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Chapter 29 Homework
Due: 8:00am on Thursday, March 11, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
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Electric Potential Ranking Task
In the figurethere are two point charges,
and
. There are also six positions, labeled A through F, at various distances from the two point
charges. You will be asked about the electric potential at the different points (A through F).
Part A
Rank the locations A to F on the basis of the electric potential at each point. Rank positive electric potentials as larger than negative electric potentials.
Hint A.1
Definition of electric potential
Hint not displayed
Hint A.2
Conceptualizing electric potential
Hint not displayed
Rank the locations from largest to smallest potential. To rank items as equivalent, overlap them.
ANSWER:
View
Correct
Conceptual Question 29.13
The figures show three points in the vicinity of two point charges. The charges have equal magnitudes.
Part A
Rank in order, from most positive to most negative, the potentials
to
on the figure a.
Rank the potentials in decreasing order. To rank items as equivalent, overlap them.
ANSWER:
View
Correct
Part B
Rank in order, from most positive to most negative, the potentials
to
on the figure b.
Rank the potentials in decreasing order. To rank items as equivalent, overlap them.
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ANSWER:
View
Correct
Problem 29.8
A water molecule perpendicular to an electric field has 1.50×10−21
more potential energy than a water molecule aligned with the field. The dipole moment of a water molecule is
.
Part A
What is the strength of the electric field?
ANSWER:
2.42×108 N/C
Correct
Electric Potential and Potential Energy
A particle with charge 8.00×10−19
is placed on the x axis in a region where the electric potential due to other charges increases in the +x direction but does not change in the y or z direction.
Part A
The particle, initially at rest, is acted upon only by the electric force and moves from point a to point b along the x axis, increasing its kinetic energy by 1.44×10−18 . In what direction and through what
potential difference
Hint A.1
does the particle move?
How to approach the problem
Hint not displayed
Hint A.2
Electric potential
Hint not displayed
Hint A.3
Find the change in potential energy of the particle
Hint not displayed
ANSWER:
The particle moves to the left through a potential difference of
The particle moves to the left through a potential difference of
1.80
1.80
The particle moves to the right through a potential difference of
1.80
The particle moves to the right through a potential difference of
The particle moves to the left through a potential difference of
.
.
1.80
18.0
The particle moves to the right through a potential difference of
18.0
.
.
.
.
Correct
Thus, if no forces other than the electric force act on a positively charged particle, the particle always moves toward a point at lower potential.
Part B
If the particle moves from point b to point c in the y direction, what is the change in its potential energy,
Hint B.1
?
How to approach the problem
Hint not displayed
ANSWER:
1.44×10−18
1.44×10−18
0
Correct
Every time a charged particle moves along a line of constant potential, its potential energy remains constant and the electric field does no work on the particle.
Electric Potential Energy of Three Point Charges
Part A
Three equal point charges, each with charge 1.30
, are placed at the vertices of an equilateral triangle whose sides are of length 0.600
. What is the electric potential energy
of the system? (Take as zero
the potential energy of the three charges when they are infinitely far apart.)
Hint A.1
How to approach the problem
Hint not displayed
Hint A.2
Find the electric potential energy of one pair
Hint not displayed
Hint A.3
How many interactions are there?
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Hint not displayed
= 8.85×10−12
Use
for the permittivity of free space.
ANSWER:
−2
= 7.59×10
Correct
The potential energy is usually written
.
This means that all pairs of charges (1-2, 1-3, and 2-3) will interact, but no charge can interact with itself (
For example,
,
will be counted, while
,
), nor can any pair be counted twice as a result of the condition
for all possible pairs.
will not.
Problem 29.12
Part A
What potential difference is needed to accelerate a
ion (charge
, mass 4 ) from rest to a speed of 1.1×106
?
Express your answer using two significant figures.
ANSWER:
4
= −2.5×10
Correct
Problem 29.19
A 1.60
1.60
spacing. The electric field strength inside the capacitor is 7.00×104
parallel-plate capacitor has a 1.90
.
Part A
What is the potential difference across the capacitor?
ANSWER:
133
V
Correct
Part B
How much charge is on each plate?
ANSWER:
1.59×10−10 C
Correct
Problem 29.45
In the figure, a proton is fired with a speed of 200,000
from the midpoint of the capacitor toward the positive plate.
Part A
Show that this is insufficient speed to reach the positive plate.
ANSWER:
My Answer:
Part B
What is the proton's speed as it collides with the negative plate?
ANSWER:
5
= 2.96×10
Correct
Potential of a Finite Rod
A finite rod of length
has total charge , distributed uniformly along its length. The rod lies on the x -axis and is centered at the origin. Thus one endpoint is located at
. Define the electric potential to be zero at an infinite distance away from the rod. Throughout this problem, you may use the constant
in place of the expression
, and the other is located at
.
Part A
What is
, the electric potential at point A (see the figure), located a distance
above the midpoint of the rod on the y axis?
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Hint A.1
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How to approach the problem
Hint not displayed
Hint A.2
Find the electric potential of a section of the rod
Hint not displayed
Hint A.3
A helpful integral
Hint not displayed
Express your answer in terms of
, , , and .
ANSWER:
=
Correct
If
, this answer can be approximated as
.
For
,
. For this problem, this means that the logarithm can be further approximated as
, and the expression for potential reduces to
. This is what we
expect, because it means that from far away, the potential due to the charged rod looks like that due to a point charge.
Part B
What is
, the electric potential at point
Hint B.1
, located at distance
from one end of the rod (on the x axis)?
How to approach the problem
Hint not displayed
Hint B.2
Find the distance from point B to a segment of the rod
Hint not displayed
Give your answer in terms of ,
, , and .
ANSWER:
=
Correct
This result can be written as
.
As before, for
,
. Thus, for
, the logarithm approaches
, in which case the result reduces to
. This is what we expect, because it means that from far away, the potential
due to the charged rod looks like that due to a point charge.
Potential Energy of a Battery
Learning Goal: To understand electrical potential, electrical potential energy, and the relationship between them.
Electric potential and electric potential energy are related but different concepts. Be careful not to confuse the terms. Electrical potential energy
relative to other charges. The electric potential
charge
has an electric potential energy
is the potential energy that a charge
at a specific position is a measure of the amount of potential energy per unit charge a particle of net charge
, the electric potential
at the location of
has due to its position
would have at that position. In other words, if a
is
.
Recall that the gravitational potential energy (
) of an object of mass
depends on where you define
. The difference
in gravitational potential energy between two points is the physically
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relevant quantity. Similarly, for electric potential energy, the important quantity is the change in electric potential energy:
say that the potential of a car battery is 12
. This is why we often just measure the potential difference
, we mean that the potential difference between the positive and negative terminals of the battery is 12
. When we
.
Consider dropping a ball from rest. This ball moves from a state of high gravitational potential energy to one of low gravitational potential energy as it falls to the ground. Similarly, charges move from a state of
high electric potential energy to one of low electric potential energy.
Part A
Mustang Sally just finished restoring her 1965 Ford Mustang car. To save money, she did not get a new battery. When she tries to start the car, she discovers that the battery is dead and she needs a jump start.
While unhooking the jumper cables, the positive and negative cables almost touch and a spark jumps between the ends of the cables. This spark is caused by the movement of electrons through the air between the
battery terminals. In what direction are the electrons traveling?
Hint A.1
Another way to think about the movement of charge
Hint not displayed
ANSWER:
The electrons are traveling from
terminal.
Correct
The positive terminal is at a higher potential than the negative terminal. Unless provided with energy, positive charges will flow from a high to a low potential, and negatively charged electrons will flow
from a low to a high potential. The table below summarizes this movement.
Direction of motion
high to low potential
low to high potential
Since potential difference is the energy per unit charge, it is measured in units of energy divided by charge. Specifically, potential difference is generally measured in volts (whose symbol is
equal to one joule per coulomb:
). One volt is
.
Part B
There is a 12
potential difference between the positive and negative ends of the jumper cables, which are a short distance apart. An electron at the negative end ready to jump to the positive end has a certain
amount of potential energy. On what quantities does this electrical potential energy depend?
Hint B.1
The expression for electric potential energy
Hint not displayed
ANSWER:
the distance between the ends of the cables
the potential difference between the ends of the cables
the charge on the electron
the distance and the potential difference
the distance and the charge
the potential difference and the charge
the potential difference, charge, and distance
Correct
Part C
Assume that two of the electrons at the negative terminal have attached themselves to a nearby neutral atom. There is now a negative ion with a charge
at this terminal. What are the electric potential and
electric potential energy of the negative ion relative to the electron?
ANSWER:
The electric potential and the electric potential energy are both twice as much.
The electric potential is twice as much and the electric potential energy is the same.
The electric potential is the same and the electric potential energy is twice as much.
The electric potential and the electric potential energy are both the same.
The electric potential is the same and the electric potential energy is increased by the mass ratio of the oxygen ion to the electron.
The electric potential is twice as much and the electric potential energy is increased by the mass ratio of the oxygen ion to the electron.
Correct
Part D
What is the electric potential energy of an electron at the negative end of the cable, relative to the positive end of the cable? In other words, assume that the electric potential of the positive terminal is 0
that of the negative terminal is
. Recall that
and
.
Enter your answer numerically in joules.
ANSWER:
=
Correct
Part E
At the negative terminal of the battery the electron has electric potential energy. What happens to this energy as the electron jumps from the negative to the positive terminal?
ANSWER:
It disappears.
It is converted to kinetic energy.
It heats the battery.
It increases the potential of the battery.
Correct
Just as gravitational potential energy is converted to kinetic energy when something falls, electrical potential energy is converted to kinetic energy when a charge goes from a high potential energy state to a
low potential energy state.
Part F
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If you wanted to move an electron from the positive to the negative terminal of the battery, how much work
Hint F.1
would you need to do on the electron?
Formula for work
Hint not displayed
Enter your answer numerically in joules.
ANSWER:
=
Correct
Because moving a negative charge from the positive to the negative terminal of the battery would increase its electric potential energy, it would take positive work to move the charge. This is simliar to
lifting a ball upward. You do positive work on the ball to increase its gravitational potential energy.
Score Summary:
Your score on this assignment is 107.1%.
You received 69.95 out of a possible total of 70 points, plus 4.99 points of extra credit.
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