MasteringPhysics_ Assignments10_9_11

Assignment 1

Due: 11:59pm on Sunday, October 9, 2011

Note: To understand how points are aw arded, read your instructor's Grading Policy.

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Charging a Conducting Rod

This problem explores the behavior of charge on conductors. We take as an example a long conductingrod suspended by insulating strings. Assume that the rod is initially electrically neutral. For conveniencewe 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 optionsfor this problem, "strongly attracted/repelled" means "attracted/repelled with a force of magnitude similar tothat which would exist between two charged balls.

Part A

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

Hint A.1 The key property of conductors

The key property of a conductor is that the charges are free to move around inside in response tointernal electric fields; in a static situation, they will arrange so that the internal field is zero.

Hint A.2 How much charge moves to end A?

It is stated that the ball is much closer to the end of the rod than the length of the rod. Therefore, ifpoints down the rod several times the distance of approach (but still much closer to end A than endB) are to experience no electric field, the charge on end A of the rod must be comparable inmagnitude to the charge on the ball (so that their fields will cancel).

ANSWER: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 nottransferred by the ball.

Now consider what happens when the small metal ball is repeatedly given a negative charge and thenbrought 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 thecharged ball is far away)?

ANSWER: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 previouscontacts with end A? Assume that the phrase "a great many" means that the total charge on the roddominates any charge movement induced by the near presence of the charged ball.






Correct

Part D

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

Hint D.1 The rod is a conductor

Hint not displayed






Correct

Placing Charges Conceptual Question

Below are free-body diagrams for three electric charges that lie in the same plane. Their relative positionsare unknown.

Part A

Along which of the lines (A to H) in the figureshould charge 2 be placed so that the free-bodydiagrams of charge 1 and charge 2 areconsistent?

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Placing charge 2

Hint not displayed

ANSWER:

Correct

Part B

Along which of the lines (A to H) in the figureshould charge 3 be placed so that the free-bodydiagrams of charge 1, charge 2, and charge 3are consistent?

ANSWER: DCorrect

Part C

Along which of the lines (A to H) in the figureshould charge 2 be placed so that the free-bodydiagrams of charge 1 and charge 2 areconsistent?

ANSWER: HCorrect

Part D

Along which lines (A to H) in the figure shouldcharge 3 be placed so that the free-bodydiagrams of charge 1, charge 2, and charge 3are consistent?

ANSWER: FCorrect

Forces in a Three-Charge System

Coulomb's law for the magnitude of the force between two particles with charges and separated

by a distance is

,

where , and is the permittivity of free space.

Consider two point charges located on the x axis: one charge, = -12.0 , is located at = -1.685 ;

the second charge, = 38.0 , is at the origin .

Part A

What is the net force exerted by these two charges on a third charge = 54.5 placed between

and at = -1.155 ?

Your answer may be positive or negative, depending on the direction of the force.

Hint A.1 How to approach the problem

Hint not displayed

Hint A.2 Calculate the force on the third charge by the first charge

Hint not displayed

Hint A.3 Calculate the force on the third charge by the second charge

Hint not displayed

Hint A.4 What are the directions of the forces?

Hint not displayed

Hint A.5 Relating the net force and the forces between pairs of charges

Hint not displayed

Express your answer numerically in newtons to three significant figures.

ANSWER: Force on = −3.49×10−5

Correct

Problem 26.13

Two 2.0 masses are 1.1 apart (center to center) on a frictionless table. Each has 9.8 of

charge.

Part A

What is the magnitude of the electric force on one of the masses?

Express your answer using two significant figures.

ANSWER: = 0.71

Correct

Part B

What is the initial acceleration of the mass if it is released and allowed to move?


ANSWER: = 0.36

Correct

Problem 26.21

The electric field at a point in space is 900 700 .

Part A

What is the x-component of the electric force on a proton at this point?

Express your answer numerically, in newtons, to three significant figures.

ANSWER: = 1.44×10−16

Correct N

Part B

What is the y-component of the electric force on a proton at this point?


ANSWER: = 1.12×10−16

Correct N

Part C

What is the x-component of the electric force on an electron at this point?


ANSWER: = −1.44×10−16

Correct N

Part D

What is the y-component of the electric force on a electron at this point?


ANSWER: = −1.12×10−16

Correct N

Part E

What is the magnitude of the proton's acceleration?

Express your answer numerically, in meters per second squared, to three significant figures.

ANSWER: = 1.09×1011

Correct

Part F

What is the magnitude of the electron's acceleration?

Express your answer numerically, in meters per second squared, to three significant figures.

ANSWER: = 2.00×1014

Correct

Problem 26.26

Part A

What is the strength of an electric field that will balance the weight of a proton?

Express your answer numerically in Newtons per Coulomb to three significant figures.

ANSWER: = 1.02×10−7

Correct

Part B

In what direction should it point?

ANSWER:downward

upward

Correct

Part C

What is the strength of an electric field that will balance the weight of an electron?

Express your answer numerically in Newtons per Coulomb to three significant figures.

ANSWER: = 5.58×10−11

Correct

Part D

In what direction should it point?

ANSWER:downward

upward

Correct

Problem 26.28

A -12 charge is located at the origin.

Part A

What is the electric field at the position ? Write electric field vector in component

form.

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

ANSWER:Answer not displayed

=

Part B

What is the electric field at the position ? Write electric field vector in

component form.


ANSWER: = Answer not displayed

Part C

What is the electric field at the position ? Write electric field vector in

component form.



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.

ANSWER:

Answernotdisplayed

Problem 26.29

Two identical metal spheres A and B are connected by a metal rod. Both are initially neutral. 1.3×1012

electrons are added to sphere A, then the connecting rod is removed.

Part A

Afterward, what are the charge of A and the charge of B?

Express your answer using two significant figures. Enter your answers numerically separatedby a comma.

ANSWER: , = Answer not displayed

Problem 26.39

Part A

What is the magnitude of the force on the -10 charge in the figure?

Express your answer using two significantfigures.


Part B

What is the direction of the force on the -10 charge in the figure? Give your answer as an angle

measured cw from the +x-axis.


ANSWER: = Answer not displayed cw from the +x-axis

Problem 26.47

A 2.4 charge is at the origin and a -5.2 charge is at 1.3 .

Part A

At what -coordinate could you place a proton so that it would experience no net force?



Part B

Would the net force be zero for an electron placed at the same position? Explain.

Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

ANSWER: Answer not displayed

Problem 26.48

The net force on the 1.0 in the figure charge is zero.

Part A

What is ?



Score Summary:

Your score on this assignment is 60%.You received 60 out of a possible total of 100 points, plus 0 points of extra credit.

MasteringPhysics_ Assignments10_9_11

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