Cleophas Rwemera: Mastering Physics Chapter 26 Answers

Chapt 26

Skills builders

A Test Charge Determines Charge on Insulating and Conducting Balls

Learning Goal: To understand the electric force between charged and uncharged conductors and insulators.

When a test charge is brought near a charged object, we know from Coulomb's law that it will experience a net force (either attractive or repulsive, depending on the nature of the object's charge). A test charge may also experience an electric force when brought near a neutral object. Any attraction of a neutral insulator or neutral conductor to a test charge must occur through induced polarization. In an insulator, the electrons are bound to their molecules. Though they cannot move freely throughout the insulator, they can shift slightly, creating a rather weak net attraction to a test charge that is brought close to the insulator's surface. In a conductor, free electrons will accumulate on the surface of the conductor nearest the positive test charge. This will create a strong attractive force if the test charge is placed very close to the conductor's surface.

Rework for Practice

Consider three plastic balls (A, B, and C), each carrying a uniformly distributed unknown charge (which may be zero), and an uncharged copper ball (D). A positive test charge (T) experiences the forces shown in the figure when brought very near to the individual balls. The test charge T is strongly attracted to A, strongly repelled from B, weakly attracted to C, and strongly attracted to D.

Assume throughout this problem that the balls are brought very close together.

Part A

What is the nature of the force between balls A and B?

	strongly attractive
	strongly repulsive
	weakly attractive
	neither attractive nor repulsive

Correct

Part B

What is the nature of the force between balls A and C?

	strongly attractive
	strongly repulsive
	weakly attractive
	neither attractive nor repulsive

Correct

Recall that ball C is composed of insulating material, which can be polarized in the presence of an external charged object such as ball A. Once polarized, there will be a weak attraction between balls A and C, because the positive and negative charges in ball C are at slightly different average distances from ball A.

Part C

What is the nature of the force between balls A and D?

	attractive
	repulsive
	neither attractive nor repulsive

Correct

Part D

What is the nature of the force between balls D and C?

	attractive
	repulsive
	neither attractive nor repulsive

Correct

Because the test charge T is neither strongly attracted to nor repelled from ball C, ball C must have zero net charge. Since ball D also has zero net charge, there will not be any force between the two balls.

Charging a Conducting Rod

This problem explores the behavior of charge on conductors. We take as an example a long conducting rod suspended by insulating strings. Assume that the rod is initially electrically neutral. For convenience we will refer to the left end of the rod as end A, and the right end of the rod as end B. In the answer options for this problem, "strongly attracted/repelled" means "attracted/repelled with a force of magnitude similar to that which would exist between two charged balls.

Rework for Practice

Part A

A small metal ball is given a negative charge, then brought near (i.e., within about 1/10 the length of the rod) to end A of the rod . What happens to end A of the rod when the ball approaches it closely this first time?

	It is strongly repelled.
	It is strongly attracted.
	It is weakly attracted.
	It is weakly repelled.
	It is neither attracted nor repelled.

Correct

This charge is said to be "induced" by the presence of the electric field of the charged ball: It is not transferred by the ball.

Now consider what happens when the small metal ball is repeatedly given a negative charge and then brought into contact with end A of the rod.

Part B

After a great many contacts with the charged ball, how is the charge on the rod arranged (when the charged ball is far away)?

	There is positive charge on end B and negative charge on end A.
	There is negative charge spread evenly on both ends.
	There is negative charge on end A with end B remaining neutral.
	There is positive charge on end A with end B remaining neutral.

Correct

Part C

How does end A of the rod react when the charged ball approaches it after a great many previous contacts with end A? Assume that the phrase "a great many" means that the total charge on the rod dominates any charge movement induced by the near presence of the charged ball.

	It is strongly repelled.
	It is strongly attracted.
	It is weakly attracted.
	It is weakly repelled.
	It is neither attracted nor repelled.

Correct

Part D

How does end B of the rod react when the charged ball approaches it after a great many previous contacts with end A?

	It is strongly repelled.
	It is strongly attracted.
	It is weakly attracted.
	It is weakly repelled.
	It is neither attracted nor repelled.

Correct

Charging an Insulator

This problem explores the behavior of charge on realistic (i.e. non-ideal) insulators. We take as an example a long insulating rod suspended by insulating wires. Assume that the rod is initially electrically neutral. For convenience, we will refer to the left end of the rod as end A, and the right end of the rod as end B . In the answer options for this problem, "weakly attracted/repelled" means "attracted/repelled with a force of magnitude similar to that which would exist between two balls, one of which is charged, and the other acquires a small induced charge". An attractive/repulsive force greater than this should be classified as "strongly attracted/repelled".

Rework for Practice

Part A

A small metal ball is given a negative charge, then brought near (i.e., within a few millimeters) to end A of the rod. What happens to end A of the rod when the ball approaches it closely this first time?

Select the expected behavior.

	strongly repelled
	strongly attracted
	weakly attracted
	weakly repelled
	neither attracted nor repelled

Correct

Currently, you can think of this in the following way: When the sphere is brought near the rod, a positive charge is induced at end A (and correspondingly, end B acquires a negative induced charge). This means that some charge must have flowed from A to B. Since charge flow is inhibited in an insulator, the induced charges are typically small. Later you will learn how to model insulators more accurately and formulate a slightly more accurate argument.

Now consider what happens when the small metal ball is repeatedly given a negative charge and then brought into contact with end A of the rod

Part B

After several contacts with the charged ball, how is the charge on the rod arranged?

Select the best description.

	positive charge on end B and negative charge on end A
	negative charge spread evenly on both ends
	negative charge on end A with end B remaining almost neutral
	positive charge on end A with end B remaining almost neutral
	none of the above

Correct

When the sphere is touched to end A, some of its negative charge will be deposited there. However, since charge cannot flow easily through an insulator, most of this charge will just sit at end A and will not distribute itself over the rod, as it would if the rod was a conductor.

Part C

How does end A of the rod react when the ball approaches it after it has already made several contacts with the rod, such that a fairly large charge has been deposited at end A?

Select the expected behavior.

	strongly repelled
	strongly attracted
	weakly attracted
	weakly repelled
	neither attracted nor repelled

Correct

More on insulators

You may have learnt that any material is made of atoms, which in turn consist of a nucleus and electrons. In the atoms of some materials, some of the electrons are "bound" to the nucleus very weakly, which leaves them free to move around the volume of the material. Such electrons are called "free" electrons, and such materials are called conductors, because the charge (i.e. electrons) can move around easily. In insulators, all the electrons in the atom are bound quite tightly to the nucleus, i.e. there are no free electrons available to move through the insulator.

Same Value Problems

Problem 26.9

Two neutral metal spheres on wood stands are touching. A negatively charged rod is held directly above the top of the left sphere, not quite touching it. While the rod is there, the right sphere is moved so that the spheres no longer touch. Then the rod is withdrawn.

Rework for Practice

Part A

Afterward, what is the charge state of each sphere?

	Both the spheres are neutral.
	Left sphere is negatively charged, another is charged positively.
	Right sphere is negatively charged, another is charged positively.
	Both the spheres are charged positively.
	Both the spheres are charged negatively.

Correct

Problem 26.16

Rework for Practice

Part A

What is the net electric force on charge A in the figure ?

0 N

Correct

Problem 26.28

A -12 ${\rm nC}$ charge is located at the origin.

Rework for Practice

Part A

What is the electric field at the position $(x_1,\;y_1)=(0\;{\rm cm},\;5.0\;{\rm cm})$ ? Write electric field vector in component form.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

$E_{1x}, E_{1y}$ =0,−4.3×10⁴ ${\rm N/C}$

Correct

Part B

What is the electric field at the position $(x_2,\;y_2)= (-5.0\;{\rm cm},\;-5.0\;{\rm cm)}$ ? Write electric field vector in component form.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

$E_{2x}, E_{2y}$ =1.5×10⁴,1.5×10⁴ ${\rm N/C}$

Correct

Part C

What is the electric field at the position $(x_3,\;y_3)=$ $(-5.0\;{\rm cm},\;5.0\;{\rm cm})$ ? Write electric field vector in component form.

Express your answers using two significant figures. Enter your answers numerically separated by a comma.

$E_{3x},E_{3y}$ =1.5×10⁴,−1.5×10⁴ ${\rm N/C}$

Correct

Part D

Draw a field diagram showing the electric field vectors at these points.

The orientation of your vectors will be graded. The exact length of your vectors will not be graded.

Correct

Problem 26.37

Rework for Practice

Part A

What is the magnitude of the force $\vec{F}$ on the 1.0 ${\rm nC}$ charge in the figure ?

Express your answer using two significant figures.

=3.1×10⁻⁴ ${\rm N}$

Correct

Part B

What is the direction of the force $\vec{F}$ on the 1.0 ${\rm nC}$ charge in the figure?

	upward
	downward
	another direction

Correct

Problem 26.41

Rework for Practice

Part A

What is the magnitude of the force $\vec{F}$ on the 5.0 ${\rm nC}$ charge in the figure ?

Express your answer using two significant figures.

=2.0×10⁻⁴ ${\rm N}$

Correct

Part B

What is the direction of the force $\vec{F}$ on the 5.0 ${\rm nC}$ charge in the figure? Give your answer as an angle measured cw from the +x-axis.

Express your answer using two significant figures.

$\theta$ =45 $^\circ$ cw from the +x-axis

Correct

Problem 26.60

Two 3.0 ${\rm g}$ point charges on 1.0- ${\rm m}$ -long threads repel each other after being equally charged, as shown in the figure .

Rework for Practice

Part A

What is the charge

Express your answer using two significant figures.

=0.75 ${\rm \mu C}$

Correct

Variable value Problems

Problem 26.4

A glass rod that has been charged to

19.0

touches a metal sphere. Afterward, the rod's charge is

1.0

Rework for Practice

Part A

What kind of charged particle was transferred between the rod and the sphere, and in which direction? That is, did it move from the rod to the sphere or from the sphere to the rod?