) Yes. The electroscope has a negative charge on the top sphere and on the leaves. Therefore the
electroscope has a total net negative charge, so it must have been charged by conduction.
11. Coulomb’s law and Newton’s law are very similar in form. When expressed in SI units, the
magnitude of the constant in Newton’s law is very small, while the magnitude of the constant in
Coulomb’s law is quite large. Newton’s law says the gravitational force is proportional to the
product of the two masses, while Coulomb’s law says the electrical force is proportional to the
product of the two charges. Newton’s law only produces attractive forces, since there is only one
kind of gravitational mass. Coulomb’s law produces both attractive and repulsive forces, since there
are two kinds of electrical charge.
12. The gravitational force between everyday objects on the surface of the Earth is extremely small.
(Recall the value of G: 6.67 1011 N m2 kg2 . ) Consider two objects sitting on the floor near each
other. They are attracted to each other, but the maximum force of static friction for each is much
greater than the gravitational force each experiences from the other, and so they don’t move. Even in
an absolutely frictionless environment, the acceleration resulting from the gravitational force would
be so small that it would not be noticeable in a short time frame. We are aware of the gravitational
force between objects if at least one of them is very massive, as in the case of the Earth and satellites
or the Earth and you.
, Physics for Scientists & Engineers wͅith Modern Physics, 5e, Global Edition Instructor Solutions Manual
The electric force between two objects is typically zero or very close to zero because ordinary
objects are typically neutral or very close to neutral. We are aware of electric forces between objects
when the objects are charged. An example is the electrostatic force (static cling) between pieces of
clothing when you pull the clothes out of the dryer.
13. Coulomb observed experimentally that the force between two charged objects is directly
proportional to the charge on each one. For example, if the charge on either object is tripled, then the
force is tripled. This is not in agreement with a force that is proportional to the sum of the charges
instead of to the product of the charges. Secondly, if two equal but opposite charges are placed near
to each other, they produce an attractive force. But the “sum” version would say the net force is 0 in
such a case. Also, a charged object is not attracted to or repelled from a neutral insulating object. If
the numerator in Coulomb’s law were proportional to the sum of the charges, then there would be a
force between a neutral object and a charged object, because the their total charge would not be 0.
14. Assume that the charged plastic ruler has a negative charge residing on its surface. That charge
polarizes the charge in the neutral paper, producing a net attractive force. When the piece of paper
then touches the ruler, the paper can get charged by contact with the ruler, gaining a net negative
charge. Then, since like charges repel, the paper is repelled by the comb.
15. The test charge creates its own electric field. The measured electric field is the sum of the original
electric field plus the field of the test charge. By making the test charge small, the field that it causes
is small. Therefore the actual measured electric field is not much different than the original field.
Also, if the test charges are large, their fields might significantly re-distribute the charges causing the
original field, and then the measurement would not represent the field of the original configuration of
charges.
16. When determining an electric field, it is best, but not required, to use a positive test charge. A
negative test charge would be fine for determining the magnitude of the field. But the direction of the
electrostatic force on a negative test charge will be opposite to the direction of the electric field. The
electrostatic force on a positive test charge will be in the same direction as the electric field. In order
to avoid confusion, it is better to use a positive test charge. If we used a negative test charge but
wanted to have the same result for the electric field, we would have to define E F q, q 0.
17. See Fig. 21–35(b). A diagram of the electric field lines around two negative charges would be just
like this diagram except that the arrows on the field lines would point towards the charges instead of
away from them. The distance between the charges is l.
l
18. The electric field will be strongest to the right of the positive charge (between the two charges) and
weakest to the left of the positive charge. To the right of the positive charge, the contributions to the
field from the two charges point in exactly the same direction, and therefore add. To the left of the
positive charge, the contributions to the field from the two charges point in exactly opposite
directions, and therefore subtract. Note that this should be confirmed by the density of field lines in
Fig. 21–35a.
