Module 18
Physics Problems
Lesson 1 Electric Charge
Mastering Problems
Mastering Concepts
1.
If you comb your hair on a dry day, the
comb can become negatively charged.
Can your hair remain neutral? Explain.
2.
If you bring a charged comb near tiny
pieces of paper, the pieces will first be
attracted to the comb, but after touching
they will fly away. Why do they fly away?
3.
List some insulators and conductors.
4.
What makes metal a good conductor and
rubber a good insulator?
Lesson 2 Electrostatic Force
11.
Atoms Two electrons in an atom are
separated by 1.5×10−10 m, the typical size of
an atom. What is the electrostatic force
between them?.
12.
A positive and a negative charge, each of
magnitude 2.5×10−5 C, are separated by a
distance of 15 cm. Find the force on each of
the particles.
13.
Two identical positive charges exert a
repulsive force of 6.4×10−9 N when
separated by a distance of 3.8×10−10 m.
Calculate the charge of each.
14.
Lightning A strong lightning bolt transfers
about 25 C to Earth. How many electrons
are transferred?
15.
A positive charge of 3.0 µC is pulled on by
two negative charges. As shown in the
diagram, one negative charge, −2.0 µC,
is 0.050 m to the west, and the other,
−4.0 µC, is 0.030 m to the east. What net
force is exerted on the positive charge?
16.
The diagram shows two positively charged
spheres, one with three times the charge of
the other. The spheres are 16 cm apart, and
the force between them is 0.28 N. What
are the charges on the two spheres?
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Mastering Concepts
5.
Laundry Why do socks taken from a
clothes dryer sometimes cling to other
clothes?
6.
Compact Discs If you wipe a compact disc
with a clean cloth, why does the CD then
attract dust?
7.
Coins The combined charge of all
electrons in a nickel is hundreds of
thousands of coulombs. Does this imply
anything about the net charge on the coin?
Explain.
8.
How does the distance between two
charges impact the force between them? If
the distance is decreased while the
charges remain the same, what happens to
the force?
9.
Explain how to charge a conductor
negatively if you have only a positively
charged rod.
10 .
Bernoulli’s experiments to measure the
strength of the electrostatic force used
metal disks about 3 cm in diameter. When
the disks were close together, would he
have found a 1/r2 dependence? Explain.
Inspire Physics
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Physics Problems
Module 18 continued
17.
Three particles are placed in a line. The left particle has a charge of −55 µC, the middle one has a
charge of +45 µC, and the right one has a charge of −78 µC. The middle particle is 72 cm from
each of the others, as shown.
a. Find the net force on the middle particle.
b. Find the net force on the right particle.
18.
Reverse Problem Write a physics problem for which the following equation would be part of the
solution:
(3.0×10−6 C)(2.0×10−6 C) (3.0×10−6 C)(5.0×10−6 C)
�
F = �9.0×109 N⋅m2 /C2 � �
−
(0.25 m)2
(0.45 m)2
19.
Charge in a Coin A nickel has a mass of about 5 g and is 75 percent Cu and 25 percent Ni. On
average, each mole of a nickel’s atoms will have a mass of about 62 g. Each Cu atom has 29
electrons; each Ni atom has 28 electrons. How many coulombs of charge are on the electrons in
a nickel?
20.
Problem Posing Complete this problem so that it must be solved using Coulomb’s Law: “A very
small sphere is given a charge of 6.25 µC …”.
21.
Ranking Task Rank the following pairs of point charges according to the magnitude of
electrostatic force they exert on each other. Specifically indicate any ties.
A. two 7.0 nC charges separated by 0.20 m
B. two 5.0 nC charges separated by 0.20 m
C. two 2.5 nC charges separated by 0.10 m
D. a 2.5 nC charge and a 5.0 nC charge separated by 0.20 m
E. 1.0 µC charge and a 2.5 µC charge separated by 0.10 m
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Lesson 3 Measuring Electric Fields
Mastering Concepts
22.
What are the two properties that a test charge must have?
23.
How is the direction of an electric field defined?
24.
What are electric field lines?
25.
How is the strength of an electric field indicated with electric field lines?
26.
Draw some of the electric field lines between each of the following:
a. two like charges of equal magnitude
b. two unlike charges of equal magnitude
c. a positive charge and a negative charge having twice the magnitude of the positive charge
d. two oppositely charged parallel plates
Inspire Physics
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Physics Problems
Module 18 continued
27.
34.
In the diagram, where do the electric field
lines that leave the positive charge end?
The electric field in the atmosphere is
about 150 N/C downward.
a. What is the direction of the force on a
negatively charged particle?
b. Find the electric force on an electron
with charge −1.602×10−19 C.
c. Compare the force in part b with the
force of gravity on the same electron
(mass = 9.1×10−31 kg).
35.
28.
What happens to the strength of an electric
field when the magnitude of the test
charge is halved?
29.
You are moving a constant positive charge
through an increasing electric field. Does
the amount of energy required to move it
increase or decrease?
a. the electric field produced by a +1.0-µC
charge
b. the electric field resulting from a
+2.0-µC charge (Make the number of
field lines proportional to the change in
charge.)
36.
A positive test charge of 6.0×10−6 C is
placed in an electric field of 50.0-N/C
intensity, as in the diagram. What is the
strength of the force exerted on the test
charge?
Mastering Problems
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Carefully sketch each of the following:
30.
What charge exists on a test charge that
experiences a force of 1.4×10–8 N at a point
where the electric field intensity is
5.0×10−4 N/C?
31.
A test charge experiences a force of 0.30
N on it when it is placed in an electric field
intensity of 4.5×105 N/C. What is the
magnitude of the charge?
32.
What is the electric field strength 20.0 cm
from a point charge of 8.0×10−7 C?
37.
A positive charge of 1.0×10−5 C experiences
a force of 0.30 N when it is located at a
certain point. What is the electric field
intensity at that point?
A force of 14.005 N exists on a positive
test charge (q') that has a charge of
4.005×10−19 C. What is the magnitude
of the electric field?
38.
Charges X, Y, and Z all are equidistant from
each other. X has a +1.0-µC charge. Y has a
+2.0-µC charge. Z has a small negative
charge.
a. Draw an arrow representing the force
on charge Z.
b. Charge Z now has a small positive
charge on it. Draw an arrow
representing the force on it.
33.
Inspire Physics
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Physics Problems
Module 18 continued
39.
40.
Mastering Problems
In a television picture tube, electrons are
accelerated by an electric field having a
value of 1.00×105 N/C.
a. Find the force on an electron.
b. If the field is constant, find the
acceleration of the electron (mass
9.11×10−31 kg).
The nucleus of a lead atom has a charge of
82 protons.
a. What are the direction and the
magnitude of the electric field at
1.0×10−10 m from the nucleus?
b. What are the direction and the
magnitude of the force exerted on an
electron located at this distance?
Lesson 4 Applications of
Electric Fields
46.
If 120 J of work is performed to move 2.4 C
of charge from the positive plate to the
negative plate shown in the diagram, what
potential difference exists between the
plates?
47.
How much work is done to transfer 0.15 C
of charge through an electric potential
difference of 9.0 V?
48.
An electron is moved through an electric
potential difference of 450 V. How much
work is done on the electron?
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Mastering Concepts
41.
What SI unit is used to measure electric
potential energy? What SI unit is used to
measure electric potential difference?
49.
A 12-V battery does 1200 J of work
transferring charge. How much charge is
transferred?
42.
Define volt in terms of the change in
potential energy of a charge moving in an
electric field.
50.
43.
Why does a charged object lose its charge
when it is touched to the ground?
The electric field intensity between two
charged plates is 1.5 ×103 N/C. The plates
are 0.060 m apart. What is the electric
potential difference, in volts, between the
plates?
44.
A charged rubber rod that is placed on a
table maintains its charge for some time.
Why is the charged rod not discharged
immediately?
51.
A voltmeter indicates that the electric
potential difference between two plates is
70.0 V. The plates are 0.020 m apart. What
electric field intensity exists between them?
45.
Computers Delicate parts in electronic
equipment are contained within a metal
box inside a plastic case. Why?
52.
A capacitor that is connected to a 45.0-V
source has a charge of 90.0 µC. What is
the capacitor’s capacitance?
Inspire Physics
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Physics Problems
Module 18 continued
53.
The oil drop shown in the diagram is
negatively charged and weighs 4.5 ×10−15
N. The drop is suspended in an electric
field intensity of 5.6 ×103 N/C.
58.
Suppose it took 25 s to energize the
capacitor in the previous problem.
a. Find the average power required to
energize the capacitor in this time.
b. When the plates are discharged through
the strobe lamp, it transfers all its energy
in 1.0 ×10−4 s. Find the power delivered
to the lamp.
c. How is such a large amount of power
possible?
a. What is the charge on the drop?
59.
The plates of a 0.047-µF capacitor are
0.25 cm apart and are charged to a
potential difference of 120 V. How much
charge is on one plate of the capacitor?
60.
Lasers Lasers are used to try to produce
controlled fusion reactions. These lasers
require brief pulses of energy that are
stored in large rooms filled with capacitors.
One such room has a capacitance of
6.1×10−2 F and is energized to a potential
difference of 10.0 kV.
b. How many excess electrons does it
carry?
54.
What electric potential difference exists
across a 5.4-µF capacitor that has a charge
of 8.1 ×10−4 C?
55.
What is the charge of a 15.0-pF capacitor
when it is connected across a 45.0-V
source?
56.
A force of 0.065 N is required to move a
charge of 37 µC a distance of 25 cm in a
uniform electric field. What is the size of the
electric potential difference between the
two points?
a. Given that PE = ½ C∆V 2, find the energy
stored in the capacitors.
b. The capacitors’ plates are discharged in
10 ns (1.0 ×10−8 s). What power is
produced?
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c. If the capacitors are energized by a
generator with a power capacity of
1.0 kW, how many seconds will be
required to energize the capacitors?
57.
Applying Concepts
Photoflash The potential energy of a
capacitor with capacitance (C) and an
electric potential difference (ΔV) is
represented by PE = ½ CΔV 2. One
application of this is in the electronic
photoflash of a strobe light. In such a unit, a
capacitor of 10.0 µF has a charge of
3.0 ×102 V. Find the electrical energy
stored.
Inspire Physics
61.
5
Coulomb measured the deflection of
sphere A when spheres A and B had equal
charges and were a distance, r, apart. If he
made the charge on B one-third the charge
on A, how far apart would the two spheres
have to be for A to have the same
deflection that it had before?
Physics Problems
Copyright ©McGraw-Hill Education
Module 18 continued
62.
Two charged bodies exert a force of 0.145
N on each other. If they are moved so they
are one-fourth as far apart, what force is
exerted?
63.
Electrostatic forces between charges are
enormous in comparison to gravitational
forces. Yet, you normally do not sense
electrostatic forces between yourself and
your surroundings, while you do sense
gravitational interactions with Earth.
Explain.
64.
How does the charge of an electron differ
from the charge of a proton? How are they
similar?
65.
Using a charged rod and an electroscope,
how can you find whether an object is a
conductor?
66.
A charged rod is brought near a pile of tiny
plastic spheres. Some of the spheres are
attracted to the rod, but as soon as the
spheres touch the rod, they are flung off in
different directions. Explain why this
happens.
67.
Explain what would happen to the leaves
of a positively charged electroscope if a
positively charged rod was brought close
to, but did not touch, the electroscope.
How would the electroscope’s leaves
behave if the rod were negatively charged?
68.
Lightning Lightning usually occurs when a
negative charge in a cloud is transported to
Earth. If Earth is neutral, what provides the
attractive force that pulls the electrons
toward Earth?
69.
The text describes Coulomb’s method for
charging two spheres, A and B, so that the
charge on B was exactly half the charge on
A. Suggest a way that Coulomb could have
placed a charge on sphere B that was
exactly one-third the charge on sphere A.
Inspire Physics
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70.
As shown in the diagram, Coulomb’s law
and Newton’s law of universal gravitation
appear to be similar. In what ways are the
electrostatic and gravitational forces
similar? How are they different?
71.
What will happen to the electric potential
energy of a charged particle in an electric
field when the particle is released and free
to move?
72.
The diagram shows three spheres with
charges of equal magnitude, with their
signs as shown. Spheres y and z are held
in place, but sphere x is free to move.
Initially, sphere x is equidistant from
spheres y and z. Which path will sphere x
will begin to follow? Assume that no other
forces act on the spheres.
Physics Problems
Module 18 continued
73.
Ranking Task Rank the following point
charges according to the magnitude of the
electric force experienced, from greatest to
least. Specifically indicate any ties.
77.How can you store different amounts of
electrical energy in a capacitor?
Mixed Review
A. a charge of 3 nC at a point where the
electric field is 70 N/C
B. a charge of 5 nC at a point where the
electric field is 600 N/C
C. a charge of 3 nC at a point where the
electric field is 20 N/C
D. a charge of 6 nC at a point where the
electric field is 35 N/C
E. a charge of 8 nC at a point where the
electric field is 10 N/C
74.
Two unlike-charged oil drops are held
motionless in a Millikan oil-drop experiment
at the same time.
a. Can you be sure that the charges are
the same?
b. The ratios of which two properties of the
oil drops have to be equal?
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75.
76.
José and Sue are standing on an insulating
platform and holding hands when they are
given a charge, as shown. José is larger
than Sue. Who has the larger amount of
charge from the machine, or do they both
have the same amount?
Reverse Problem Write a physics problem
for which the following equation would be
part of the solution:
9 V−0 V
E=
0.85 cm
Inspire Physics
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78.
A small metal sphere with charge 1.2×10−5 C
is touched to an identical neutral sphere
and then placed 0.15 m from the second
sphere. What is the electrostatic force
between the two spheres?
79.
Atoms What is the electrostatic force
between an electron and a proton placed
5.3×10−11 m apart, the approximate radius of
a hydrogen atom?
80.
A small sphere of charge 2.4 µC
experiences a force of 0.36 N when a
second sphere of unknown charge is
placed 5.5 cm from it. What is the charge of
the second sphere?
81.
Two identically charged spheres placed 12
cm apart have an electrostatic force of 0.28
N between them. What is the charge on
each sphere?
82.
In an investigation using Coulomb’s
apparatus, a sphere with a charge of
3.6×10−8 C is 1.4 cm from a second sphere
of unknown charge. The force between the
spheres is 2.7×10−2 N. What is the charge of
the second sphere?
83.
How much work does it take to move 0.25
µC between two parallel plates that are
0.40 cm apart if the field between the
plates is 6400 N/C?
84.
How much charge is on a 0.22-µF parallel
plate capacitor if the plates are 1.2 cm apart
and the electric field between them is
2400 N/C?
Physics Problems
Module 18 continued
85.
Two identical small spheres 25 cm apart
carry equal but opposite charges of
0.060 µC. If the potential difference
between them is 300 V, what is the
capacitance of the system?
86.
Problem Posing Complete this problem
so that it must be solved using the concept
indicated: “ A point charge of 4.0 mC is at
rest…”
a. electric field
89.
b. electric potential difference
87.
The graph represents the amount of
charge stored on one plate of a capacitor
as a function of the charging potential.
a. What does the slope of the line
represent?
b. What is the capacitance of the
capacitor?
c. What does the area under the graph
line represent?
The plates of a 0.047-µF capacitor are 0.25
cm apart and are charged to a potential
difference of 120 V.
Copyright ©McGraw-Hill Education
Thinking Critically
a. How much charge is on the capacitor?
b. What is the strength of the electric field
between the plates of the capacitor?
c. An electron is placed between the
plates of the capacitor. What force is
exerted on that electron?
88.
Apply Concepts Calculate the ratio of the
electrostatic force to the gravitational force
between the electron and the proton in a
hydrogen atom.
91.
Analyze and Conclude Sphere A, with a
charge of +64 µC, is positioned at the
origin. A second sphere, B, with a charge of
−16 µC, is placed at +1.00 m on the x-axis.
a. Where must a third sphere, C, of charge
112 µC be placed so there is no net
force on it?
b. If the third sphere had a charge of 16 µ
C, where should it be placed?
How much work would it take to move an
additional 0.010 µ C between the plates at
120 V in the previous problem?
Inspire Physics
90.
8
Physics Problems
Module 18 continued
92.
95.
Three charged spheres are at the positions
shown. Find the net force on sphere B.
Two charges, qA and qB, are at rest near a
positive charge, qT, of 7.2 µC. The first
charge, qA, is a positive charge of 3.6 µC
located 2.5 cm away from qT at 35°; qB is a
negative charge of 26.6 µC located 6.8 cm
away at 125°.
a. Determine the magnitude of each of the
forces acting on qT.
b. Sketch a force diagram.
c. Graphically determine the resultant
force on qT.
96.
93.
The two pith balls in the diagram each have
a mass of 1.0 g and an equal charge. One
pith ball is suspended by an insulating
thread. The other is brought to 3.0 cm from
the suspended ball. The suspended ball is
now hanging, with the thread forming an
angle of 30.0° with the vertical. The ball is
in equilibrium with FE, Fg, and FT. Calculate
each of the following.
Analyze and Conclude Two small
spheres, A and B, lie on the x-axis, as in the
diagram. Sphere A has a charge of
+3.00×10−6 C. Sphere B is 0.800 m to the
right of sphere A and has a charge of
−5.00×10−6 C. Find the magnitude and the
direction of the electric field strength at a
point above the x-axis that would form the
apex of an equilateral triangle with spheres
A and B.
a. Fg on the suspended ball
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b. FE
c. the charge on the balls
94.
A device to trap positively charged ions
has four charged rods, equally spaced from
the center. The top and bottom rods are
charged positively, the left and right rods
negatively. Explain why when the ion is at
the center of the rods there is no force on
it. If the ion moves a small distance up or
down, does the net force push it toward or
away from the center? What if it moves a
small distance to the left or right?
Inspire Physics
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Physics Problems
Module 18 continued
97.
Analyze and Conclude In an ink-jet
printer, drops of ink are given a certain
amount of charge before they move
between two large, parallel plates. The
plates deflect the charged ink particles as
shown. The plates have an electric field of
E = 1.2×106 N/C between them and are
1.5 cm long. Drops with a mass m = 0.10 ng
and a charge q = 1.0×10−16 C are moving
horizontally at a speed, v = 15 m/s, parallel
to the plates. What is the vertical
displacement of the drops when they leave
the plates? To answer this question,
complete the following steps.
a. What is the vertical force on the drops?
b. What is their vertical acceleration?
98.
History of Science Research several
devices that were used in the seventeenth
and eighteenth centuries to study static
electricity. Examples that you might
consider include the Leyden jar and the
Wimshurst machine. Discuss how they
were constructed and how they
were used?
99.
When you studied states of matter, you
learned that forces exist between water
molecules that cause water to be denser
as a liquid between 0°C and 4°C than as a
solid at 0°C. These forces are electrostatic
in nature. Research electrostatic
intermolecular forces, such as van der
Waals forces and dipole-dipole forces, and
describe their effects on matter.
100. Choose the name of an electric unit, such
as coulomb, volt, or farad, and research the
life and work of the scientist for whom it
was named. Write a brief essay on this
person and include a discussion of the
work that justified the honor of having a
unit named for him.
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c. How long are they between the plates?
d. How far are they displaced?
Writing in Physics
Inspire Physics
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Physics Problems