Download How could you find out which strip of tape, the one pulled off the

1
How could you find out which strip of tape, the one pulled off
the desk or the one pulled off the back of the other tape, is
positively charged ?
7
List some insulators and conductors.
Answer
Answer
Student answers will vary, but may include dry air, wood,
plastic, glass, cloth, and deionized water as insulators; and
metals, tap water, and your body as conductors.
Rub a piece of hard plastic with wool. The plastic is
charged negatively. It will repel the negatively charged
strip of tape and attract the positively charged one.
8
2
Suppose you attach a long metal rod to a plastic handle so the
rod is isolated. You touch a charged glass rod to one end of the
metal rod. Describe the charges on the metal rod.
Answer
Metals contain free electrons; rubber has bound electrons.
Answer
The glass rod was positively charged. This charge spreads
over the entire metal rod, charging it positively.
3
In the 1730s, Stephan Gray tried to see how far electrical
charge could be conducted by metal rods. He hung metal rods
by thin silk cords from the ceiling. When the rods were longer
than 293 feet, the silk broke. Gray replaced the silk with
stronger wires made of brass, but now the experiments failed.
The metal rod would no longer transmit charge from one end
to the other. Why?
What property makes a metal a good conductor and rubber a
good insulator?
9
Why does a woolen sock taken from a clothes dryer sometimes
cling to other clothes?
Answer
It has been charged by the tumbling of the clothes and is
attracted to the other clothing.
10
If you wipe a stereo record with a clean cloth, why does the
record now attract dust?
Answer
Answer
Brass is a conductor. The electric charge flowed into the
ceiling instead of along the metal rod.
4
Suppose there was a third type of charge. What experiments
could you suggest to explore its properties?
Rubbing the record charges it. Neutral particles such as
dust are attracted to a charged object.
11
How does the charge of an electron differ from the charge of a
proton?
Answer
Answer
If the new type is different from the other two types, then it
should repel (or attract) both positively and negatively
charged objects.
5
6
If you comb your hair on a dry day, the comb can become
positively charged. Can your hair remain neutral? Explain.
The charge of the proton is exactly the same size as the
electron, but has the opposite sign.
12
If you scuff electrons from your feet while walking across a
rug, are you now negatively charged or positively charged?
Answer
Answer
No. By conservation of charge, your hair must become
negatively charged.
When you lose electrons, you become positively charged.
The combined charge of all electrons in a nickel coin is
hundreds of thousands of coulombs, a unit of electrical charge.
Does that imply anything about the net charge on the coin?
Explain.
Answer
No. Net charge is the difference between positive and
negative charges. It can still be zero.
13
Using a charged rod and an electroscope, how can you find if
an object is a conductor?
Answer
Use a known insulator to hold one end of the object against
the electroscope. Touch the other end with the charged rod.
If the electroscope indicates a charge, the object is a
conductor.
14
Explain why an insulator that is charged can be discharged by
passing it above a flame.
20
Answer
Salt water drips slowly from a narrow dropper inside a
negatively-charged metal ring, as seen in the figure.
(a) Will the drops be charged?
(b) If they are charged, are they positive or negative?
The hot gases above the flame are a plasma, which acts as
a conductor and pulls excess charges away from the
insulator.
15
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 they
touch the rod, they fly away in different directions. Explain .
Answer
The neutral spheres are initially attracted to the charged
rod and all acquire the same charge as the rod when they
touch it. subsequently, they are repelled from each other
and from the rod.
Answer
(a) yes
(b) The drops will be positive by induction.
16
A rod-shaped insulator is suspended so it can rotate. A
negatively-charged comb held nearby attracts the rod.
(a) Does this mean the rod is positively charged? Explain.
(b) If the comb repelled the rod, what could you conclude, if
anything, about the charge on the rod?
21
When a rubber rod is rubbed with wool, the rod becomes
negatively charged. What can you conclude about the
magnitude of the wool's charge after the rubbing process?
Why?
Answer
Answer
(a) No. Neutral objects are attracted by either charge.
(b) It must be negative. Neutrals are never repelled .
17
Explain why a balloon that has been rubbed on a wool shirt
sticks to the wall .
magnitude of wool's charge equals magnitude of rod's
charge; charge is conserved
22
Answer
The balloon becomes charged by rubbing. It is attracted to
the neutral wall because it separates the charges in the
wall.
If you stick a piece of transparent tape on your desk and then
quickly pull it off, you will find that the tape is attracted to
other areas of your desk that are not charged. Why does this
happen?
Answer
The tape induces a surface charge on the desk, so the two
are attracted to one another.
18
Name three methods to charge an object.
Answer
23
conduction,
friction,
induction
19
The text describes Coulomb's method for obtaining two
charged spheres, A and B, so that the charge on B was exactly
half the charge on A. Suggest a way Coulomb could have
placed a charge on sphere B that was exactly one third the
charge on sphere A.
Metals such as copper and silver can become charged by
induction while plastic materials cannot. Explain why.
Answer
Because plastic, an insulator, does not easily conduct
charge
24
Why is an electrostatic spray gun more efficient than an
ordinary spray gun?
Answer
Answer
More paint hits the object being painted due to an electrical
attraction between the charged droplets and the oppositely
charged object.
After charging spheres A and B equally, sphere B is
touched to two other equally sized balls that are touching
each other. The charge on B will be divided equally among
all three balls, leaving 1/3 the total charge on it.
25
How are conductors different from insulators?
Answer
Conductors transfer charge easily; insulators do not.
26
27
When a conductor is charged by induction, is the induced
surface charge on the conductor the same or opposite the
charge of the object inducing the surface charge?
32
Answer
Answer
opposite
repulsion, because attraction can be the result of an
induced surface charge, but repulsion only occurs when
two objects each have a net charge
Which activity does not produce the same results as the other
three?
(a) sliding over a plastic-covered automobile seat
(b) walking across a woolen carpet
(c) scraping food from a metal bowl with a metal spoon
(d) brushing dry hair with a plastic comb
33
c
the signs of the charges
34
If a suspended object is attracted to another object that is
charged, can you conclude that the suspended object is
charged?
Answer
No; if a charged object induces a surface charge on the
suspended object, the two are attracted, but the suspended
object has no net charge.
29
What determines the direction of the electric force between two
charges?
Answer
Answer
28
Which effect proves more conclusively that an object is
charged, attraction to or repulsion from another object?
Explain.
A metal can is placed on a wooden table. If a positively
charged ball suspended by a thread is brought close to the can,
the ball will swing toward the can, make contact, then move
away.
(a) Explain why this happens and predict whether the ball is
likely to make contact a second time.
(b) Sketch diagrams showing the charges on the ball and on
the can at each phase.
(c) How can you test whether your explanation is correct?
(d) If your teacher approves of your plan, try testing your
explanation.
Answer
The ball induces an opposite charge, some of which is
transferred upon contact, repelling the ball. Student plans
should include methods for measuring charge polarity.
Explain from an atomic viewpoint why charge is usually
transferred by electrons.
Answer
Protons are relatively fixed in the nucleus, whereas
electrons can be transferred from one atom to another.
30
35
The figure shows five pairs of plates: A, B, and D are charged
plastic plates and C is an electrically neutral copper plate. The
electrostatic forces between the pairs of plates are shown for
three of the pairs. For the remaining two pairs, do the plates
repel or attract each other?
Because of a higher moisture content, air is a better conductor
of charge in the summer than in the winter. Would you expect
the shocks from static electricity to be more severe in summer
or winter? Explain your answer.
Answer
winter, because more charge can accumulate before
electric discharge occurs
Answer
31
A balloon is negatively charged by rubbing and then clings to a
wall. Does this mean that the wall is positively charged?
Answer
No; the balloon clings because its charge induces a surface
charge or the wall.
C and D attract;
B and D attract
36
A positively charged ball is brought close to an electrically
neutral isolated conductor. The conductor is then grounded
while the ball is kept close. Is the conductor charged positively,
charged negatively, or neutral if
(a) Is the conductor charged positively, charged negatively, or
neutral if the ball is first taken away and then the ground
connection is removed?
(b) Is the conductor charged positively, charged negatively, or
neutral if the ground connection is first removed and then the
ball is taken away?
43
Answer
4.8 x 10-6 C
44
Answer
(a) neutral;
(b) negatively
37
Calculate the net charge on a substance consisting of a
combination of 7.0 x 1013 protons and 4.0 x 1013 electrons.
The figure shows three pairs of identical spheres that are to
be touched together and then separated. The initial charges
on them are indicated.
(a) Rank the pairs according to the magnitude of the
charge transferred during touching.
(b) Rank the pairs according to the charge left on the
positively charged sphere, greatest first.
Explain how to charge a conductor negatively if you have only
a positively-charged rod.
Answer
Answer
Without touching the conductor, bring it close to, but not
touching, the rod. Momentarily touch the side of the
conductor farthest from the rod. The conductor will be
charged by induction.
38
How many excess electrons are on a ball with a charge of -4.00
x 10-17 C?
Answer
250 electrons
39
A strong lightning bolt transfers about 25 C to Earth. How
many electrons are transferred?
Answer
(a) 3, 1, 2;
(b) all tie
45
In figure a, two identical, electrically isolated conducting
spheres A and B are separated by a (center-to-center)
distance a that is large compared to the spheres. Sphere A
has a positive charge of +Q, and sphere B is electrically
neutral. Initially, there is no electrostatic force between the
spheres. (Assume that there is no induced charge on the
spheres because of their large separation.)
(a) Suppose the spheres are connected for a moment by a
conducting wire. The wire is thin enough so that any net
charge on it is negligible. What is the electrostatic force
between the spheres after the wire is removed?
(b) Next, suppose sphere A is grounded momentarily, and
then the ground connection is removed. What now is the
electrostatic force between the spheres?
1.6 x 1020 electrons
40
How many electrons would be required to have a total charge
of 1.00 C on a sphere?
Answer
6.25 x 1018 electrons
41
A typical lightning bolt has about 10.0 C of charge. How many
excess electrons are in a typical lightning bolt? The charge of
an electron is 1.6 x 10-19 C
Answer
6.25 x 1019 electrons
42
A negatively charged balloon has 3.5 µC of charge. How many
excess electrons are on this balloon?
Answer
2.2 x 1013 electrons
Answer
46
Benjamin Franklin once wrote that he had "erected an iron rod
to draw the lightning down into my house, in order to make
some experiment on it, with two bells to give notice when the
rod should be electrify'd...." The chime had two small bells
mounted side by side. One bell was connected to the iron rod
for a charge; the other bell was attached to Earth. Between the
two bells, a small metal ball was suspended on a silk thread so
it could swing back and forth, striking the two bells. Explain
why, when the one bell was charged, the ball would keep
swinging, hitting first one bell then the other.
52
Answer
-9.7 x 10-6C
53
Answer
(The metal ball is neutral initially. It is attracted toward the
charged bell. When it hits, it becomes charged. The ball is
now repelled. It is now attracted to the uncharged bell. It
hits this bell, becomes discharged, and starts up the process
again.
Two positive charges of 6.0 x 10-6 C are separated by 0.50 m.
What force exists between the charges?
Answer
1.296 N
54
47
A charge of 4.0 x 10-5 C is attracted by a second charge with a
force of 350 N when the separation is 10.0 cm. Calculate the
size of the second charge.
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?
A negative charge of -2.0 x 10-4 C and a positive charge of 8.0
x 10-4 C are separated by 0.30 m. What is the force between the
two charges?
Answer
Answer
(The charge in the cloud repels electrons on Earth, causing
a charge separation by induction. The side of Earth closest
to the cloud is positive, resulting in an attractive force.
48
-1.6 x 104N
55
Explain what happens to the leaves of a positively-charged
electroscope when rods with the following charges are nearby
but not touching the electroscope.
(a) positive
(b) negative
Answer
Answer
3.0 x 10-6C
56
(a) The leaves will move farther apart.
(b) The leaves will droop slightly.
49
A negative charge of -6.0 x 10-6 C exerts an attractive force of
65 N on a second charge 0.050 m away. What is the magnitude
of the second charge?
Object A has a charge + 1.8 x 10-6 C. Object B has a charge
-1.0 x 10-6 C. They are 0.014 m apart.
(a) What is the force on A?
(b) What is the force on B?
Answer
If two identical charges, 1.000 C each, are separated by a
distance of 1.00 km, what is the force between them?
83 N toward A;
83 N toward B
Answer
+9.0 x 103 N
50
57
Two point charges are separated by 10.0 cm. If one charge is
+20.00 mC and the other is -6.00 mC, what is the force
between them?
A positive and a negative charge, each of magnitude 1.5 x 10-5
C, are separated by a distance of 15 cm. Find the force on each
of the particles.
Answer
90 N, toward the other charge
Answer
-1.1 x 108 N; the force is attractive.
51
Two identical point charges are 3.00 cm apart. Find the charge
on each of them if the force of repulsion is 4.00 x 10-7N
58
Two negatively-charged bodies with -5.0 x 10-5 C are 0.20 m
from each other. What force acts on each particle?
Answer
5.6 x 102 N
Answer
+2.0 + 10-10C
59
A force of -4.4 x 103 N exists between a positive charge of 8.0
x 10 -4 C and a negative charge of -3.0 x 10-4 C. What distance
separates the charges?
66
Answer
0.70 m
60
A small cork with an excess charge of +6 µC (1µ C = 10-6 C) is
placed 0.12 m from another cork, which carries a charge of
-4.3 µC.
(a) What is the magnitude of the electric force between the
corks?
(b) Is theis force atractive or repulsive
(c) How man excessive electrons are on te negative cork?
(d) How many electrons has the postive cork lost?
Answer
Two identical positive charges exert a repulsive force of 6.4 x
10-9 N when separated by a distance of 3.8 x 10-10 m. Calculate
the charge of each.
(a) 16 N
(b) attractive
(c) 2.7 x 1013 electrons
(d) 3.8 x 1013 electrons
Answer
3.2 x 10-19C
67
61
What is the force between two equal positive charges of 2.0 x
10-4 C that are 2.0 m apart?
Two electrostatic point charges of +60 µC and +50.0 µC exert
a repulsive force on each other of 175 N. What is the distance
between the two charges?
Answer
Answer
39.3 cm
89.9 N
68
62
Find the force between a positive charge of 1.0 microcoulombs
and a positive charge of 2.0 microcoulombs when they are
0.030 m apart? (1 microcoulomb = 1 x 10-6 coulombs)
Answer
Answer
20 N
63
64
Two positive charges of 6.0 x 10-6 C are separated by 0.50 m.
What force exists between the charges
3.2 x 10-8 C
69
Answer
What must be the distance between point charge q1 = 26.0 µC
and point charge q2 = -47 µC for the electrostatic force
between them to have a magnitude of 5.70 N?
1.3 N
Answer
A negative charge of -2.0 x 10-4 C and a positive charge of 8.0
x 10-4 C are separated by 0.30 m. What is the force between
the two charges?
1.39 m
70
Answer
-15,964 N
65
Kalyan Ramji Sain, of India, had a mustache that measured
3.39 m from end to end in 1993. Suppose two charges, q and
3q, are placed 3.39 m apart. If the magnitude of the electric
force between the charges is 2.4 x 10-6 N, what is the value of
q?
Two electrons in an atom are separated by 1.5 x 10-10 m, the
typical size of an atom. What is the force between them?
Answer
The charges on the large metal sphere are repelled and
move away from the small sphere, reducing the force.
Answer
1.0 x 10-8 N
Suppose you are testing Coulomb's law using a small, charged
plastic sphere and a large, charged metal sphere. Both are
charged positively. According to Coulomb's law, the force
depends on 1/d2, where d is the distance between the centers of
the spheres. As the two spheres get close together, the force is
smaller than expected from Coulomb's law. Explain.
71
Two charges, q1, and q2, are separated by a distance, d, and
exert a force on each other. What new force will exist if d is
doubled?
Answer
F/4
72
73
Two identical point charges are separated by a distance of 3.0
cm and they repel each other with a force of 4.0 x 10-5 N. What
is the new force if the distance between the point charges is
doubled?
78
At the point of fission, a nucleus of 235U with 92 protons is
divided into two smaller spheres, each with 46 protons and a
radius of 5.9 x 10-15 m. What is the repulsive force pushing
these two spheres apart?
Answer
Answer
1.0 x10-5 N
3.5 x 103 N
An electric force of 2.5 x 10-4 N acts between two small
equally-charged spheres which are 2.0 cm apart. Calculate the
force acting between the spheres if the charge on one of the
spheres is doubled and the spheres move to a 5.0-cm
separation.
79
Suppose you separate the electrons and protons in 1.01 g of
hydrogen and place the protons at Earth's North Pole and the
electrons at Earth's South Pole. What is the magnitude of the
electric force compressing Earth? The number of atoms in 1.01
g of hydrogen is 6.02 x 1023 atoms. Earth's diameter is 1.27 x
107 m.
Answer
Answer
7.9 x 10-5 N
5.17 x 105 N
74
Two charged bodies exert a force on each other of 16
millinewtons. What will be the force between the same two
bodies if the distance between them is halved?
80
Answer
64 millinewtons or .064 newtons
75
In 1990, a French team flew a kite that was 1,034 m long.
Imagine two charges, +2.0 nC and -2.8 nC, at opposite ends of
the kite.
(a) Calculate the magnitude of the electric force between them.
b) If the separation of charges is doubled, what absolute value
of equal and opposite charges would exert the same electric
force?
Answer
A small sphere is given a charge of 20 microcoulombs and a
second sphere of equal diameter located 10 cm away is given a
charge of -5.0 microcoulombs.
(a) What is the force of attraction between the charges?
(b) The two spheres are now allowed to touch and again
spaced 10 cm apart. What force now exists between them?
(a) 4.7 x 10-14 N
(b) 2.88 x 10-9 C
81
Answer
(a) -89.87 N
(b) 50.55 N
What is the magnitude of the electrostatic force between a
singly charged sodium ion (Nal, of charge +e) and an adjacent
singly charged chlorine ion (Cl-, of charge -e) in a salt crystal
if their separation is 2.82 x 10-10 m?
Answer
76
The electric force between a negatively charged paint droplet
and a positively charged automobile body is increased by a
factor of two, but the charges on each remain constant. How
has the distance between the two changed? (Assume that the
charge on the automobile is located at a single point.)
Answer
2.89 x 10-9 N
82
In the figure, particle 1 of charge +4e is above a floor by
distance d1 = 2.00 mm and particle 2 of charge +6e is on the
floor, at distance d2 = 6.00 mm horizontally from partcle 1.
What is the x component of the electrostatic force on
particle 2 due to particle 1?
New distance = 1/√2
77
Answer the following questions:
(a) How does the electric force between two charges change
when the distance between them is doubled?
(b) How does it change when the distance is halved?
Answer
(a) The force becomes 1/4 the initial value;
(b) the force becomes 4 times the initial value.
Answer
+16e
83
Coulomb's law and Newton's Law of Universal Gravitation
appear similar. In what ways are the electrical and gravitational
forces similar? How are they different?
88
Answer
Similar: inverse-square dependence on distance, force
proportional to product of two masses or two charges.
Different: only one sign of mass, so gravitational force is
always attractive, while there are two signs of charge, so
electrical force is either attractive or repulsive.
84
Two 10-10 kg meteorites are traveling in deep space 1000 km
apart. Each has 1.00 C of positive charge.
(a) Will their trajectories converge or diverge?
(b) How would your answer change if the meteorites had
greater masses?
(c) What if they had greater charges?
Answer
The meteorites will diverge less with greater mass and
more with greater charge.
Coulombs Law and the Universal gravitational Law are very
similar.
(a) Calculate the repulsive Coulomb force between two
protons of mass 1.67 x 0-24 g that are 4 x 10-15 m apart inside a
nucleus.
(b) Calculate the gravitational force of attraction between the
two protons.
(c) Why doesn't a force of such magnitude, acting on a proton
cause the nucleus to fly apart?
89
Answer
90
Earth's mass is about 6.0 x 1024 kg, while the moon's mass is
7.3 x 1022 kg. What equal charges must be placed on Earth and
the moon to make the net force between them zero?
Answer
5.7 x 1013 C
(a) 14.4 N
(b) 1.17 x 10-35 N
(c)
How far apart must two protons be if the magnitude of the
electrostatic force acting on either one due to the other is equal
to the magnitude of the gravitational force on a proton at
Earth's surface?
Answer
85
The electron and proton of a hydrogen atom are separated on
average by a distance of about 5.3 x 10-11 m. Find the
magnitudes of the electric force and the gravitational force that
each particle exerts on the other.
11.9 cm
91
Answer
Felectric = -8.2 x 10-8 N
Fg = 3.6 x 10-49 N
86
Answer the following questions:
(a) What are some similarities between the electric force and
the gravitational force?
(b) What are some differences between the two?
Answer
(a) 5.7 x 1013 C;
(b) cancels out;
(c) 6.0 x 105 kg
Answer
both are field forces, both are inverse square laws; electric
forces are attractive or repulsive while gravitational forces
are always attractive, electric force is significantly stronger
than gravitational force
87
Answer the following questions.
(a) What equal positive charges would have to be placed on
Earth and on the Moon to neutralize their gravitational
attraction?
(b) Why don't you need to know the lunar distance to solve this
problem?
(c) How many kilograms of hydrogen ions (that is, protons)
would be needed to provide the positive charge calculated in
(a)?
92
The moon (m = 7.36 x 1022 kg) is bound to Earth (m = 5.98 x
1024 kg) by gravity. The moon is 3.82 x 108 m from the earth.
If, instead, the force of attraction were the result of each having
a charge of the same magnitude but opposite in sign, find the
quantity of charge that would have to be placed on each to
produce the required force.
The nucleus in an iron atom has a radius of about 4.0 x 10-15 m
and contains 26 protons.
(a) What is the magnitude of the repulsive electrostatic force
between two of the protons that are separated by 4.0 x 10-15 m?
(b) What is the magnitude of the gravitational force between
those same two protons?
Answer
(a) 14.38 N
(b) 1.17 x 10-39 N
Answer
5.72 x 1013 C
93
A positive charge of 3.0 x 10-6 C is pulled on by two negative
charges. One, -2.0 x 10-5 C, is 0.050 m to the north and the
other, -4.0 x 10-6 C, is 0.030 m to the south. What total force is
exerted on the positive charge?
Answer
96 N, North
94
Three particles are placed in a line. The left particle has a
charge of -67 x 10-6 C, the middle, +45 x 10-6C,and the right,
-83 x 10-6 C. The middle particle is 72 cm from each of the
others.
(a) Find the net force on the middle particle.
(b) Find the net force on the right particle.
99
In 1994, a group of British and Canadian athletes
performed a rope slide off the top of Mount Gibraltar, in
Canada. The speed of the sliders at times exceeded 160
km/h. The total length of the slide was 1,747 m. Suppose
several sliders are located on the rope as shown. Due to
friction, they acquire the electric charges shown. Find the
magnitude and direction of the resultant electric force
acting on the athlete at the far right of the diagram.
Answer
(a) 12.5 N, right
(b) 40.7 N, left
95
A charge Q1 = +10 x 10-9 C on the x axis at x = 0, and a second
charge Q2 = +3 x 10-9 C is on the x axis at x = 5 m. A third
charge Q3 = -10 x 10-9 C is placed on the x axis at x = 15 m.
Calculate the magnitude and direction of the force on Q2.
Answer
13.7 x 10-9 N toward the right
96
Three charges, each of +80 x 10-6 C, are equally spaced along a
straight line, successive charges being 6 m apart.
(a) Calculate the force on one of the end charges.
(b) Calculate the force on the central charge.
Answer
3.2 x 10-13 N, up the rope
100
Answer
(a) 2.00 N away from the center
(b) 0 newtons on the center charge.
97
Three charges are located on the x-axis. A 5.0 µC charge is
located at x = 0. 0 cm, a 1. 5 µC charge is located at x = 3.0
cm, and a -3.0 µC charge is located at x = 5.0 cm. Find the
resultant force on the 5.0 µC charge.
Answer
(a) leftward;
(b) llleftward;
(c) lleftward
Answer
21 N, along the negative x-axis
98
In 1919 in Germany, a train of eight kites was flown 9,740 m
above the ground. This distance is 892 m higher than Mount
Everest. Consider the arrangement of charges located at the
various heights shown below. If q1 = 2.80 mC, q2 = -6.40 mC,
and q3 = 48.0 mC, find the magnitude and direction of the
resultant electric force acting on q1.
The figure shows two protons (symbol p) and one electron
(symbol e) on an axis.
(a) What is the direction of the electrostatic force on the central
proton due to the electron?
(b) What is the direction of the electrostatic force on the central
proton due to the other proton?
(c) What is the direction of the net electrostatic force on the
central proton?
101
In the figure, four particles are fixed along an x axis, separated
by distances d = 2.00 cm. The charges are q1 = +2e, q2 = -e, q3
= +e , and q4 = +4e, with e = 1.60 x 10-19 C.
(a) In unit-vector notation, what is the net electrostatic force on
particle 1 due to the other particles?
(b) In unit-vector notation, what is the net electrostatic force on
particle 2 due to the other particles?
Answer
(a) (3.52 x 10-25 N)ˆi ;
(b) 0
Answer
0.189 N downward
102
The figure shows four situations in which five charged
particles are evenly spaced along an axis. The charge values
are indicated except for the central particle, which has the same
charge in all four situations. Rank the situations according to
the magnitude of the net electrostatic force on the central
particle, greatest first.
106
Equal charges of +15 x 10-6 C are placed at the four corners of
a square 0.3 m on a side. Calculate the magnitude and
direction of the force on one of the charges.
Answer
43.1 N outward along the diagonal
107
Equal masses of 15 x 106 kg are placed at the four corners of a
square 3 m on a side. Calculate the magnitude and direction of
the force on one of the masses.
Answer
3206 N
Answer
3, 1, & 2 same, 4 (zero)
103
Three particles are placed on a straight line. The left particle
has a charge of +4.6 x l0-6 C, the middle particle has a charge
of -2.3 x l0-6 C, and the right particle has a charge of -2.3 x l0-6
C.
(a) The left particle is 12 cm from the middle particle and the
right particle is 24 cm from the middle particle. Find the force
on the middle particle.
(b) The left particle is now moved directly above the middle
particle, still 12 cm away. Find the force on the middle particle.
108
Equal charges of +8 x 10-6 C are placed at the three corners of
an equilateral triangle 2 m on a side. Calculate the magnitude
and direction of the force on one of the charges.
Answer
.249 N away from the triangle, perpendicular to the
opposite base.
109
Consider three point charges at the corners of a triangle, as
shown in the figure, where q1 = 6.00 x 109 C, q2 = -2.00 x 109
C, and q3 = 5.00 x 109 C. Find the magnitude and direction of
the resultant force on q3.
Answer
Hard
(a) 7.42 N when Horizontal
(b) 7.2° to the left or vertical6.6 N
104
Two charges, q1, and q2, are at rest near a positive test charge,
q, of 7.2 x 10-6 C. The first charge, q1, is a positive charge of
3.6 x 10-6 C, located 0.025 m away from q at 350; q2 is a
negative charge of -6.6 x 10-6 C, located 0.068 m away at 1250.
(a) Determine the magnitude of each of the forces acting on q.
(b) Sketch a force diagram.
(c) Graphically determine the resultant force acting on q.
Answer
Answer
(a) 3.7 x 102 N,away
(b) 92 N, toward
(c) Refer to Problems and Solutions Manual for diagram.
105
A triangle ABC, marked out on a flat surface, has sides of the
following lengths: AB = 4 m, BC = 5 m, and AC = 3 m. At
the corners are the following charges: -40 x 10-6 C at A, -160 x
10-6 C at B, and +90 x 10-6 C at (C) What are the magnitude
and direction of the net force on the charge at A?
Answer
5.09 N, 45 degrees from AC, 135 degrees from AB
7.16 x 1027 N
θ = 65.20
110
Four equal charges of 1.5,uC are placed at the corners of a
square with 5.0 cm sides.
(a) Find the net force on a fifth charge placed in the center of
the square if the new charge is -1.5 µC
(b) Find the net force on a fifth charge placed in the center of
the square if the new charge is +3.0 µC
Answer
(a) -1.5 µC
(b) +3.0 µC
111
Four charged particles are placed so that each particle is at the
corner of a square. The sides of the square are 15 cm. The
charge at the upper left corner is +3.0 µC, the charge at the
upper right corner is -6.0 µC, the charge at the lower left corner
is -2.4 µC, and the charge at the lower right corner is -9.0 µC.
(a)
What is the net electric force on the +3.0 µC charge?
(b)
What is the net electric force on the -6.0 µC charge?
(c)
What is the net electric force on the -9.0 µC charge?
115
Answer
Answer
(a) 13.0 N, 3 V below the positive x-axis
(b) 25 N, 780 above the negative x-axis
(c) 18 N, 750 below the positive x-axis
112
to the left
116
Three charges lie along the x-axis. One positive charge, q1 = 15
µC, is at x= 2.0 m, and another positive charge, q2 = 6.0 µC, is
at the origin. At what point on the x-axis must a negative
charge, q3, be placed so that the resultant force on it is zero?
Answer
Three charges lie along the x-axis. One positive charge, q1 = 15
µC, is at x= 2.0 m, and another positive charge, q2 = 6.0 µC, is
at the origin. At what point on the x-axis must a negative
charge, q3, be placed so that the resultant force on it is zero?
Three positive point charges of 3.0 nC, 6.0 nC, and 2.0 nC,
respectively, are arranged in a triangle, as shown in the figure
below. Find the magnitude and direction of the electric force
on the 6.0 nC charge.
Answer
p = 0.80 m from q2.
113
In which direction will the electric force from the two equal
positive charges pull the negative charge shown in the figure
below?
9.73 x 10-8 N
11.50 below the positive x-axis
117
In 1993, a chocolate chip cookie was baked in Arcadia,
California. It contained about three million chips and was 10.7
m long and 8.7 m wide. Suppose four charges are placed in the
corners of that cookie as follows: q1 = -12.0 nC at the lower left
corner, q2 = 5.6 nC at the upper left corner, q3 = 2.8 nC at the
upper right corner, and q4 = 8.4 nC at the lower right corner.
(a) Draw a picture of the rectangular cooke
(b) Find the magnitude and direction of the resultant electric
force acting on q1.
Answer
Answer
.77 m from q2
114
A +2.2 x 10-9 C charge is on the x-axis at x = 1. 5 m, a +5.4 x
10-9 C charge is on the x-axis at x = 2.0 m, and a + 3.5 x 10-9 C
charge is at the origin. Find the net force on the charge at the
origin.
Answer
7.3 x 10-8 N
along the negative x-axis
(a) Picture
(b) 12.7 x 10-89N
44.6 0 above the positive x-axis
118
119
In 1988, a giant firework was exploded at the Lake Toya
festival, in Japan. The shell had a mass of about 700 kg
and produced a fireball 1.2 km in diameter. Consider a
circle with this diameter. Suppose four charges are placed
on the circle's perimeter so that the lines between them
form a square with sides parallel to the x- or y-axes. The
charges have the following strengths and locations: q1 =
16.0 mC at the upper left "corner," q2 = 2.4 mC at the
upper right corner, q3 = -3.2 mC at the lower right corner,
and q4 = -4.0 mC at the lower left corner. Find the
magnitude and direction of the resultant electric force
acting on q1. (Hint: Find the distances between the charges
first.)
123
In the figure, particle 1 of charge +1.0 μC and particle 2 of
charge -3.0 μC are held at separation L = 10.0 cm on an x
axis. Assume particle 3 of unknown charge q3 is to be located
such that the net electrostatic force on it from particles 1 and 2
is zero.
(a) What must be the x coordinates of particle 3?
(b) What must be the y coordinates of particle 3?
Answer
Answer
1.0 N
770 below the negative x axis
(a) 14 cm;
(b) 0
In 1955, a water bore that was 2,231 m deep was drilled in
Montana. Consider two charges, q2 = 1.60 mC and q1,
separated by a distance equal to the depth of the well. If a third
charge, q3 1.998 mC is placed 888 m from q2 and is between q2
and q1, this third charge will be in equilibrium. What is the
value of q1?
124
In the figure, six charged particles surround particle 7 at
radial distances of either d = 1.0 cm or 2d, as drawn. The
charges are q1 = +2e, q2 = +4e, q3 = +e, q4 = +4e, q5 = +2e, q6
= +8e, q7 = +6e, with e = 1.60 x 10-19 C. What is the
magnitude of the net electrostatic force on particle 7?
Answer
366 mC
120
Hans Langseth's beard measured 5.33 m in 1927. Consider two
charges, q1 = 2.5 nC and q2 = 8.0 nC, separated by the length of
Langseth's beard. How far from q1 should a third charge of 1.0
nC be placed so that no force is exerted on the third charge?
Answer
Answer
0
1.9 m
125
121
In more than 30 years, Albert Klein, of California, drove 2.5 x
106 km in one automobile. Consider two charges, q1 = 2.0 C
and q2 = 6.0 C, separated by Klein's total driving distance. A
third charge, q3 = 4.0 C, is placed on the line connecting q1 and
q2. How far from q1 should q3 be placed for q3 to be in
equilibrium?
The figure shows four identical conducting spheres that are
actually well separated from one another. Sphere W (with
an initial charge of zero) is touched to sphere A and then
they are separated. Next, sphere W is touched to sphere B
(with an initial charge of -32e) and then they are separated.
Finally, sphere W is touched to sphere C (with an initial
charge of +48e), and then they are separated. The final
charge on sphere W is +18e. What was the initial charge on
sphere A?
Answer
9.3 x 108 m
122
A charge of +2.00 x 10-9C is placed at theorigin, and another
charge of +4 x 10-9 C is placed at x = 1.5 m. find the point
between these two charges where a charge of +3.00 x 10-9C
should be paced so that the net electric force on it is zero.
Answer
(a) (0.829 N)ˆi ;
(b) (-0.621 N)ˆj
Answer
x = 0.64 m
126
In the figure, three identical conducting spheres form an
equilateral triangle of side length d = 20.0 cm. The sphere radii
are much smaller than d, and the sphere charges are qA = -2.00
nC, qB = -4.00 nC, and qC = +8.00 nC.
(a) What is the magnitude of the electrostatic force between
spheres A and C?
The following steps are then taken: A and B are connected by a
thin wire and then disconnected; B is grounded by the wire,
and the wire is then removed; B and C are connected by the
wire and then disconnected.
(b) What now is the magnitude of the electrostatic force
between spheres A and C?
(c) What now is the magnitude of the electrostatic force
between spheres B and C?
128
In the figure, a central particle of charge -q is surrounded by
two circular rings of charged particles. What are the magnitude
and direction of the net electrostatic force on the central
particle due to the other particles? (Hint: Consideration of
symmetry can greatly reduce the amount of work required
here.)
Answer
2kq2/r2 , up the page
Answer
(a) 3.60 µN;
(b) 2.70 µN;
(c) 3.60 µN
127
The figure shows two charged particles on an axis. The charges
are free to move. However, a third charged particle can be
placed at a certain point such that all three particles are then in
equilibrium.
(a) Is that point to the left of the first two particles, to their
right, or between them?
(b) Should the third particle be positively or negatively
charged?
(c) Is the equilibrium stable or unstable?
129
In the figure, a central particle of charge -2q is surrounded by a
square array of charged particles, separated by either distance d
or d/2 along the perimeter of the square. What are the
magnitude and direction of the net electrostatic force on the
central particle due to the other particles? (Hint: Consideration
of symmetry can greatly reduce the amount of work required
here.)
Answer
(a) between;
(b) positively charged;
(c) unstable
Answer
6kq2/d2 , leftward
24q2/d2
130
The figure shows four arrangements of charged particles. Rank
the arrangements according to the magnitude of the net
electrostatic force on the particle with charge +Q, greatest first.
135
Two small spheres each having a mass of 0.10 g are suspended
from the same point on silk threads 20 cm long. When given
equal charges, they repel each other, coming to rest 24 cm
apart. Find the charge on each sphere?
Answer
6.86 x 10-8 C
136
An electron is released above the Earth's surface. A second
electron directly below it exerts just enough of an electric force
on the first electron to cancel the gravitational force on it. Find
the distance between the two electrons.
Answer
5.07 m
Answer
a and d tie, then b and c tie
137
131
A charge q1 of -6.00 x 10-9 C and a charge q2 of -3.00 x 10-9 C
are separated by a distance of 60.0 cm. Where could a third
charge be placed so that the net electric force on it is zero?
Answer
Answer
35.2 cm from q1
(24.8 cm from q2)
132
Three point charges lie along the y-axis. A charge of q1 = -9.0
µC is at y = 6.0 m, and a charge of q2 = -8.0 µC is at y= -4.0 m.
The net electric force on the third charge is zero. Where is this
charge located?
Two small metallic spheres, each with a mass of 0.20 g, are
suspended as pendulums by light strings from a common point.
They are given the same electric charge, and the two come to
equilibrium when each string is at an angle of 5.00 with the
vertical. If the string is 30.0 cm long, what is the magnitude of
the charge on each sphere?
7.17 x 10-9 C
138
The most accurate balance can measure objects with masses as
small as 1.0 x 10-11 kg, which is less than the mass of the ink in
the period at the end of this sentence. Suppose a mass this
small is suspended by electric repulsion over a charge of -4.0
nC. How many extra electrons must be placed on the mass so
that it will float 2.0 cm directly over the -4.0 nC charge?
Answer
Answer
y = 0.8 m from the zero point or 5.1 from one end
6.8 x 103 electrons
133
Two Ping-Pong balls painted with aluminum paint are
suspended from the same point by threads 50 cm long. The
mass of each ball is 20 g. When equal charges are given to the
two balls, they come to rest in an equilibrium position in which
their centers are 60 cm apart. Calculate the charge on each
ball.
139
In 1959, Alf Dean caught a 1,208 kg white shark with a fishing
rod. Consider a 1,208 kg block hung from a cable. Suppose the
mass has an extra charge of 4.80 nC. By what percent would
the electric force increase the tension of the cable (compared to
the situation with the mass only) if an equal and opposite
charge is placed 20.0 cm directly underneath the block?
Answer
Answer
2.42 x 10-6 C
4.7 x 10-8 percent
134
Two small spheres each having a mass of 0.050 g are
suspended by silk threads from the same point. When given
equal charges, they separate, the threads make an angle of 10
degrees with each other. What is the force of repulsion acting
on each sphere?
140
The CN Tower, in Toronto, Canada, is 553 m tall. Suppose two
balls, each with a mass of 5.00 kg and a charge of 40.0 mC, are
placed at the top and bottom of the tower, respectively. The
ball at the top is then dropped. At what height is the
acceleration on the ball zero?
Answer
4.3 x 10-5 N
Answer
542
141
In 1995, a single diamond was sold for more than 16 million. It
was not the largest diamond in the world, but its mass was an
impressive 20.0 g. Consider such a diamond resting on a
horizontal surface. It is known that if the diamond is given a
charge of 2.0 µC and a charge of at least -8.0 µC is placed on
that surface at a distance of 1.7 m from it, then the diamond
will barely keep from sliding. Calculate the coefficient of static
friction between the diamond and the surface.
146
Answer
147
Answer
0.25
142
Answer
(a) 2.3 x 10-9 m/s2
(b) 2.3 x 10-28 N
The parasitic wasp Carapractus cinctus has a mass of 5.0 x 10-6
kg, which makes it one of the smallest insects in the world. If
two such wasps are given equal and opposite charges with an
absolute value of 2.0 x 10-15 C and are placed 1.00 m from each
other on a horizontal smooth surface, what extra horizontal
force must be applied to each wasp to keep it from sliding?
Take into account both gravitational and electric forces
between the wasps.
Answer
145
2.0 x 10-6 C
148
A DNA molecule (deoxyribonucleic acid) is 2.17 mm long.
The ends of the molecule become singly ionized so that there is
an increase of 1.00 percent upon becoming charged. Find the
effective spring constant of the molecule.
Answer
2.25 x 10-9 N/m
An electron is in a vacuum near Earth's surface and located at y
= 0 on a vertical y axis. At what value of y should a second
electron be placed such that its electrostatic force on the first
electron balances the gravitational force on the first electron?
Two particles are fixed on anx axis. Particle 1 of charge 40 μC
is located at x = -2.0 cm; particle 2 of charge Q is located at x
= 3.0 cm. Particle 3 of charge magnitude 20 μC is released
from rest on the y axis at y = 2.0 cm.
(a) What is the value of Q if the initial acceleration of particle 3
is in the positive direction of the x axis?
(b) What is the value of Q if the initial acceleration of particle
3 is in the positive direction of the y axis?
Answer
Answer
-5.1 m
(a) -83 µC;
(b) l55 µC
3.77 x 10-20 N
144
Three identical point charges, each of mass m = 0.10 kg, hang
from three strings, as shown in the figure below. If L = 30.0
cm. and θ = 450, what is the value of θ?
Mycoplasma is the smallest living organism known. Its mass
has an estimated value of 1.0 x 10-16 g.
(a) If two specimens of this organism are placed 1.0 m apart
and one electron is placed on each, what is their initial
acceleration due to the electric force?
(b) If the medium through which the Allycoplasma move
exerts a resistive force on the organisms, how large must that
force be to balance the force of electrostatic repulsion?
Answer
143
Four objects of equal mass and equal charge are placed at the
corners of a square with 4 meter sides. A charge of 12 x 10-5C
are placed on each object. What is the mass of each object if
the Gravitational Force on each object is equal to the
electrostatic force.
A small plastic sphere coated with a thin metalized surface has
mass 0.05 g and carries a charge of +8 x 10-9 C. It is suspended
by a light insulating thread at a point 3 cm below the center of
a small fixed conducting sphere carrying -5 x 10-9 C. The
thread is cut.
(a) What is the electrostatic force upward?
(b) What is the net force?
(b) What is the observed acceleration?
Answer
(a)
(b) 1 x10-4 N
(c) 2 m/s2 downward
149
150
The figure shows an arrangement of four charged particles,
with angle θ = 30.00 and distance d = 2.00 cm. Particle 2 has
charge q2 = +8.00 x 10-19 C; particles 3 and 4 have charges q3 =
q4 = -1.60 x 10-19 C.
(a) What is distance D between the origin and particle 2 if the
net electrostatic force on particle 1 due to the other particles is
zero?
(b) If particles 3 and 4 were moved closer to the x axis but
maintained their symmetry about that axis, would the required
value of D be greater than, less than, or the same as in part (a)?
Answer
(a) 1.92 cm;
(b) less than
151
In the figure, all four particles are fixed in the xy plane,
and q1 = -3.20 x 10-19 C, q2 = +3.20 x 10-19 C, q3 = +6.40 x 10
-19
C, q4 = +3.20 x 10-19 Q, θ, = 35.00, d1 = 3.00 cm, and d2 =
d3= 2.00 cm.
(a) What is the magnitude of the net electrostatic force on
particle 4 due to the other three particles?
(b) What is the direction of the net electrostatic force on
particle 4 due to the other three particles?
Answer
(a) 6.16 x 10-24 N;
(b) 2080