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Chapter 30 Homework
Due: 8:00am on Tuesday, March 23, 2010
Electric Potential, Potential Energy, and Force
Learning Goal: To review relationships among electric potential, electric potential energy, and force on a test charge
This problem is a review of the relationship between an electric field
, its associated electric potential
, the electric potential energy
, and the direction of force on a test charge.
Part A
Electric field lines always begin at _______ charges (or at infinity) and end at _______ charges (or at infinity). One could also say that the lines we use to represent an electric field indicate the direction in which a
_______ test charge would initially move when released from rest. Which of the following fills in the three missing words correctly?
(positive; negative; negative)
(positive; negative; positive)
(negative; positive; negative)
(negative; positive; positive)
Correct
Note that the electric field vector
is everywhere tangent to the electric field lines. Like electric field lines, the electric field vector generally points away from positive charges and toward negative charges.
Part B
Would a positive test charge released from rest move toward a region of higher or lower electric potential (compared to the electric potential at the point where it is released)?
Hint B.1
Potential, field, and force
Hint not displayed
higher electric potential
lower electric potential
Correct
Part C
Now imagine that the sign of our test particle is changed from positive to negative, but the electric potential remains the same. Which of the following statements is correct?
Hint C.1
Direction of field and force
Hint not displayed
Hint C.2
Direction of force and potential energy gradient
Hint not displayed
The direction of the force will change and it will point to regions of higher potential energy.
The direction of the force will not change and it will point to regions of higher potential energy.
The direction of the force will not change and it will point to regions of lower potential energy.
The direction of the force will change and it will point to regions of lower potential energy.
Correct
Problem 30.37
The electric field in a region of space is
-1900
, where
is in meters.
Part A
What is the potential difference between
and
?
= 760
Correct
Problem 30.47
The electric potential in a region of space is
210
100
, where
and
are in meters.
Part A
What is the strength of the electric field at
?
= 1400
Correct
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Part B
What is the direction of the electric field at
= 155
Correct
? Give the direction as an angle (in degrees) counterclockwise from the positive -axis.
counterclockwise from the positive -axis
Capacitance: A Review
Learning Goal: To review the meaning of capacitance and ways of changing the capacitance of a parallel-plate capacitor.
Capacitance is one of the central concepts in electrostatics. Understanding its meaning and the difference between its definition and the ways of calculating capacitance can be challenging at first. This tutorial is meant to
help you become more comfortable with capacitance. Recall the fundamental formula for capacitance:
,
where
is the charge stored on the plates in coulombs, and
voltage is related to the strength of the electric field
is the potential difference (or voltage) between the plates. In the following problems it may help to keep in mind that the
and the distance between the plates, , by
.
Part A
What property of objects is best measured by their capacitance?
the ability to conduct electric current
the ability to distort an external electrostatic field
the ability to store charge
Correct
Capacitance is a measure of the ability of a system of two conductors to store electric charge and energy. It is defined as
. This ratio remains constant as long as the system retains its geometry and the
amount of dielectric does not change. Capacitors are special devices designed to combine a large capacitance with a small size. However, any pair of conductors separated by a dielectric (or vacuum) has some
capacitance. Even an isolated electrode has a small capacitance. That is, if a charge is placed on it, its potential with respect to ground would change, and the ratio
is its capacitance .
Part B
Consider an air-filled charged capacitor. How can its capacitance be increased?
Hint B.1
What does capacitance depend on?
Hint not displayed
Increase the charge on the capacitor.
Decrease the charge on the capacitor.
Increase the spacing between the plates of the capacitor.
Decrease the spacing between the plates of the capacitor.
Increase the length of the wires leading to the capacitor plates.
Correct
Part C
Consider a charged parallel-plate capacitor. How can its capacitance be halved?
Check all that apply.
Double the charge.
Double the plate area.
Double the plate separation.
Halve the charge.
Halve the plate area.
Halve the plate separation.
Correct
Part D
Consider a charged parallel-plate capacitor. Which combination of changes would quadruple its capacitance?
Double the charge and double the plate area.
Double the charge and double the plate separation.
Halve the charge and double the plate separation.
Halve the charge and double the plate area.
Halve the plate separation and double the plate area.
Double the plate separation and halve the plate area.
Correct
Problem 30.19
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A switch that connects a battery to a
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capacitor is closed. Several seconds later you find that the capacitor plates are charged to
.
Part A
What is the emf of the battery?
3.00
Correct
Equivalent Capacitance
Consider the combination of capacitors shown in the diagram, where
= 3.00
,
= 11.0
,
= 3.00
, and
= 5.00
.
Part A
Find the equivalent capacitance
Hint A.1
of the network of capacitors.
How to reduce the network of capacitors
Hint not displayed
Hint A.2
Find the capacitance equivalent to
,
, and
Hint not displayed
Hint A.3
Two capacitors in series
Hint not displayed
= 2.59
Correct
Part B
Two capacitors of capacitance
= 6.00
and
= 3.00
are added to the network, as shown in the diagram. Find the equivalent capacitance
of
the new network of capacitors.
Hint B.1
How to reduce the extended network of capacitors
Hint not displayed
Hint B.2
Find the equivalent capacitance of
,
,
,
, and
Hint not displayed
Hint B.3
Two capacitors in series
Hint not displayed
= 2.54
Correct
Problem 30.25
You need a capacitance of 50.0
, but you don't happen to have a 50.0
capacitor. You do have a 75.0
capacitor.
Part A
What additional capacitor do you need to produce a total capacitance of 50.0
150
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Correct
Part B
Should you join the two capacitors in parallel or in series?
in parallel
in series
Correct
A Simple Network of Capacitors
In the figure are shown three capacitors with capacitances
applied potential
. The capacitor network is connected to an
. After the charges on the capacitors have reached their final values, the charge
on the second capacitor is 40.0
.
Part A
What is the charge
Hint A.1
on capacitor
?
How to approach the problem
Hint not displayed
Hint A.2
Series or parallel?
Hint not displayed
Hint A.3
Calculate the potential difference across the second capacitor
Hint not displayed
Hint A.4
Calculate the potential difference across the first capacitor,
Hint not displayed
= 80.0
Correct
Part B
What is the charge on capacitor
Hint B.1
?
How to approach the problem
Hint not displayed
Hint B.2
Series or parallel?
Hint not displayed
Hint B.3
Capacitors in series
Hint not displayed
Hint B.4
Calculate the total charge in the initial section
Hint not displayed
= 120
Correct
Part C
What is the applied voltage,
Hint C.1
?
How to approach the problem
Hint not displayed
Hint C.2
Calculate the equivalent capacitance
Hint not displayed
Hint C.3
Find the total charge
Hint not displayed
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= 37.3
Correct
Problem 30.61
What are the charge on and the potential difference across each capacitor in the figure ?
Part A
4.00
Correct
Part B
1.00
Correct
Part C
12.0
Correct
Part D
1.00
Correct
Part E
16.0
Correct
Part F
8.00
Correct
Problem 30.73
The flash unit in a camera uses a 3.0
battery to charge a capacitor. The capacitor is then discharged through a flashlamp. The discharge takes
, and the average power dissipated in the flashlamp is 10
.
Part A
What is the capacitance of the capacitor?
22.2
Correct
Problem 30.33
Two 4.6-
-diameter metal disks are separated by a 0.23-
-thick piece of paper. (Dielectric constant for paper is
, its dielectric strength is
.)
Part A
What is the capacitance?
= 0.24
Correct
Part B
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What is the maximum potential difference between the disks?
= 3.7
Correct
The Capacitor as an Energy-Storing Device
Learning Goal: To understand that the charge stored by capacitors represents energy; to be able to calculate the stored energy and its changes under different circumstances.
An air-filled parallel-plate capacitor has plate area
and plate separation . The capacitor is connected to a battery that creates a constant voltage
.
Part A
Find the energy
Hint A.1
stored in the capacitor.
Formula for the energy of a capacitor
Hint not displayed
, ,
, and
. Remember to enter
as epsilon_0.
=
Correct
Part B
The capacitor is now disconnected from the battery, and the plates of the capacitor are then slowly pulled apart until the separation reaches
Hint B.1
. Find the new energy
of the capacitor after this process.
What quantity remains constant?
What characteristic of the capacitor does not change in this process?
charge
voltage between the plates
capacitance
energy
Correct
In particular, look carefully at the quantities that do change.
Hint B.2
Find the charge on the capacitor
What is the charge
that resides on the plates of the capacitor?
Express your answer in terms of some or all of the variables
,
, and . Remember to enter
as epsilon_0.
=
Correct
Hint B.3
How does the capacitance change?
How does the capacitance change in this process?
remains constant
increases by a factor of 3
decreases by a factor of 3
increases by a factor of 9
decreases by a factor of 9
Correct
Hint B.4
What is the formula for the energy?
Which of the following formulas is most useful in finding
for this situation?
Correct
, ,
, and
.
=
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Correct
The increase in energy of the capacitor comes from the external work that must be done to pull the plates apart. Keep in mind that the plates have opposite charges and attract each other; some work must be done
by an external agent to pull them apart.
Part C
The capacitor is now reconnected to the battery, and the plate separation is restored to
. A dielectric plate is slowly moved into the capacitor until the entire space between the plates is filled. Find the energy
the dielectric-filled capacitor. The capacitor remains connected to the battery. The dielectric constant is
, ,
,
, and
of
.
.