positively charged - Colorado Mesa University

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Electrostatics
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1
Question 1
A plastic rod is rubbed and touched
to a small metal ball. After this the
rod is observed to repel the ball.
Which of the following is correct?
1. The force exerted by the rod on the ball is a contact
force.
2. The force exerted by the rod on the ball is a
gravitational force.
3. The force exerted by the rod on the ball is not
a gravitational force since only Earth can exert
gravitational forces.
4. The force exerted by the rod on the ball is not a
gravitational force since it is repulsive.
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2
Question 2
A plastic rod is rubbed and touched
to a small metal ball. After this the
rod is observed to repel the ball.
Which of the following is correct?
1. The force exerted by the rod on the ball is a contact
force.
2. The force exerted by the rod on the ball is a
gravitational force.
3. The force exerted by the rod on the ball is not
a gravitational force since only Earth can exert
gravitational forces.
4. The force exerted by the rod on the ball is not a
gravitational force since . . . .
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3
Question 3
Congratulations! You now know how to navigate the
course website. The following is a photograph of a
well-known city.
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Describe as accurately as you can
the name of this city, its country
and continent.
4
Question 4
Two balls are suspended and are observed to
repel each other.
Which of the following is true?
1. One ball is positive, the other negative.
2. Both are positive.
3. Both are negative.
4. Either both are positive or else both are
negative.
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5
Question 5
Two pairs of balls are suspended next to
each other. Each pair is observed to repel
and the green ball is the same in both cases.
The red and blue balls are placed near to
each other. Which of the following will be
observed?
1. The red and blue repel each other.
2. The red and blue attract each other.
3. The red does not exert a force on the blue
but the blue does exert a force on the red.
4. The blue does not exert a force on the red
but the red does exert a force on the blue.
5. Neither ball exerts a force on the other.
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6
Question 6
A small metal sphere is initially neutral. It
is placed into contact with a small negatively
charged metal cube and then released.
Which of the following is true after the two
objects have been in contact?
1. They attract each other and stay in
contact.
2. They repel each other and move apart.
3. They neither attract nor repel but still stay
in contact.
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7
Question 7
Two negatively charged metal balls are
connected by a metal wire and suspended
over a wooden (insulating) peg as illustrated.
Which of the following best describes the rod?
1. The rod is positively charged.
2. The rod is negatively charged.
3. The rod is uncharged.
4. The rod is magic.
−
−
A rod is brought near to but not touching the
peg and it is observed that the separation of
the balls increases.
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8
Question 8
A negatively charged rod is held near to a
neutral oval object, which becomes polarized
as illustrated.
Which of the following is true about the
forces exerted by the rod on the oval object?
1. The force on the right edge (of the oval)
is the same as that on the left edge (of
the oval) since the charges at the edges
are the same.
−
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+
−
−
−
−
2. The force on the right edge is larger than
as that on the left edge.
3. The force on the right edge is smaller than
as that on the left edge.
9
Question 9
A positively charged rod is held above a
metal ball on an insulating stand. The ball is
connected to the earth by a wire. While the
rod is in place, the wire is removed. After
this, the rod is removed.
+++++
Which of the following best describes the
charge on the ball at the end of this
procedure?
1. Positive.
2. Negative.
3. No net charge but polarized.
4. No net charge and not polarized.
5. There is not enough information.
It is important to note that the earth can
supply or remove plentiful electrons from any
object with which it is in contact.
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10
Question 10
Two identical subatomic particles, labeled X,
are separately placed near to two different
particles, labeled A and B. The forces exerted
by X on either A or B are as illustrated.
A
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3. The charge of X is larger in case 1 than
in case 2.
4. The charge of X is smaller in case 1 than
in case 2.
Case 2
X
1. The charge of X in case 1 is opposite to
that of X in case 2.
2. The charge of X in the same in both cases.
Case 1
X
Which of the following is true?
B
11
Question 11
An isolated particle has charge +16 C. Consider the
following statements:
Which of the statements are true?
1. Only A.
A) The particle always exerts a force of 16 N but can
feel a force of any size.
B) The particle always feels a force of 16 N but can
exert a force of any size.
2. Only B.
3. Only C.
4. None of them.
C) The particle always exerts a force of 16 N and
always feels a force of 16 N.
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12
Question 12
A point particle, named Zog, has charge +16 C and
is in the vicinity of another point charged particle.
Consider the following statements:
Which of the statements are true?
A) Zog definitely exerts a force of 16 N but the force
Zog feels could be of another size.
2. Only B.
B) Zog definitely feels a force of 16 N but the force
Zog exerts could be of another size.
4. None of them.
1. Only A.
3. Only C.
C) Zog definitely exerts a force of 16 N and definitely
feels a force of 16 N.
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13
Question 13
A proton gun fires a proton toward
another subatomic particle. After it
leaves the gun, it travels in a straight
line with constant speed toward another
particle.
The two particles are isolated and the gravitational
forces between them are negligible (i.e. ignore the
gravitational forces). Which of the following is
true?
1. The particle on the right is positively charged.
+
?
2. The particle on the right is negatively charged.
3. The particle on the right contains absolutely
no charge.
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14
Question 14
Two charges are aligned as illustrated.
Denote the electrostatic force exerted by the
~blue on red
blue charge on the red charge as F
~red on blue .
and that by the red on blue as F
Which of the following is true regarding the
magnitude of the two forces?
1. Fred on blue = Fblue on red
2. Fred on blue > Fblue on red
+2 C
+
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−4 C
−
3. Fred on blue < Fblue on red
4. The sizes of forces depends on the masses
of the particles.
15
Question 15
Two metal balls are supported on fixed
insulating stands and they are given distinct
charges. Which of the following correctly
illustrates the electrostatic forces on the two
balls?
Case 1
+ +
+ +
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+ +
+ +
+
+
Case 4
+
+
Case 2
+ +
+ +
Case 3
+ +
+ +
+
+
Case 5
+
+
+ +
+ +
+
+
16
Question 16
Three charges are aligned as illustrated.
+2 C
+
−2 C
−
−4 C
−
Which of the following gives the direction of
the net force exerted on the charge at the
right?
1.
2.
3.
4.
→
←
↑
↓
5. Zero net force.
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17
Question 17
Three charges are aligned as illustrated.
+2 C
+
−2 C
−
+4 C
+
Which of the following gives the direction of
the net force exerted on the blue charge?
1.
2.
3.
4.
→
←
↑
↓
5. Zero net force.
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18
Question 18
In which of the following is the magnitude of
the net electrostatic force exerted on the blue
charge largest? All distances between the red
and blue charges are equal.
1.
−e
+e
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2.
+e
+e
−e
+e
−e
+e
3.
+e
19
Question 19
Two particles with charges that are identical
in magnitude but opposite in sign are placed
along the x axis as illustrated.
Which of the following best represents the
direction of the net force exerted on the
charge on the y axis?
y
1.
−Q
−q
2.
3.
+q
x
4.
A negatively charged particle is placed along
the y axis.
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5.
→
←
ր
ց
↑
20
Question 20
Two identically charged particle are placed
along the x axis as illustrated.
y
3.
−ĵ
4.
î − ĵ
5.
î + ĵ
+q
x
A negatively charged particle is placed along
the y axis.
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2.
î
ĵ
1.
−Q
+q
Which vector best represents the direction
of the net force exerted on the charge on
the y axis?
21
Question 21
The electric field produced by a hidden charge
collection of charged particles (sources) is
illustrated below. Initially a probe charge
with charge 5 C is placed at point P. This is
removed and replaced by a new probe charge
with charge 10 C, also placed at P.
Which is true at point regarding the electric
field produced by the sources at P and the
forces on the probe charges?
1. Field is same (for both probes), force is
same (for both probes).
2. Field is same, force differs.
3. Field differs, force is same.
4. Field differs, force differs.
P
×
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22
Question 22
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Consider the statement regarding the electric
field produced by the ring and the plate:
“The electric field at point P describes, or is
used to describe, whether the plate attracts
or repels the ring.”
Is this statement true or false?
1. True
P×
+++++++++++++++++++++
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2. False
3. Depends on the situation.
23
Question 23
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Consider the statement regarding the electric
field produced by the ring and the plate:
“The electric field at point P is always the
force exerted at P.”
Is this statement true or false?
1. True
2. False
P×
3. Depends on the situation.
+++++++++++++++++++++
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24
Question 24
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Consider the statement regarding the electric
field produced by the ring and the plate:
“The electric field consists of two vectors,
one indicating a downward attraction on the
ring and the other an upward attraction on
the plate.”
Is this statement true or false?
P×
+++++++++++++++++++++
1. True
2. False
3. Depends on the situation.
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25
Question 25
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Consider the statement regarding the electric
field produced by the ring and the plate:
“The electric field at P produced by the plate
and ring consists of one vector and this is the
same regardless of any other charge which is
placed at P.”
Is this statement true or false?
P×
+++++++++++++++++++++
1. True
2. False
3. Depends on the situation.
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26
Question 26
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Consider the statement regarding the electric
field produced by the ring and the plate:
“The electric field at P produced by the plate
and ring consists of one vector and thus will
exert the same force on a charge placed at P
as on any other charge placed at P.”
Is this statement true or false?
P×
+++++++++++++++++++++
1. True
2. False
3. Depends on the situation.
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27
Question 27
A positively charged plate is placed in the
vicinity of a negatively charged ring. The
plate and ring are held fixed as illustrated
and the charges are evenly distributed on
each.
−−−
−
−
−−−
Which of the following best represents the
direction of the electric field produced by
the ring and the plate at P?
1.
2.
↑
↓
for
↓
↑
for
for positive probe charge
negative probe charge.
for positive probe charge
negative probe charge.
↑ for any probe charge.
4. ↓ for any probe charge.
3.
P×
+++++++++++++++++++++
5. Zero field.
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28
Question 28
The electric field produced by a hidden charge
collection of charged particles (sources) is
illustrated below.
A charged particle is placed at point P.
Which of the following is true of the force
exerted by the electric field on the charged
particle?
1. The force will definitely be to the right.
2. The force will definitely be to the left.
P
×
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3. The force could be either right or left.
4. The force depends on the direction of
motion of the particle.
29
Question 29
The electric field produced by a hidden
charge collection of charged particles is
illustrated below.
Q
×
P
×
Which of the following is true?
1. The magnitude of the force exerted on
a charge at P is always larger than that
exerted on another charge at Q.
2. The magnitude of the force exerted on a
charge at P is always smaller than that
exerted on another charge at Q.
3. The magnitude of the force exerted on a
charge at P could be larger or smaller than
that exerted on another charge at Q.
4. The magnitude of the force exerted on a
charge at P can never be the same as that
exerted on another charge at Q.
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30
Question 30
A positive charge, labeled A, of magnitude
+5 C, and another charge B, of magnitude
−8 C, are placed as illustrated. The distance
between the charges is 10 m.
A
+
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B
−
Which of the following is true for the electric
field produced by A at the location of B?
~ =k
1. E
8C
(10 m)2
→
~ =k
2. E
8C
(10 m)2
←
~ =k
3. E
5C
(10 m)2
→
~ =k
4. E
5C
(10 m)2
←
2
40
C
~ =k
5. E
(10 m)2
←
31
Question 31
A positive charge, Zog, is placed in
the vicinity of a collection of source
charges. The net force exerted on
the positive charge is as illustrated.
+
Zog
~
F
Zog is replaced by another charge, Geraldine, of the
same magnitude but of opposite sign. The source
charges are unaltered. Which of the following is true
regarding the electric field produced by the source
~ and the force on Geraldine compared to
charges, E,
those when Zog was present?
~ same direction.
1. Force same direction, E
~ reverses direction.
2. Force same direction, E
~ same direction.
3. Force reverses direction, E
~ reverses direction.
4. Force reverses direction, E
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32
Question 32
In the following separate scenarios two source
charges produce electric fields. Consider
the magnitude of the field at the location
midway between the two source charges.
Case A
+4 C
+
×
+4 C
+
Which of the following describes the rank of
the magnitudes of the fields at the midpoint?
1. EC > EA = EB
2. EA = EB = EC
3. EA = EB > EC
Case B
+2 C
+
Case C
+2 C
+
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×
+2 C
+
×
−2 C
−
4. EA > EB > EC
5. EC > EA > EB
33
Question 33
Two point charges of equal magnitude but
opposite sign are located as illustrated.
A
+
P
×
B
−
Which of the following best represents the
net electric field produced by A and B at the
location of Z?
1.
A third charge, Z, is placed at point P.
2.
3.
4.
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→ if Z is positive; ← if Z is negative.
← if Z is positive; → if Z is negative.
→ if Z is positive; → if Z is negative.
← if Z is positive; ← if Z is negative.
34
Question 34
Two plates, held 0.050 m apart are charged.
The electric field between them is uniform
and points down with a magnitude of
1200 N/C. A small ball of 100 electrons is
placed between the plates.
Which of the following represents the
magnitude of the force exerted by the field
on the ball of electrons?
1. F = 100 N
2. F = 1200 N
3. F = 120000 N
1.6 × 10−17 C × 100 C
4. F = k
(0.050 m)2
5. None of the above.
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35
Question 35
The electric field produced by a hidden
charge collection of charged particles is
illustrated below.
Which vector best represents the direction
of the force exerted on a positively
charged particle placed at (1, 1)?
1.
î + ĵ
2.
î − ĵ
3.
−î + ĵ
4.
−î − ĵ
y
1
-2
-1
1
-1
2
x
5. None of the above/not enough info.
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36
Question 36
The electric field produced by a hidden
charge collection of charged particles is
illustrated below.
Which vector best represents the direction
of the force exerted on a negatively
charged particle placed at (1, −1)?
1.
î + ĵ
2.
î − ĵ
3.
−î + ĵ
4.
−î − ĵ
y
1
-2
-1
1
-1
2
x
5. None of the above/not enough info.
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37
Question 37
Two particles with charges that are identical
in magnitude but opposite in sign are placed
along the x axis as illustrated.
Which vector best represents the direction
of the Electric field at the origin?
2.
î
ĵ
3.
−ĵ
4.
−î
1.
y
−q
+q
x
5. None of the above.
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38
Question 38
Two point charges of equal magnitude but
opposite sign are located as illustrated.
+
-3
–
-2
A
-1
0
1
2
3
B
A third charge, Z, is placed at (1, 0).
Which of the following best represents the
net electric field produced by A and B at the
location of Z?
1.
2.
3.
4.
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→ if Z is positive; ← if Z is negative.
← if Z is positive; → if Z is negative.
→ if Z is positive; → if Z is negative.
← if Z is positive; ← if Z is negative.
39
Question 39
Four charged particles are arranged as
illustrated where distances are in meters.
y
4
q
î
8
q
2. −k î
8
1. k
+q
2
+q
-4
-2
2
-2
-4
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+q
Which of the following best represents the
electric field at the origin?
−2q
4
x
3q
î
8
q
4. k î
4
3. k
5. None of the above/not enough info.
40
Question 40
The illustrated arc contains a uniform
distribution of positive charge.
y
Which of the following best describes the
direction of the electric field at the center of
the arc?
3.
î
-î
ĵ
4.
-ĵ
5.
î + ĵ
1.
x
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2.
41
Question 41
The illustrated arc of radius R
contains a uniform distribution
of positive charge.
Consider the
contribution of the portion located at
angle θ and containing charge dq as
illustrated.
y
Which of the following best describe the components
~ produced by this segment?
of dE
1. dEx = k
dq
2. dEx = −k 2 cos θ
R
3. dEx = k
θ
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x
dq
cos θ
R2
dq
cos θ
R2
dEy = k
dq
sin θ
R2
dq
dEy = k 2 sin θ
R
dEy = −k
dq
sin θ
R2
4. dEx = −k
dq
cos θ
R2
dEy = −k
5. dEx = −k
dq
sin θ
2
R
dEy = −k
dq
sin θ
R2
dq
cos θ
2
R
42
Question 42
The illustrated arc of radius R contains a
uniform distribution of positive charge.
y
α
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x
Which of the following best describe the x
component of the electric field E produced
by the entire arc?
kλ
1. Ex = −
R
Z
R
kλ
2. Ex = −
R
Z
−(π−α/2)
kλ
3. Ex = −
R
Z
π−α/2
kλ
4. Ex = −
R
Z
α
kλ
5. Ex = −
R
Z
2π
cos θ dθ
0
cos θ dθ
π−α/2
cos θ dθ
−(π−α/2)
cos θ dθ
0
cos θ dθ
0
43
Question 43
A proton enters a region of constant electric
field as illustrated.
b
Which of the following best represents the
trajectory of the proton while it is in the field?
~
E
Case 1
Case 2
Case 3
Case 4
Case 5
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44
Question 44
The following diagrams illustrate a dipole
placed in electric fields.
Case (a)
Case (b)
−+
+
−
In which of these cases is the net force on
the dipole equal to zero?
1. (a) and (b)
2. (a) and (c)
3. (c) and (d)
4. (b) and (d)
Case (c)
Case (d)
5. (c) only
−+
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+
−
45
Warm Up Question 1
Some molecules such as water have what is known as a permanent electric dipole. Consider
the example of a permanent electric dipole as illustrated in the text. Is it possible for a
permanent electric dipole to have a net (total) charge of zero? Explain your answer.
1. No. The dipole will not be symmetrical and so there will be an imbalance of
forces.
2. No. There is positive and negative charge so the dipole is charged and cannot
have a charge of zero.
3. Yes. The molecule is divided into a positive side and a negative side, each with
equal magnitude, the molecule as a whole has a neutral charge.
4. Yes. The force exerted by the positive cancels that exerted by the negative.
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46
Warm Up Question 2
Go to the course website at:
http://myhome.mesastate.edu/∼dacollin/teaching/2011Spring/Phys112
Look in the navigation bar on the left and click “Calendar”. This will open a new page
with a day-by-day listing of the course activities. Click on the link for the “Quiz” on 19
January. You should see the quiz questions that were covered in the class. Now answer
question 2.
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47
Warm Up Question 3
A charge of interest, Zog, is placed in the vicinity of a collection of charged metal objects.
The force exerted by Zog is determined to point directly up. Is is true that the electric
field at Zog’s location and produced by the charged metal objects points directly up?
Explain your answer.
1. Yes. The force points away from Zog, so Zog is positive and the field must also
point away.
2. No. The charges of the metal objects point opposite to Zog.
3. No. Depending on the charges on the metal objects, Zog could be pulled up or
down.
4. No. There could be many objects producing fields in all directions. These could
add up to a net force upwards.
5. No. Zog’s charge is not known. If it’s charge is positive then the field would be
up. However, if it’s charge is negative the field would be down.
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48
Warm Up Question 4
Source charges are placed on two differently sized and separated balls and kept fixed.
Various probe charges are placed at the location exactly midway between the two balls.
Will the electric field produced (by the charged balls) at this location point one way for a
positive probe charge and the other way for a negative probe charge? Explain your answer.
1. Yes. The electric field points away from a positive charge and toward a negative
charge.
2. Yes. The field depends on whether the probe is attracted or repelled. This
depends on the probe charge.
3. No. The electric field produced by the source charges is dependent solely upon
the source charges. The probe charges do not influence the source charge
electric field.
4. This depends on the sources. If they are like then the fields point away. If
opposite toward.
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49
Warm Up Question 5
A vacuum is a region in which there is absolutely no matter, not even a single electron. Is
it possible to establish an electric field in a box, inside which there is a vacuum? Explain
your answer.
1. No. There is no matter inside the box so there is nothing to produce a field.
2. Yes. One can have an electron without mass. This would not be matter and
could produce a field.
3. Yes. There is gravity in a vacuum. The formula for gravity is very similar to the
formula for electrostatic force.
4. Yes. If the vacuum is surrounded by charged particles, the electric field can
travel through the into the vacuum, even without any particles being in the
vacuum.
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50
Warm Up Question 6
During a thunderstorm in the middle of a flat prairie, you have the choice of sitting inside
either a small fiberglass trailer or else an aluminum trailer (Airstream!). Inside which of
these will you be safer from a lightening strike? Explain your answer.
1. Airstream. Aluminum is a better conductor of electricity. A conductor can
”shield” the inside from external electric fields.
2. Fiberglass. Fiberglass insulates and cannot carry charges.
3. Airstream because Airstreams rule!
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51
Electrostatic Potential
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52
Question 45
A positively charged particle (source) is
held fixed.
Another charged particle,
Zog, fired toward the source a long
time ago, moves toward the source particle.
Assume that the only force acting on Zog is the
electrostatic force due to the positively charged
particle. Which of the following is true during
this motion?
1. ∆Uelec > 0 regardless of Zog’s charge.
2. ∆Uelec < 0 regardless of Zog’s charge.
+
Zog: final
Zog: initial
3. ∆Uelec > 0 for positive Zog, ∆Uelec < 0
for negative Zog.
4. ∆Uelec < 0 for positive Zog, ∆Uelec > 0
for negative Zog.
– Typeset by FoilTEX –
53
Question 46
A negatively charged particle (source)
is held fixed. Another charged particle,
Zog, fired toward the source a long
time ago, moves toward the source particle.
Assume that the only force acting on Zog is
the electrostatic force due to the negatively
charged particle. Which of the following is true
during this motion?
1. ∆Uelec > 0 regardless of Zog’s charge.
2. ∆Uelec < 0 regardless of Zog’s charge.
−
Zog: final
Zog: initial
3. ∆Uelec > 0 for positive Zog, ∆Uelec < 0
for negative Zog.
4. ∆Uelec < 0 for positive Zog, ∆Uelec > 0
for negative Zog.
– Typeset by FoilTEX –
54
Question 47
A hidden collection of fixed charges produces
the uniform electric field as illustrated. A
positively charged particle moves in a straight
line from the indicated initial to final location.
Which of the following is true regarding the
work done by the electric field on the particle?
1. W > 0.
2. W < 0.
3. W = 0.
Initial
+
– Typeset by FoilTEX –
Final
+
4. W depends on the speed of the charge.
55
Question 48
A hidden collection of fixed charges produces
the uniform electric field as illustrated.
A negatively charged particle moves in a
straight line from the indicated initial to final
location.
Which of the following is true regarding the
work done by the electric field on the particle?
1. W > 0.
2. W < 0.
3. W = 0.
Final
−
– Typeset by FoilTEX –
Initial
−
4. W depends on the speed of the charge.
56
Question 49
A hidden collection of fixed charges produces
the uniform electric field as illustrated.
A charged particle moves in a straight
line from the indicated initial to final location.
Final
Initial
Which of the following is true regarding the
work done by the electric field on the particle?
1. W > 0 in all cases.
2. W < 0 in all cases.
3. W > 0 for positive charge and W < 0
for negative charge.
4. W < 0 for positive charge and W > 0
for negative charge.
5. W = 0 in all cases.
– Typeset by FoilTEX –
57
Question 50
A positively charged particle (source) with
charge +Q is held fixed. Another object,
Zog, with charge +q , fired toward the source
a long time ago, moves as illustrated.
Assume that the only force acting on the
positively charged particle is the electrostatic
force due to the source. Which of the
following is true for Zog during this motion?
1. Welec = 0 and ∆K = 0.
+q
+
+q
+
2. Welec > 0 and ∆K > 0.
Zog: final
Zog: initial
3. Welec > 0 and ∆K < 0.
+Q
+
4. Welec < 0 and ∆K > 0.
5. Welec < 0 and ∆K < 0.
– Typeset by FoilTEX –
58
Question 51
A negatively charged particle (source) with
charge −Q is held fixed. Positive probe
charges move between the same points as
illustrated.
Probe A has charge 2.0 C and probe B had
charge 10.0 C Which of the following is
true?
1. Work done on probe A is same as that on
probe B.
+q
+
+q
+
Probe: final
Probe: initial
−Q
−
2. Work done on probe B is 5 times larger
than on probe A.
3. Work done on probe B is more than 5
times larger than on probe A.
4. Work done on probe B is more between 1
and 5 times larger than on probe A.
5. Work done on probe B is smaller than on
probe A.
– Typeset by FoilTEX –
59
Question 52
A positively charged object with charge
+Q is held fixed and a negatively
charged object,
Zog,
with charge
−q is released in such a way that at a
later instant it is closer to the positive charge.
Assume that the only force acting on the
negatively charged particle is the electrostatic
force due to the positively charged particle.
Which of the following is true for Zog during
this motion?
1. ∆K > 0 and ∆Uelec > 0.
+Q
+
−q
−
Zog: final
−q
−
Zog: initial
2. ∆K > 0 and ∆Uelec < 0.
3. ∆K < 0 and ∆Uelec > 0.
4. ∆K < 0 and ∆Uelec < 0.
5. Not enough info/none of the above.
– Typeset by FoilTEX –
60
Question 53
Consider the following arrangements of
charges. The source charge is the same
in all cases and charge Zog was moved at
constant speed from infinitely far away to its
illustrated final location.
+Q
Case A +
+6 C
+
– Typeset by FoilTEX –
1. UA = UB < UC .
2. UB < UC < UA .
3. UC < UB < UA .
+Q
Case B +
+Q
Case C +
Which of the following is true for the
electrostatic potential energy stored in the
system?
+3 C
+
4. UB = UC < UA .
5. UB < UC = UA .
+3 C
+
61
Question 54
Consider the following arrangements of
charges. The source charge is at rest on the
left and the probe charge was moved from
the right at constant speed from infinitely far
away to its illustrated final location.
+40 C +4 C
+
Case A +
+40 C +8 C
+
Case B +
Which of the following is true for the
electrostatic potential energy stored in the
system?
1. UC < UA < UB .
2. UA < UC = UB .
3. UC < UA = UB .
4. UA < UC < UB .
5. UB < UA < UC .
+10 C +8 C
+
Case C +
– Typeset by FoilTEX –
62
Question 55
Two metal plates are charged in such a
way that the electric potential at each is
as indicated. On each plate the electric
potential is constant.
Separately, two
particles with identical charges of +10 C
move as illustrated.
12 V
2V
Which of the following is true regarding the
change in electric potential energy?
1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB .
2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB .
3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB .
4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB .
5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB .
Particle B
Particle A
– Typeset by FoilTEX –
63
Question 56
Two metal plates are charged in such a
way that the electric potential at each
is as indicated.
On each plate the
electric potential is constant. Separately,
two positively charged particles move as
illustrated. Particle A has a smaller charge
than that of particle B.
2V
12 V
+
Which of the following is true?
1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB .
2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB .
3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB .
4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB .
5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB .
+
Particle B
+
+
Particle A
– Typeset by FoilTEX –
64
Question 57
Two metal plates are charged in such a
way that the electric potential at each is
as indicated. On each plate the electric
potential is constant.
Separately, two
particles move as illustrated. Particle A
has charge of +5 C and particle B has
charge +10 C.
2V
12 V
+
Which of the following is true?
1. ∆Uelec A = ∆Uelec B and ∆VA = ∆VB .
2. ∆Uelec A < ∆Uelec B and ∆VA = ∆VB .
3. ∆Uelec A > ∆Uelec B and ∆VA = ∆VB .
4. ∆Uelec A < ∆Uelec B and ∆VA < ∆VB .
5. ∆Uelec A = ∆Uelec B and ∆VA < ∆VB .
+
Particle B
+
+
Particle A
– Typeset by FoilTEX –
65
Question 58
Hidden source charges produce an electric
potential. Another positively charged particle
moves from a location where the electric
potential is +20 V to a location where it is
−50 V.
+20 V
+
Initial
– Typeset by FoilTEX –
Which of the following is true of the kinetic
energy of the particle between these two
locations?
1. ∆K = 0
2. ∆K > 0
−50 V
+
Final
3. ∆K < 0
66
Question 59
A hidden source produces the following
electrostatic potential. A charge, Zog, is
at rest at the indicated location.
Zog is made to move toward the origin. Which
of the following is true?
1. ∆Uelec > 0 regardless of Zog’s charge.
V
2. ∆Uelec < 0 regardless of Zog’s charge.
3. ∆Uelec = 0 regardless of Zog’s charge.
4. ∆Uelec > 0 for positive Zog, ∆Uelec < 0
for negative Zog.
5. ∆Uelec < 0 for positive Zog, ∆Uelec > 0
for negative Zog.
Zog: initial
– Typeset by FoilTEX –
67
Question 60
A source charge produces the following
electrostatic potential. Another charge, Z, is
at rest at the indicated location on the x
axis. The charge Z can move left or right
along the x axis.
Z is released. In which direction does the
charge Z move?
1. Left.
2. Right.
V
3. Left if Z is positive and right if Z is
negative.
4. Right if Z is positive and left if Z is
negative.
5. This cannot be determined without more
information about the source charge.
Zog: initial
– Typeset by FoilTEX –
x
68
Question 61
An infinite line of charge and two point
charges produce an electric potential, which,
along the x-axis has the following form. An
electron moves, purely under the influence of
these charge distributions, from the indicated
intial to final points along the x axis.
Which is true of the electron’s speed?
1. vi = vf
2. vi > vf
3. vi < vf
V
4. Not enough information.
initial
– Typeset by FoilTEX –
final
x
69
Question 62
A collection of fixed source particles produce
an electric potential. Separately, two probe
charges are placed in the potential (without
altering the source charges). They are each
placed at the same initial location and move
to the same final location. The first probe
particle Zog, has charge +4.0 C and the
second, Geraldine, has charge +8.0 C.
+
final
+
initial
– Typeset by FoilTEX –
Which of the following is true regarding the
change in electric potential (between initial
and final locations) for the probe charges?
1. ∆VZog =
1
∆VGeraldine
4
2. ∆VZog =
1
∆VGeraldine
2
3. ∆VZog = ∆VGeraldine
4. ∆VZog = 2∆VGeraldine
5. ∆VZog = 4∆VGeraldine
70
Question 63
A charged particle, Zog, is in the vicinity
of various source charges. The only forces
exerted on Zog are those exerted by the
source charges. Initially Zog is at location A
and moves with speed 20 m/s. Later Zog is
at location B and moves with speed 5 m/s.
Which of the following is true regarding the
electric potential difference
∆V = VB − VA
where VA is the potential at A, etc, . . . ?
1. ∆V = 0.
2. ∆V > 0 always.
3. ∆V < 0 always.
4. ∆V > 0 for positive Zog, ∆V < 0 for
negative Zog.
5. ∆V < 0 for positive Zog, ∆V > 0 for
negative Zog.
– Typeset by FoilTEX –
71
Question 64
Hidden source charges produce an electric
potential which has equipotentials as
illustrated. Probe charges moving through
the initial location reach the indicated final
location
Which of the following is true regarding the
probe charge?
1. ∆K = 0 regardless of charge.
2. ∆K < 0 regardless of charge.
10 V
30 V
3. ∆K > 0 regardless of charge.
4. ∆K > 0 for positive probe, ∆K < 0
for negative probe.
initial
final
– Typeset by FoilTEX –
50 V
5. ∆K < 0 for positive probe, ∆K > 0
for negative probe.
72
Question 65
Two metal plates are charged as illustrated.
+
+
+
+ A
+
+
+
+
b
b
b
B
C
−
−
−
D−
−
−
−
−
b
Which of the following is true regarding the
potentials (note that negative is always less
than positive, e.g. −50 V < 10 V)?
1. VA = VB = VC = VD
2. VA > VB = VC > VD
3. VA < VB = VC < VD
4. VA < VB < VC < VD
5. VA > VB > VC > VD
– Typeset by FoilTEX –
73
Question 66
A positive source charge produces an electric
potential.
C
×
Which of the following is the correct rank of
the electric potential at the various points (a
negative potential ranks lower than a positive
potential, i.e. −20 V < 10 V)?
1. VA = VB = VC = VD
A
×
+
Source
B
×
2. VA = VB < VC = VD
3. VC = VD < VA = VB
4. VD < VA = VB < VC
D
×
– Typeset by FoilTEX –
5. VA < VD = VC < VB
74
Question 67
A negative source charge produces an electric
potential.
C
×
Which of the following is the correct rank of
the electric potential at the various points (a
negative potential ranks lower than a positive
potential, i.e. −20 V < 10 V)?
1. VA = VB = VC = VD
A
×
−
Source
B
×
2. VA = VB < VC = VD
3. VC = VD < VA = VB
4. VD < VA = VB < VC
D
×
– Typeset by FoilTEX –
5. VA < VD = VC < VB
75
Question 68
An electron moves away from a positive
source charge as illustrated.
−
Final
−
Initial
+
Source
Which of the following is true regarding the
electric potential (produced by the source)
felt by the electron between initial and final
locations?
1. ∆V = 0
2. ∆V > 0
3. ∆V < 0
4. It depends on how fast the electron is
moving.
– Typeset by FoilTEX –
76
Question 69
An electron moves away from a positive
source charge as illustrated.
−
Final
−
Initial
+
Source
Which of the following is true regarding
the electric potential energy of the electron
between initial and final locations?
1. ∆Uelec = 0
2. ∆Uelec > 0
3. ∆Uelec < 0
4. It depends on how fast the electron is
moving.
– Typeset by FoilTEX –
77
Question 70
Two source charges are located as illustrated.
+
+2 C
−
−10 C
Consider the following statement regarding
the potential produced by the pair of charges:
“The potential produce by these charges is
negative since the negatively charged particle
has a larger magnitude of charge.”
Is this statement correct?
1. Correct.
2. Incorrect.
3. Neither.
– Typeset by FoilTEX –
78
Question 71
Two source charges are located as illustrated.
The magnitudes of the charges are equal but
their signs are opposite.
Which of the following represents the rank of
the potentials at the various points?
1. VA = VB = VC = VD
2. VA = VB < VC = VD
A
×
3. VD < VA = VB < VC
B
×
+
+q
D
×
– Typeset by FoilTEX –
C
×
−
−q
4. VC < VA = VB < VD
79
Question 72
Two source charges are located as illustrated.
The magnitudes of the charges are equal but
their signs are opposite.
Which of the following represents the rank of
the potentials at the various points?
1. VA < VB = VC
2. VB < VC < VA
3. VC < VB < VA
A
×
+
+q
C
×
– Typeset by FoilTEX –
B
×
−
−q
4. VA < VB < VC
5. VB < VA < VC
80
Question 73
Two arrangements of source charges are
illustrated.
A
×
+
+q
Which of the following is true of the
potentials at the various points?
1. VA > VB
−
−q
2. VA < VB
3. VA = VB 6= 0
4. VA = VB = 0
B
×
+
+q
– Typeset by FoilTEX –
−
−q
81
Question 74
Two source charges are located as illustrated.
The magnitudes of the charges are equal but
their signs are opposite.
Which of the following represents the rank of
the potentials at the various points?
1. VA < VB = VC
2. VB < VC < VA
3. VC < VB < VA
A
×
+
+q
C
×
– Typeset by FoilTEX –
B
×
−
−q
4. VA < VB < VC
5. VB < VA < VC
82
Question 75
A positive point charge, S, is located at the
origin as illustrated.
C
4
3
Which of the following best represents
the rank of the electrostatic potential
differences between each point and O, e.g.
∆VAO = VA − VO ?
O
2
1. ∆VBO > ∆VAO = ∆VCO
1
Z
0
A
2. ∆VAO = ∆VCO > ∆VBO
-1
3. ∆VAO > ∆VBO > ∆VCO
B
-2
4. ∆VCO > ∆VBO > ∆VAO
-3
-4
-4
-3
-2
– Typeset by FoilTEX –
-1
0
1
2
3
4
83
Question 76
Two charged particles A with charge qA and
B with charge qB are located as illustrated
below. A third particle Z with charge qZ is
placed at the indicated location. Distances
are measured in meters.
A
B
Z
The electrostatic potential energy of Z is to
be calculated using Uelec = qZ V. Which of
the following represents V that should be
used here?
2. V =
3. V =
4. V =
5. V =
– Typeset by FoilTEX –
qA
qB
+k
4
1
qA
qB
k
+k
5
1
qB
qZ
qA
+k
+k
k
4
1
1
qA
qB
k 2 +k 2
5
1
qA qZ
qB qZ
k
+k
5
1
1. V = k
84
Question 77
Four source charges are placed at the corners
of a square as illustrated. The point P is a
distance r from each corner.
−
−1 C
b
−
−1 C
Which of the following is true for the electric
potential at the point P in the center of the
square?
1. V = 0 C
2. V = +1 C
P
3. V = k
+
+1 C
+
+2 C
4. V = −k
5. V = k
– Typeset by FoilTEX –
1C
r
1C
r
5C
r
85
Question 78
Two source charges are located as illustrated.
Which of the following represents the electric
potential at point P?
1. V = 3 V
+
+1 C
d
– Typeset by FoilTEX –
+
+2 C
d
P
×
2. V = k
1C
d
3. V = k
3C
d
4. V = k
1C
2C
+k
d
d
5. V = k
2C
1C
+k
d
2d
86
Question 79
The diagrams illustrate arrangements of
charges where the symbols Q and q represent
particular fixed values of charge.
Rank the situations in order of increasing
electrostatic potential energy.
1. A > B > C
A
−Q
−
2. A > B = C
−q
−
3. A > C > B
4. C > B > A
B
−Q
−
+q
+
5. C = B > A
C
−Q
−
– Typeset by FoilTEX –
+4q
+
87
Question 80
Two source charges are located as illustrated.
The magnitudes of the charges are equal but
their signs are opposite.
A B
D
Which represents an equipotential?
1. A only.
2. B only.
3. C only.
C
+
+q
– Typeset by FoilTEX –
−
−q
4. D only.
5. B and C.
88
Question 81
The following diagram illustrates evenly
spaced (in terms of voltage) equipotentials
for a negative source charge.
Identical positively charged particles are
successively moved from C to another point.
Which of the following are true regarding the
change in the electric potential energy of the
positively charged particle?
C
1. ∆Uelec (C → A) > ∆Uelec (C → B)
A
−
B
2. ∆Uelec (C → A) < ∆Uelec (C → B)
3. ∆Uelec (C → A) = ∆Uelec (C → B)
4. ∆Uelec (C → A) = −∆Uelec (C → B)
5. None of the above/not enough info.
– Typeset by FoilTEX –
89
Question 82
Source charges produce equipotential lines as
illustrated.
Which of the following represents the rank
of the magnitude of the electric field at the
illustrated points?
b
B
b
C
1. EA = EB = EC
A
b
2. EA < EB < EC
3. EC < EB < EA
4. EB < EC < EA
5. EB < EA < EC
– Typeset by FoilTEX –
90
Question 83
An electric field produced by some sources
charges is as illustrated.
A
b
B
b
C
b
Which of the following represents the rank
of the magnitude of the electric potential at
the illustrated points?
1. VA = VB = VC
2. VA > VB > VC
3. VA < VB < VC
4. VA = VB < VC
5. VA < VB = VC
– Typeset by FoilTEX –
91
Question 84
The electric field lines produced by a charge
distribution are as illustrated.
– Typeset by FoilTEX –
Which of the following
equipotential line?
represents
Case 1
Case 2
Case 3
Case 4
an
92
Question 85
Three pairs of uniformly charged infinite plates
are separated by the same distance. Each plate is
held at a constant voltage as indicated.
Which of the following is the correct
ranking of the magnitude of the force
exerted on an proton placed between
the plates?
1. A > B > C
−200 V 100 V
50 V
200 V
−180 V −10 V
2. A > C > B
3. B > A > C
4. B > C > A
A
– Typeset by FoilTEX –
B
C
93
Question 86
A simple electron gun is configured as
illustrated. An electron is at rest on the
left electrode. Each electrode is at a fixed
electric potential.
Left electrode Right electrode
The electron must be accelerated from the
left to the right electrode. For this to happen
which of the followings must be true?
1. VL = VR
2. VL < VR
3. VL > VR
−
VL
– Typeset by FoilTEX –
VR
94
Question 87
A simple electron gun is configured as
illustrated. An electron moves between the
electrodes, each of which is held at the fixed
electric potentials. The distance between the
potentials is 0.20 m. The electron is initially
at rest at the left electrode and moves to the
right.
The electron is midway between the
two electrodes and we would like to
determine the electron’s speed.
Which
electric potential is most useful in this regard?
1. V = 250 V
2. V = 125 V
Left electrode Right electrode
−19
kq
−9 −1.6 × 10
4. V =
= 9.0 × 10
r
0.20
−
0V
– Typeset by FoilTEX –
3. V = 0 V
250 V
−19
kq
−9 −1.6 × 10
5. V =
= 9.0 × 10
r
0.10
95
Question 88
A small neutral conductor is placed
near to a positively charged sheet.
Which of the following best describes the subsequent
motion of the ball?
1. The ball is immediately repelled from the plate.
+
+
+
+
+
+
+
+
+
+
2. The ball is attracted to the plate and then adheres
to the plate.
3. The ball is attracted to the plate, then moves away
from the plate, coming to rest at an angle to the
left of vertical.
4. The ball is attracted to the plate, then moves away
from the plate, coming to rest in a vertical position.
5. The ball is attracted to the plate, then moves away
from the plate, coming to rest at an angle to the
right of vertical.
– Typeset by FoilTEX –
96
Question 89
Two capacitor plates are closely separated.
A conducting ball is placed between them.
The plates are connected to a power supply,
allowed to charge and then disconnected
from the power supply.
Which of the following is subsequently true?
1. The ball sticks to the plate to which it
was attracted.
2. The ball is repelled and hangs midway
between the plates
+
+
+
+
+
+
+
+
+
+
−
−
−
−
−
−
−
−
−
−
3. The ball is repelled to the opposite plate
and sticks to that plate.
4. The ball bounces back and forth between
the plates.
The ball is initially attracted to one of the
plates.
– Typeset by FoilTEX –
97
Question 90
Two oppositely charged plates are closely
separated.
A conducting ball is placed
between them.
+
+
+
+
+
+
+
+
+
+
−
−
−
−
−
−
−
−
−
−
Initially the ball bounces repeatedly, with very
gradually diminishing frequency, between the
two plates.
– Typeset by FoilTEX –
A wire is connected from one plate to the
other. Which of the following is true?
1. The ball continues to bounce with no
change in frequency.
2. The rate at which the ball bounces slows
to a lower steady rate.
3. The ball bounces a few more times and
then stops.
4. The ball bounces a few more times, stops
briefly and resumes bouncing.
98
Warm Up Question 7
An electron is fired toward a negatively charged metal plate. As the electron approaches
the plate does its electric potential energy decrease, increase or stay the same? Explain
your answer.
1. Increase. The kinetic energy is decreasing meaning that the potential energy is
increasing as it come closer to the metal plate.
2. Decrease. The negative charges repel the electron and this must decrease the
potential.
3. Decrease.
decreases.
As a charge moves toward a negative plate, its energy always
4. Stay same.
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99
Warm Up Question 8
Consider the scenario illustrated in Fig 21.4. Suppose that the plates are charged as
illustrated in b) and an electron (negatively charged) moves from the right plate to the
left. Will the electric potential energy of the electron increase, decrease or stay the same?
Explain your answer.
1. Increase. If a negative electron moves from point B to point A, its potential
energy will increase because it is moving closer to the negative side from which
it experiences a stronger and stronger repulsive force.
2. Increase. A force of a hand would have to do work on the electron to bring it
closer to the capacitor.
3. Decrease. Since ∆Uelec = −Welec and Welec is positive.
4. Stay the same. No force is needed to move the electron.
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100
Warm Up Question 9
The text describes the mechanism by which lightning is produced. Consider a lightning
strike between the bottom of the cloud and ground. Suppose that the lightning consists of
a stream of moving electrons. In which direction (cloud to ground or ground to cloud) do
the electrons travel? Does the electric potential energy (Uelec ) of the electron increase,
decrease or stay constant during this process? Is the electric potential (V ) higher or lower
at the bottom of the cloud than at the ground? Explain your answers.
1. Uelec decreases, V decreases. There must be a higher V at the bottom of the
cloud where the charge build up occurs.
2. Uelec decreases, V decreases. The electric potential is converted to KE and so
must be smaller at the bottom of the cloud.
3. Uelec decreases, V decreases. The electric potential energy is converted to KE
and so must be smaller at the bottom of the cloud - the same is true for electric
potential.
4. Uelec decreases, V increases.
increasing kinetic energy.
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The electric potential energy is released as
101
Warm Up Question 10
An ion is an atom from which charge has been removed or added. Various ions can be
accelerated by placing them in a region where there is an electric potential difference.
Suppose that a sodium ion (neutral sodium atom with one electron removed) is accelerated
from rest through the same electric potential difference as a potassium ion (a potassium
atom with one electron removed). How will their kinetic energies compare? Explain your
answer, describing which equation in the text is most useful for this problem.
1. Potassium KE larger since potassium is heavier.
2. Different. Since the atoms have different charge arrangements, they will produce
different electric potentials.
3. Both ions would have the same kinetic energies as they both have the same
charge (each is missing a single electron) and the problem states that the ∆V s
are the same. Using ∆K = −q∆V gives same KE.
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102
Warm Up Question 11
An electric field between two charged metal plates consists of vectors which all have the
same size and point up. Which way are the equipotential lines oriented?
1. Perpendicular to the electric field and thus horizontal.
2. There is only one equipotential and it is located midway between the plates.
3. Same direction as the electric field and thus up.
4. Opposite to the electric field and thus down.
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103
Warm Up Question 12
A sphere made of a perfect conductor is neutral and is placed to the left of a single
positive point charge. How does the electric potential on the left side (farthest from the
point charge) of the sphere compare to that on the right side (closer to the point charge)?
Explain your answer.
1. The same. The whole surface of the sphere is a has the same potential and is a
equipotential surface. Pg. 693 states that any two points inside a conductor in
electrostatic equilibrium are at the same potential.
2. Right side higher potential since V =
which is closer to the positive charge.
kq
r
and r is smaller for the right side
3. Left side higher potential since the sphere becomes polarized, sending positive
charge to the left.
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104
Warm Up Question 13
Look at Problem 25 on page 707. Consider points 1 and 3 in the accompanying figure
(P21.25). During which point in the heart’s cycle is V3 − V1 negative? Explain your
answer.
1. Stage c. Here V3 is positive and V1 is negative.
2. Stage b. V3 − V1 will be negative during septal depolarization. This is because
V3 will be negative and V1 will be positive.
3. Stage b. The blood flows from the top, closer to 1, to the bottom, closer to 3.
Since the blood flows down the potential at 3 must be lower.
4. Stage b. The charge at 1 is positive and at 3 negative.
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105
Warm Up Question 14
A parallel-plate capacitor consists of two metal plates that are parallel to each other. The
distance between the plates is held steady and their area stays constant. Suppose that
the electric potential difference across the capacitor is increased. Does the capacitance
increase, decrease or stay constant? Explain your answer.
1. Response
2. Response
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106
Currents and Circuits
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107
Question 91
Charged particles pass along wires as illustrated. In
each case, the number of charged particles that pass
through the end of the wire is N, the charge of each
particle is q and the time during which this is observed
is ∆t.
Case A
b
b
b
b
b
b
N = 40 q = 6 C ∆t = 4 s
b
b
Rank the situations in order of
magnitude of current through the
shaded end of the wire.
1. IA > IB > IC
2. IA > IC > IB
3. IB = IC > IA
4. IB > IC > IA
Case B
Case C
b
b
b
b
b
b
b
b
b
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b
b
b
b
b
b
b
N = 100 q = 1 C ∆t = 4 s
b
b
b
b
b
b
b
b
5. IC > IB > IA
N = 100 q = 2 C ∆t = 4 s
108
Question 92
Charged particles pass along wires as illustrated. In
each case, the number of charged particles that pass
through the end of the wire is N, the charge of each
particle is q and the time during which this is observed
is ∆t.
Case A
b
b
b
b
b
b
N = 40 q = −6 C ∆t = 4 s
b
b
Rank the situations in order of
magnitude of current through the
shaded end of the wire.
1. IA = IB = IC
2. IA > IB > IC
3. IA > IC > IB
4. IB > IC > IA
Case B
Case C
b
b
b
b
b
b
b
b
b
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b
b
b
b
b
b
b
N = 100 q = 1 C ∆t = 4 s
b
b
b
b
b
b
b
b
5. IC > IB > IA
N = 100 q = 2 C ∆t = 4 s
109
Question 93
Charged particles pass along wires as illustrated. In
each case, the number of charged particles that pass
through the end of the wire is N, the charge of each
particle is q and the time during which this is observed
is ∆t.
Case A
b
b
b
b
b
b
N = 40 q = −6 C ∆t = 10 s
b
b
Rank the situations in order of
magnitude of current through the
shaded end of the wire.
1. IC > IB > IA
2. IA > IC > IB
3. IA > IC = IB
4. IB = IC > IA
Case B
Case C
b
b
b
b
b
b
b
b
b
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b
b
b
b
b
b
b
N = 100 q = 1 C ∆t = 5 s
b
b
b
b
b
b
b
b
5. IB > IA = IC
N = 100 q = 2 C ∆t = 10 s
110
Question 94
Charged particles pass along wires as illustrated. In
each case, the number of charged particles that pass
through the end of the wire is N, the charge of each
particle is q and the time during which this is observed
is ∆t.
Case A
b
b
b
b
b
b
N = 40 q = −5 C ∆t = 10 s
b
b
Which of these currents are
identical (both in magnitude and
direction)?
1. All of them.
2. None of them.
3. A and B.
4. A and C.
b
Case B
Case C
b
b
b
b
b
b
b
b
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b
b
b
b
b
b
b
N = 100 q = −2 C ∆t = 10 s
b
b
b
b
b
b
b
b
5. B and C.
N = 100 q = 2 C ∆t = 10 s
111
Question 95
Consider circuit devices (e.g. bulb) with two
connecting ends. Several conceivable current
flow scenarios are illustrated.
In which case/s does charge accumulate
within the device as time passes?
1. It accumulates in all of these.
Case A
10 A
Case B
10 A
Case C
10 A
2. Only A.
3. Only B.
4. Only C.
10 A
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10 A
20 A
5. Only B and C.
112
Question 96
A bulb is connected to a battery as illustrated.
A
b
b
C
Which of the following is true for the currents
at different points?
1. IA = Ibulb = IC
2. IA > Ibulb > IC
3. IA = IC > Ibulb
4. IA < Ibulb < IC
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113
Question 97
A bulb is connected to a battery as
illustrated. A thicker wire is used to connect
one terminal of the bulb to the battery.
Which of the following represents the rank of
the magnitude of the currents?
1. IA = IB
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b
A
b
B
2. IA > IB
3. IB > IA
114
Question 98
Two identical batteries are connected in
two different scenarios as illustrated. In the
scenario on the left a thicker wires (smaller
resistance) are used.
b
A
b
C
Which of the following represents the rank of
the magnitude of the currents?
1. IA = IB = IC
2. IA = IB > IC
3. IC > IA = IB
b
B
4. IB > IA = IC
5. IC = IA > IB
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115
Question 99
Two identical bulbs are connected to
identical batteries in two different scenarios
as illustrated. In the scenario on the left
a thicker wire (smaller resistance) is used
to connect one terminal of the bulb to the
battery.
Which of the following represents the rank of
the magnitude of the currents?
1. IA = IC
2. IA > IC
3. IC > IA
b
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A
b
C
116
Question 100
Two resistors are connected to a battery.
R1 = 100 Ω
b
It is found that 1000 electrons pass point A
in 1.0 s. How many electrons pass point B in
2.0 s?
1. 250
B
R2 = 200 Ω
b
A
2. 500
3. 1000
4. 2000
5. 4000
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117
Question 101
A bulb is connected to a battery as
illustrated.
Which of the following is true?
1. In 10 s the total charge that flows through
the bulb is 3 C and through the battery 3 C.
5V
3A
The current through the bulb and potential
difference across the battery are indicated.
The wires offer negligible resistance.
2. In 10 s the total charge that flows through
the bulb is 5 C and through the battery 5 C.
3. In 10 s the total charge that flows through
the bulb is 30 C and through the battery
5 C.
4. In 10 s the total charge that flows through
the bulb is 30 C and through the battery
30 C.
5. In 10 s the total charge that flows through
the bulb is 30 C and through the battery
50 C.
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118
Question 102
A bulb is connected to a battery as illustrated.
5V
3A
In 2 s a total of 6 C moves from the positive
to negative terminal of the battery. Which of
the following is true?
1. The energy lost by this charge is 0 J.
2. The energy lost by this charge is 3 J.
The current and potential difference across
the battery are indicated. The wires offer
negligible resistance.
3. The energy lost by this charge is 5 J.
4. The energy lost by this charge is 6 J.
5. The energy lost by this charge is 30 J.
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119
Question 103
A bulb is connected to a battery as illustrated.
6V
3Ω
Which of the following represents the power
produced by the bulb?
1. 0 W
2. 0.5 W
3. 2 W
The wires offer negligible resistance.
4. 6 W
5. 12 W
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120
Question 104
Two resistors are connected to a battery.
Which of the following is true?
1. I1 = I2.
R1 = 10 Ω
15 V
R2 = 5 Ω
2. I1 is larger than I2.
3. I1 is smaller than I2 .
Let I1 and I2 denote the current through
resistors 1 and 2 respectively. Similarly V1
and V2 denote the potential differences across
resistors 1 and 2 respectively.
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121
Question 105
Two resistors are connected to a battery.
Which of the following is true?
1. V1 = V2 = 15 V.
R1 = 10 Ω
2. V1 = V2 = 7.5 V.
R2 = 5 Ω
3. V1 = V2 but both are some other value
than the previous options.
15 V
4. V1 is larger than V2 .
Let V1 and V2 denote the electric
potential differences across resistors 1 and
2 respectively.
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5. V1 is smaller than V2 .
122
Question 106
Two identical resistors are connected to a
battery.
b
b
b
a
5Ω
c
10 V
b
b
e
b
5Ω
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d
Which of the following concerning voltages
is correct?
1.
∆Ve→a = 10 V
∆Vb→c = 5 V
2.
∆Ve→a = 10 V
∆Vb→c = −5 V
3.
∆Ve→a = −10 V
∆Vb→c = −5 V
4.
∆Ve→a = −10 V
∆Vb→c = 5 V
5.
None of the above/not enough info.
123
Question 107
Consider the following circuit.
R1 = 5 Ω
10 V
R2 = 15 Ω
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Which of the following best represents
the potential difference across each of the
resistors?
1.
∆V1 =
1
3
∆V2
2.
∆V1 =
1
2
∆V2
3.
∆V1 = ∆V2
4.
∆V1 = 3∆V2
5.
Not enough info/none of the above.
124
Question 108
Several identical bulbs are connected in a
circuit as illustrated.
Which of the following is true?
1. A is brighter than E.
A
2. A is dimmer than E.
B
D
3. A and E have the same brightness.
C
E
The relative brightnesses of these bulbs
depend only on the relative currents which
flow through them.
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125
Question 109
Several identical bulbs are connected in a
circuit as illustrated.
A
D
Which of the following statements about
brightness is true (choose one)?
1. A > B > C
B
2. A < B < C
C
3. A > B = C
E
4. A < B = C
5. A = B = C
The relative brightnesses of these bulbs
depend only on the relative currents which
flow through them.
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126
Question 110
Several identical bulbs are connected in a
circuit as illustrated.
A
D
Which of the following statements about
brightness is true (choose one)?
1. A > B > D
B
2. A > D > B
C
3. A > B = D
E
4. A = D > B
5. A = B = D
The relative brightnesses of these bulbs
depend only on the relative currents which
flow through them.
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127
Question 111
Consider the following circuit,
R1 = 5 Ω and R1 = 10 Ω.
∆V
R1
where
Let ∆V1 be the potential difference across
R1 and ∆V2 be the potential difference
across R2 . How are these related? (Hint:
Consider energy between points on the
circuit).
R2
1. ∆V1 = ∆V2
2. ∆V1 = 2∆V2
3. ∆V1 =
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1
2
∆V2
128
Question 112
Consider the following
R1 = R2 = R3 .
circuit,
where
Consider the current through resistor 3 when
the switch is open versus when it is closed.
1. Iclosed =
2
3
Iopen
2. Iclosed = Iopen
∆V
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R1
R2
R3
3. Iclosed =
3
2
Iopen
129
Question 113
Consider the following circuit,
R1 = R2 = 10 Ω, R3 = 20 Ω.
where
Which of the following is true of
the equivalent resistance of the entire
combination?
1. Req > 40 Ω
∆V
R1
R2
R3
2. 40 Ω > Req > 20 Ω
3. 20 Ω > Req > 10 Ω
4. 10 Ω > Req > 5 Ω
5. 5 Ω > Req
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130
Question 114
Consider the following circuit, where
R1 = 10 Ω, R2 = 6 Ω, R2 = 12 Ω and
∆V = 7 V.
The current through the battery is 0.5 A.
Which of the following is true?
1. ∆V2 = 7 V
R1
2. ∆V2 = 5 V
∆V
R2
R3
3. ∆V2 = 3.5 V
4. ∆V2 = 2 V
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131
Question 115
Consider the following circuit.
R1
Suppose that resistor 4 is removed from the
circuit. Which of the following happens to the
current through the battery?
R2
1. The current through the battery increases.
∆V
2. The current through the battery decreases.
R3
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R4
3. The current through the battery does not
change.
132
Question 116
A parallel plate capacitor is connected to a
battery. The distance between the plates is
increased.
Which of the following is true?
1. The charge on the capacitor decreases.
Initial
∆V
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Final
∆V
2. The charge on the capacitor increases.
3. The charge on the capacitor stays the
same.
133
Question 117
A parallel plate capacitor is connected to a
battery and allowed to charge. The capacitor
is then disconnected, without any charge
leaking from the capacitor, and the distance
between the plates is doubled.
Initial
Final
Which of the following is true regarding the
potential difference across the plates?
1. ∆Vafter = 4∆Vbefore
2. ∆Vafter = 2∆Vbefore
3. ∆Vafter = ∆Vbefore
∆V
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4. ∆Vafter =
1
∆Vbefore
2
5. ∆Vafter =
1
∆Vbefore
4
134
Question 118
Two capacitors are connected in parallel as
illustrated.
Suppose that C1 6= C2. Which of the
following is true?
1. ∆V1 = ∆V2 and q1 = q2
C1
C2
2. ∆V1 = ∆V2 and q1 6= q2
3. ∆V1 6= ∆V2 and q1 = q2
Let ∆V1 and q1 be the potential difference
across and the charge on capacitor 1. Let
∆V2 and q2 be the potential difference across
and the charge on capacitor 2.
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4. ∆V1 6= ∆V2 and q1 6= q2
135
Question 119
A parallel plate capacitor is connected to a
battery which provides a potential difference
of 10 V. The capacitor is allowed to charge
and the then the battery is disconnected.
After this, the plates of the capacitor are
pulled apart.
Which of the following are true of the energy
stored in the capacitor during this process?
1. The energy increases.
2. The energy decreases.
3. The energy stays constant.
4. Not enough information to answer.
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136
Question 120
A parallel plate capacitor is connected to a
battery which provides a potential difference
of 10 V. There is a dielectric between the
capacitor plates. The capacitor is allowed
to charge and the then the battery is
disconnected. After this, the dielectric is
removed.
Which of the following are true of the energy
stored in the capacitor during this process?
1. The energy increases.
2. The energy decreases.
3. The energy stays constant.
4. Not enough information to answer.
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137
Warm Up Question 15
A battery can succeed in pushing positive charges around a circuit. As described on page
718, these charges move through a wire from the positive terminal (at higher V) to the
negative terminal (at lower V). Consider one of these charges as it completes a circuit. As
the charge moves through the wire, does its electric potential energy increase, decrease
or stay constant? As the charge moves through battery from the negative to positive
terminal, does its electric potential energy increase, decrease or stay constant?
1. Constant in wire, increase in battery. The V is the same throughout the wire
but increases from positive to negative in the battery.
2. Constant in the wire since the charges move at a constant rate. Increasing teh
the battery.
3. Stays constant since the V produced by the battery stays constant.
4. Decrease in wire, increase in battery. If positive charge flows from positive to
negative in wire then ∆V is negative and q∆V is negative.
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138
Warm Up Question 16
One wire is made from copper and the other from tungsten, whose resistivity is larger.
Suppose that the wires have the same length. It is claimed that the resistance of the
tungsten wire is larger because its resistivity is higher. Is this claim true or not? Explain
your answer.
1. True. Higher resistivity implies higher resistance in all cases.
2. True. Higher resistivity and identical lengths gives higher resistance.
3. Not necessarily. The areas could be different. If tungsten had a larger area it
could have a lower resistance.
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139
Warm Up Question 17
A conventional light bulb operates by passing current through a narrow strand of tungsten
wire. This causes the tungsten’s temperature to rise, eventually becoming hot enough to
glow. The resistivity of tungsten changes as its temperature increases (there is a table
which indicates this in the text). Suppose that such a bulb is connected to a power
source which provides a constant voltage. What will happen to the current as time passes
(increase, decrease or stay constant)? Explain your answer.
1. Decrease. As tungsten heats up it resists more or it gets harder to push charges
through the tungsten.
2. Decrease. The potential provided by the battery drops.
3. Decrease. The current will initially flow but eventually the entire circuit will be
charged and current will stop.
4. Increase. The resistivity decreases, so resistance decreases and current increases.
5. Stay constant. Whatever current enters the bulb must leave the bulb too.
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140
Magnetic Fields and Forces
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141
Question 121
Which of the following correctly illustrates
the magnetic field in the vicinity of the north
pole of a bar magnet?
Case 1
Case 3
Case 2
Case 4
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142
Question 122
Two current carrying wires point out of the
page as illustrated. The currents are equal in
magnitude but flow in opposite directions.
Which of the following best indicates the
direction of the magnetic field at the
midpoint?
↑
2. ↓
3. ←
4. →
1.
×
b
b
5. Magnitude is zero ⇒ no direction.
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143
Question 123
In two separate scenarios, three current
carrying wires point out of the page as
illustrated. The currents are equal in
magnitude.
Which of the following is true?
1. The magnetic field at A is larger than at B.
2. The magnetic field at A is smaller than at B.
b
×
×
b
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B
×
3. The magnetic field at A is the same as B.
A
×
b
b
144
Question 124
Three current carrying wires point out of
the page as illustrated. The currents are
equal in magnitude.
Which of the following is true?
1. The magnetic field at A is larger than at B.
2. The magnetic field at A is smaller than at B.
×
A
×
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b
B
×
b
3. The magnetic field at A is the same as B.
145
Question 125
Two current-carrying wires are arranged as
illustrated.
Which of the following is true regarding the
net direction of the magnetic field at the
location midway between the wires?
1. Definitely into the board/page.
I1
I2
2. Definitely out of the board/page.
3. Either into or out of the board/page.
4. Clockwise.
5. Counter clockwise.
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146
Question 126
Two current-carrying wires are arranged as
illustrated. The loop is situated at a specific
location so that the net magnetic field is zero.
Suppose that the loop is moved to another
location further away from the wire. Which
of the following is true regarding the net
direction of the magnetic field?
1. Into the board/page.
I1
I2
2. Out of the board/page.
3. It remains zero.
4. Clockwise.
5. Counter clockwise.
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147
Question 127
Two current-carrying wires are placed near
each other. The straight wire is infinitely
long. The currents are such that the net
magnetic field at the center of the loop is zero.
What is the direction of the current in the
circular wire?
1. Clockwise
2. Counter-clockwise
3. Current is zero.
I
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148
Question 128
A solenoid carries current and is placed next
to a bar magnet. When viewed from its
right end, the current circulates as illustrated.
N
S
Which of the following is true regarding the
force exerted by the solenoid on the magnet?
1. Left
2. Right
3. Up
Right end
4. Down
5. No force.
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149
Question 129
Two infinitely long solenoids each carry the
same current. Each has the same length
and the same number of coils. The radius
of the outer solenoid is double that of the
inner solenoid. One solenoid is inside the
other. When viewed end-on, they appear as
illustrated.
Which of the following is true?
1. The magnetic field inside the inner
solenoid is the same as that between
the two solenoids and is non-zero.
2. The magnetic field inside both solenoids
is zero.
3. The magnetic field inside the inner
solenoid is zero and that between the
two solenoids is non-zero.
4. The magnetic field inside the inner
solenoid is non-zero and that between
the two solenoids is zero.
– Typeset by FoilTEX –
150
Question 130
Identical positively charged particles move
through identical magnetic fields with
identical speeds, in directions indicated by
black vectors, as illustrated.
Case A
Case B
Case C
Ranking the cases in order of magnitude of
magnetic force, which is correct?
1. B > A = C
2. C > B > A
3. B > A > C
~
B
+
+
+
4. C > A > B
5. A > C > B
– Typeset by FoilTEX –
151
Question 131
Identical positively charged particles move
through identical magnetic fields with
identical speeds, in directions indicated by
black vectors, as illustrated.
Case A
Case B
Case C
Ranking the cases in order of magnitude of
magnetic force, which is correct?
1. B > A = C
2. C > B > A
3. B > A > C
+
+
+
4. C > A > B
5. A > C > B
~
B
– Typeset by FoilTEX –
152
Question 132
A negatively charged particle moves vertically
down at the instant that a magnetic field
is turned on. The relative directions are
indicated below.
Determine the direction of the force exerted
by the magnetic field on the charged particle.
1.
2.
3.
−
~
B
→
←
↓
4. Into the screen/board.
5. Out of the screen/board.
– Typeset by FoilTEX –
153
Question 133
A positively charged particle, whose mass is
not zero, moves horizontally at one moment
as illustrated.
+
An experimenter attempts to provide an
external magnetic field which will prevent the
particle from falling under the influence of
the earth’s gravity. What must the direction
of this field be?
1.
2.
3.
→
↑
↓
4. Into the screen/board.
5. Out of the screen/board.
– Typeset by FoilTEX –
154
Question 134
A negatively charged particle (with charge
−8 C) moves as illustrated at the instant
that a magnetic field is turned on. The
particle is moving at an angle of 70◦ above
the horizontal and the magnetic field is
vertical.
Which of the following is the magnitude of
the force exerted by the magnetic field on
the particle?
1. F = 8vB sin (20◦)
2. F = 8vB sin (70◦)
~
B
−
– Typeset by FoilTEX –
3. F = −8vB sin (20◦)
4. F = −8vB sin (70◦)
5. F = 8vB cos (20◦)
155
Question 135
An alpha particle (two protons and two
neutrons) is fired into the gap between two
closely spaced magnets as illustrated.
←
2. →
b
N
– Typeset by FoilTEX –
Which of the following best represents the
direction of the force exerted by the magnets
on the alpha particle while it is between them?
1.
S
3. Into the board
4. Out of the board
156
Question 136
Two charged particles each move with
constant speed in a region containing a
uniform and constant magnetic field. Their
trajectories when viewed from above are as
illustrated.
Which is true regarding the charges of the
particles?
1. Both are positive.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Both are negative.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
A
B
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. They are opposite but one cannot say
which is positive.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. A is positive, B is negative.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
~
B
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
5. B is positive, A is negative.
– Typeset by FoilTEX –
157
Question 137
Two positively charged particles each move
with constant speed in a region in which a
constant magnetic field points directly out
of the board/screen. Their trajectories are
indicated below.
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
1. mA = mB
b
b
b
b
b
b
b
b
b
b
b
b
b
b
3. mA > mB
4. None of the above/not enough info.
A
– Typeset by FoilTEX –
relationship
2. mA < mB
b
B
Which best describes the
between the particle masses?
158
Question 138
A charged particle is fired into a
region in which there is a uniform but
time varying magnetic field. That is,
at any instant the magnetic field is
the same at all points but as time
passes the magnetic field vectors all
change in the same way. The particle
is fired into the field perpendicular to
the field. The direction of the field
remains constant but its strength
increases as time passes.
Which of the following is true as time passes?
1. The particle moves with constant speed in a
circle.
2. The particle moves with constant speed in a
spiral of decreasing radius.
3. The particle moves with constant speed in a
spiral of increasing radius.
4. The particle moves with increasing speed in a
circle.
5. The particle moves with increasing speed in a
spiral of decreasing radius.
– Typeset by FoilTEX –
159
Question 139
A wire carries a current, consisting of moving
electrons. The positive nuclei in the wire
remain stationary. The wire is placed into a
~ , pointing out of the screen.
magnetic field, B
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
+
b
b
b
+
b
b
b
+
b
b
b
+
b
b
b
b
b
+
b
b
b
+
b
b
b
b
b
+
b
b
b
+
b
b
b
b
b
b
+
b
b
b
b
b
b
~ exerts a force on the positive charges
3. B
and a force on the negative charges. The
force on the negative charges is larger
since they are smaller.
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
~
B
~ exerts no force on the wire since the
1. B
net charge of the wire is zero.
~ exerts a force on the positive charges
2. B
and a force on the negative charges and
these cancel.
+
b
b
Which of the following is true?
~ exerts a force on the negative charges
4. B
but no force on the positive charges.
~ exerts a force on the positive charges
5. B
but no force on the negative charges.
– Typeset by FoilTEX –
160
Question 140
A current flows through wire in the indicated
direction. The wire is placed in the indicated
magnetic field.
Which of the following describes the direction
of the force exerted on the wire?
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
1. ↑ if the charges are positive and ↓ if the
charges are negative,
⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
b
b
b
b
b
b
b
b
b
b
b
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. ↑ if the charges are positive and ↑ if the
charges are negative,
3. ↓ if the charges are positive and ↑ if the
charges are negative,
4. ↓ if the charges are positive and ↓ if the
charges are negative, or
5. Not enough info/none of the above.
– Typeset by FoilTEX –
161
Question 141
Wires of different lengths carrying the same
currents are placed in identical magnetic
fields.
Which of the following is true regarding the
magnitudes of the magnetic forces exerted
on the wires?
Case B
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
1.
FA = FB ,
⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗
2.
FA < FB , or
3.
FA > FB .
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
Case A
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗I ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
162
Question 142
An non-magnetic axle with two wheels is
free to roll along two rails. The rails are
connected to a battery and this is illustrated
from above. The north pole of a magnet is
held above the axle.
The axle is initially at rest and is then
released. Which of the following is true after
the wheel is released?
1. It remains stationary.
2. It lifts off the rails.
Battery
+
−
3. It rolls left.
4. It rolls right.
5. It slides down to the lower rail.
– Typeset by FoilTEX –
163
Question 143
A circular loop carries a uniform current.
Another long straight wire lies along the axis
of the loop and this also carries a current.
View along the line of the straight wire, the
currents are as illustrated.
Which of the following represents the force
exerted by the straight wire on the loop?
1. The force is zero.
2. The force is counterclockwise.
3. The force is clockwise.
× I1
I2
4. The force is out of the page/screen.
5. The force is into of the page/screen.
– Typeset by FoilTEX –
164
Question 144
A rectangular loop is placed into the
indicated magnetic field.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
~
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗B
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
Which (choose one) of the following is true?
1. There is a net force on the loop.
2. There is a net torque on the loop.
3. There is a net force and a net torque on
the loop.
4. There is neither a net force nor a net
torque on the loop.
165
Question 145
A rectangular loop is placed into the
indicated magnetic field.
Which (choose one) of the following is true?
1. The entire loop moves out of the screen.
2. The entire loop moves into of the screen.
~
B
3. The loop rotates with its center fixed.
4. The loop rotates and its center moves out
of the screen.
5. The loop rotates and its center moves
into the screen.
– Typeset by FoilTEX –
166
Question 146
Two current-carrying wires are placed near
each other. The vertical wire is infinitely long.
Which of the following best represents the
direction of the force exerted by the vertical
wire on the horizontal wire?
→
2. ←
3. ↑
4. ↓
1.
ID
IC
5. Out of the page/board.
– Typeset by FoilTEX –
167
Question 147
Three wires each carry currents of identical
magnitudes. The distance between adjacent
wires are equal.
Rank the wires in order of the magnitudes of
the net magnetic force on each.
1. FA = FB
2. FA > FB = 0
3. FA > FB 6= 0
4. FB > FA = 0
A
– Typeset by FoilTEX –
B
C
5. FB > FA 6= 0
168
Question 148
Three wires, each perpendicular to the board,
carry currents of identical magnitudes. The
distance between adjacent wires are equal.
A
B
b
b
C
×
Rank the wires in order of the magnitudes of
the net magnetic force on each.
1. FA = FB = FC
2. FA = FC > FB = 0
3. FC = FA > FB = 0
4. FB > FC = FA
5. FB > FC > FA
– Typeset by FoilTEX –
169
Question 149
Various current carrying loops are placed in a
magnetic field as illustrated.
Loop A
Loop B
Rank the loops in order of increasing
torque exerted by the magnetic field.
Loop C
The currents through the loops are:
1.
A=B<C
2.
A<B<C
3.
C =A<B
4.
C <A<B
5.
B<C<A
6. Not enough info/none of the above.
IA = 25 A
IB = 25 A
IC = 10 A
– Typeset by FoilTEX –
170
Question 150
A loop is placed in a region of uniform
magnetic field as illustrated. The left edge of
the loop can slide, maintaining contact with
the rest of the loop.
At the instant depicted in the illustration the
left edge is dragged (by hand) to the left.
Which of the following is true about the
current in the loop:
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
1. Counter-clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
171
Question 151
A loop is placed in a region of uniform
magnetic field as illustrated. The left edge of
the loop can slide, maintaining contact with
the rest of the loop.
At the instant depicted in the illustration the
left edge slides to the left. Which of the
following is true about the current in the loop:
1. Counter-clockwise current.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise current.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero current.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
172
Question 152
A loop passes through a region of constant
magnetic field at a constant speed as
illustrated.
At the instant depicted in the illustration the
current in the loop is:
1. Counter-clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
173
Question 153
A loop passes through a region of constant
magnetic field at a constant speed as
illustrated.
At the instant depicted in the illustration the
current in the loop is:
1. Counter-clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
174
Question 154
A loop passes through a region of constant
magnetic field at a constant speed as
illustrated.
At the instant depicted in the illustration the
current in the loop is:
1. Counter-clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
175
Question 155
A rail/rod loop is placed in a magnetic field.
The diagram shows a view of this from
above. The gray rod is initially at rest and
is given a sharp kick directly right. The rail
arrangement has a non-zero resistance.
Which of the following is true?
1. The rod continues to move to the right
at a constant speed.
2. The rod moves to the right with a
decreasing speed.
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
3. The rod moves to the right with an
increasing speed.
4. The rod moves right, slows down, reverses
direction and moves left.
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
– Typeset by FoilTEX –
176
Question 156
A loop is stationary in a region of uniform
magnetic field as illustrated.
The field
strength decreases at a steady rate.
While the field decreases, the current in the
loop is:
1. Counter-clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. Clockwise
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. Zero
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. None of the above/not enough info.
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
177
Question 157
Several loops are placed in a uniform
magnetic field (restricted to shaded region)
as illustrated.
Which of the following represents the rank of
the fluxes through the loop?
Loop A
Loop B
Loop C
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
1. ΦA = ΦB = ΦC
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
2. ΦA < ΦB < ΦC
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
3. ΦA < ΦC < ΦB
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
4. ΦC < ΦA < ΦB
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
5. ΦC = ΦA < ΦB
⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗ ⊗
– Typeset by FoilTEX –
178
Question 158
A magnetic field is as illustrated. A square
coil is situated so that only one side is visible
from this perspective.
Which of the following is the correct
expression for the flux through the loop?
1. Φ = BA
2. Φ = BA cos 10◦
3. Φ = BA cos 20◦
◦
110
~
B
4. Φ = BA cos 110◦
5. Φ = BA cos 120◦
10◦
– Typeset by FoilTEX –
179
Question 159
A magnet is pulled away from a loop in the
indicated direction.
N
S
Which of the following is true as the magnet
moves away from the loop?
1. The
current
in
the
loop
counterclockwise (viewed from right).
is
2. The current in the loop is clockwise
(viewed from right).
3. There is no current in the loop.
– Typeset by FoilTEX –
180
Question 160
A magnet is pushed toward a loop in the
indicated direction.
N
S
Which of the following is true as the magnet
approaches the loop?
1. The
current
in
the
loop
counterclockwise (viewed from right).
is
2. The current in the loop is clockwise
(viewed from right).
3. There is no current in the loop.
– Typeset by FoilTEX –
181
Question 161
A magnet is pushed through a loop in the
indicated direction.
N
S
Which of the following is true immediately
after the north pole of the magnet passes
through the loop?
1. The
current
in
the
loop
counterclockwise (viewed from right).
is
2. The current in the loop is clockwise
(viewed from right).
3. There is no current in the loop.
– Typeset by FoilTEX –
182
Question 162
A magnet is pushed toward a loop in the
indicated direction.
N
S
Which of the following is true regarding the
force exerted by the loop on the magnet as
the magnet approaches the loop?
1. The loop exerts a force to the left.
2. The loop exerts a force to the right.
3. The loop exerts no force.
4. The loop exerts a force up.
5. The loop exerts a force down.
– Typeset by FoilTEX –
183
Question 163
A magnet is pushed through a loop in the
indicated direction.
N
S
Which of the following is true immediately
after the north pole of the magnet passes
through the loop?
1. The loop exerts a force to the left.
2. The loop exerts a force to the right.
3. The loop exerts no force.
4. The loop exerts a force up.
5. The loop exerts a force down.
– Typeset by FoilTEX –
184
Question 164
A circular loop of wire is such that it can
be made to expand and contract. The loop
is placed in a uniform magnetic field. The
initial configuration of the loop is indicated
by a dashed line; the final by a solid line.
Which of the following is true while the loop
expands?
1. There is no current in the loop.
2. There is a clockwise current in the loop.
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
3. There is a counter-clockwise current in
the loop.
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
– Typeset by FoilTEX –
185
Question 165
A loop is placed in an external magnetic
field. The flux through the loop as time
passes is plotted below.
Which of the following is true regarding the
magnitude of the induced EMF, E ?
1. E is largest from 0 s to 2 s
2. E is largest from 2 s to 5 s
Φ in Wb
3. E is largest from 5 s to 7 s
10
5
1
2
3
−5
4
5
6
7
t in s
4. E is larger at 3 s than 4 s
5. E is larger at 4 s than 3 s
−10
– Typeset by FoilTEX –
186
Question 166
A loop rotates in a uniform magnetic field
with orientations as described in class. The
axle of the loop is perpendicular to the
magnetic field.
Zog claims that: “If the speed with which
the loop rotates increases steadily then the
current through the loop stays constant, since
the magnetic field and the area of the loop
are constant.” Is this:
1. Definitely true.
2. Definitely false.
3. Possibly/partly true.
4. Possibly/partly false.
– Typeset by FoilTEX –
187
Question 167
Two circular loops are initially placed
perpendicular to the same magnetic field.
The area of loop B is twice that of loop A.
Each loop is rotated through 90◦ . The time
taken to rotate loop B is twice that of loop A.
⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙
⊙
Initial
Final
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
Loop A
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
❀
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
Initial
Final
⊙ ⊙
⊙ ⊙ ⊙ ⊙ ⊙
⊙
Which of the following is true regarding the
(magnitudes of the) induced EMFs?
1. EA = EB = 0
2. EA = EB 6= 0
3. EA = 2EB
4. EA = 4EB
5. EA =
1
EB
2
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
Loop B
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
❀
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
– Typeset by FoilTEX –
188
Warm Up Question 18
The configuration of a solenoid is described on page 788. Two long solenoids are
constructed using the same type of wire. They each have the same length and the number
of turns of the wire is the same along their lengths. However, solenoid A has double the
diameter of solenoid B. How does the magnetic field inside A compare to that inside B
(same, smaller, larger, twice as large, half as large, etc.,...)? Explain your answer.
1. A smaller than B. The current is distributed over a larger region in A and the
field is more concentrated in B.
2. A larger than B. There is greater volume available for the magnetic field in A.
3. Same. The equation to calculate the magnetic field does not include area in the
equation: B = µ0 I N
L , so area does not matter and they will be the same.
4. Same. It is zero everywhere inside in each case.
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189
Warm Up Question 19
A proton is fired toward a current-carrying solenoid and it enters the solenoid traveling in
a direction down the axis of the solenoid. Will the solenoid exert a force on the proton?
Explain your answer.
1. Yes. A magnetic field always exerts a force on a moving charged particle.
2. Yes. The angle between the magnetic field and the velocity is 90◦ so there will
be a force.
3. No. The solenoid exerts no force on the proton since the proton is moving down
the axis of the solenoid and therefore is parallel to the magnetic field within the
solenoid so there is no force.
4. No. There is no magnetic field inside a solenoid and there will be no force.
5. No. The field is uniform and so there cannot be any force.
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190
Warm Up Question 20
The cords that connect a household appliance to the mains outlet consist of two strands
of wire that run parallel to each other. At any instant the current in one strand is opposite
to that in the other strand. Describe the direction of the force exerted by one strand
on the other. In household circuits, the currents in the strands simultaneously reverse
direction many times every second. Do the wires still exert forces in the same directions in
this circumstance? Explain your answer.
1. No forces. Magnetic fields do not exert forces on parallel moving charges.
2. Attractive since currents are opposite. Still attractive when reversed.
3. Repel since the currents are opposite. Still repel when reversed since currents
are still opposite.
4. Repel since the currents are opposite. Forces reverse when currents are reversed.
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191
Warm Up Question 21
Consider the left loop in Fig 24.43 (pg 798) and suppose that the current flows as
indicated. Suppose that the right loop has been removed and bar magnet is placed to the
left of the left loop. The south pole of the bar magnet is closest to the left side of the
left loop. Will it exert a force on the loop and, if so, what is the direction of the force?
Explain your answer.
1. Yes. It will exert a force attracting the loop toward the bar magnet. If the
current is flowing up on the side closest to us, then the magnetic field is will be
flowing to the left. Therefore the south end will be or the right and the north
end will be on the left closest to the south end of the bar magnet.
2. Yes. The left side of the loop will be the south end and the right side the north
end. So the magnet will repel.
3. Yes. The magnet will exert a force on the current and the force will repel the
current loop because magnets repel currents.
4. No force.
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192
Warm Up Question 22
A square loop of wire is held in such a way that the Earth’s magnetic field is perpendicular
to the plane of the loop. The loop is held stationary relative to the Earth and the Earth’s
field does not change. Two claims are made: 1) There is a non-zero flux through the loop
and 2) as a result of this there is a current through the loop. Are these claims true or not?
Explain your answers.
1. 1) No 2) No. The magnetic field is not changing and so there is no flux. Since
there is no flux, there is no induced current.
2. 1) No 2) No. The angle is 0◦ and so the flux is zero. So there is no induced
current.
3. 1) Yes 2) No. The flux through the loop is non-zero because the loop is
perpendicular to the Earths magnetic field so the flux is at its greatest. There is
no current through the loop however because the flux is not changing.
4. 1) Yes 2) Yes. The angle between the plane of loop and field is 90◦. Thus
the flux is non-zero. A non-zero flux also implies that there is current flowing
through the loop.
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193
Warm Up Question 23
A loop is held near a long straight wire as illustrated in Fig 25.17 on page 825 except that
the loop is held stationary. The current in the straight wire is made to decrease gradually.
Will there be a current in the loop and if so what will the direction of the current be?
Explain your answer.
1. No. Because they are stationary the wire will not induce a current in the loop.
2. Yes. When the current in the straight wire decreases, the flux from the loop will
decrease also. To oppose the change in the flux, this would lead to a clockwise
current being induced.
3. Yes. When the current in the straight wire decreases, the flux from the loop
will decrease also. To oppose the change in the flux, this would lead to a
counter-clockwise current being induced.
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194
Electromagnetic Waves
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195
Question 168
The following diagrams show snapshots of
electromagnetic waves. Red represents the
electric field and blue the magnetic field.
In which directions
propagating?
are
the
waves
1. A in +x, B in +x
y
2. A in +x, B in −x
Case A
3. A in −x, B in +x
x
4. A in −y , B in +y
5. A in +y , B in −y
y
Case B
x
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196
Question 169
The electric field for various electromagnetic
waves at one instant is indicated.
Ey
Rank the waves in order of wavelength.
1. A = B = C
Case A
2. A = B < C
x
Ey
3. A = B > C
4. A < B = C
Case B
5. A < B < C
x
Ey
Case C
x
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197
Question 170
The electric field for two electromagnetic
waves at one instant is indicated. These
wave patterns travel to the right with the
same speed.
Ey
Which of the following is true regarding the
number of times the electric field at one
position along the x axis oscillates?
1. The number of oscillations per second for
A is the same as that for B.
Case A
x
2. The number of oscillations per second for
A is half that for B.
3. The number of oscillations per second for
A is twice that for B.
Ey
Case B
4. None of the above/not enough info.
x
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198
Question 171
The electric field for an electromagnetic wave
at one instant is illustrated.
Ez
Which of the following best represents the
wavenumber?
1. k = 30
x
10
20
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30
40
50
60
2. k = 40
2π
3. k =
20
4. k =
2π
30
5. k =
2π
40
199
Question 172
A beam of light has a circular cross
section.
The beam passes through a
polarizing filter and the transmitted light
has an electromagnetic wave whose electric
field vector at each location oscillates up and
down along the z axis. The transmitted light
beam strikes a screen.
Which of the following is true?
1. The light travels along the z axis.
2. The light travels along an axis
perpendicular to the z axis and produces
a circular spot on the screen.
3. The light travels along an axis
perpendicular to the z axis and produces
a streak (along z ) on the screen.
4. The light travels along an axis
perpendicular to the z axis and produces a
streak (perpendicular to z ) on the screen.
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200
Question 173
Unpolarized light of intensity Iincident is
incident on a polarizer (labeled A) whose
transmission axis is oriented vertically.
Subsequently this light passes through a
polarizer (labeled B) whose transmission axis
is oriented horizontally.
Which of the following represents the
intensity of the light transmitted by B?
1. 0
2.
1
Iincident
4
3.
1
Iincident
2
1
4. √ Iincident
2
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201
Question 174
Unpolarized light, whose intensity is Iincident ,
is incident upon a linear polarizer, whose
axis of transmission is oriented horizontally.
A second polarizer has transmission axis
oriented vertically.
Which of the following represents the
intensity of the light transmitted by the final
polarizer?
1. 0
2.
1
Iincident
4
3.
1
Iincident
2
1
4. √ Iincident
2
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202
Question 175
Unpolarized light of intensity Iincident is
incident on a polarizer (labeled A) whose
transmission axis is oriented vertically.
Subsequently this light passes through a
polarizer (labeled B) whose transmission axis
is oriented vertically.
Which of the following represents the
intensity of the light transmitted by B?
1. 0
2.
1
Iincident
4
3.
1
Iincident
2
1
4. √ Iincident
2
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203
Question 176
Unpolarized light of intensity Iincident is
incident on a polarizer (labeled A) whose
transmission axis is oriented vertically.
Subsequently this light passes through a
polarizer (labeled B) whose transmission axis
is oriented midway between horizontal and
vertical.
Which of the following represents the
intensity of the light transmitted by B?
1. 0
2.
1
Iincident
4
3.
1
Iincident
2
1
4. √ Iincident
2
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204
Question 177
Polarized light, whose axis of polarization is
at an angle of 45◦ between the horizontal
and vertical is incident upon a linear
polarizer, whose axis of transmission is
oriented horizontally. A second polarizer
has transmission axis at an angle of 45◦
degrees above the horizontal and a third has
transmission axis oriented vertically.
The middle polarizer is removed. What does
this do to the intensity of the light after the
final polarizer?
1. Reduces the intensity.
2. Increases the intensity.
3. Intensity stays the same.
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205
Question 178
Unpolarized light is incident upon a linear
polarizer, whose axis of transmission is
oriented horizontally. A second polarizer
has transmission axis at an angle of 45◦
degrees above the horizontal and a third has
transmission axis oriented vertically.
The middle polarizer is removed. What does
this do to the intensity of the light after the
final polarizer?
1. Reduces the intensity.
2. Increases the intensity.
3. Intensity stays the same.
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206
Question 179
A spherical wave propagates outwards in
empty space. Two spherical “windows” at
which the wave is observed at one instant
are shown.
1. IA = IB since the energy passing through
the window at A is the same as that
passing through B.
2. IA < IB since the energy passing through
the window at A is the same as that
passing through B.
Location A
3. IA > IB since the energy passing through
the window at A is the same as that
passing through B.
4. IA > IB since energy is lost between A
and B.
Location B
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207
Warm Up Question 24
A pair of sunglasses is designed so that the polarization axis is vertical when worn by
someone who stands upright. The person lies down on a bench on his side with one side
of his head against the bench (i.e. one ear against the bench). Will these sunglasses
eliminate the glare from a horizontal reflecting surface? Explain your answer.
1. Yes. The wave is still travels perpendicular to the sunglasses and so it will still
be blocked.
2. Yes. The axis of polarization is still vertical and so the glare will still be blocked.
3. No. When turned on the side the axis of polarization is now horizontal. This
will allow horizontal waves to pass through and not eliminate the glare.
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208
Warm Up Question 25
Electromagnetic waves can be produced by forcing electrons in an antenna to oscillate.
The strength of the waves that are produced depends on the length of the antenna and is
largest when the length of the antenna is exactly a quarter wavelength (with all else the
same). Using this information, determine whether antennas for radio waves are larger or
smaller than those for microwaves. Explain your answer.
1. Radio antenna larger. Microwaves have a smaller wavelength inturn making the
need for a smaller antena for the microwave in comparison to the radio waves.
2. Radio antenna larger. Radio waves travel further and so they must be larger and
have a longer wavelength.
3. Radio antenna smaller. Larger antennas are not practical.
4. Radio antenna smaller. Radio waves are not as energetic as microwaves and
they thus require smaller antennas.
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209
Warm Up Question 26
A laser produces a narrow beam of light. The diameter of the beam is noticeable. The
beam is focused by a lens to a point whose diameter is much smaller than that of the
beam. As the beam is focused to a point does the intensity of the beam increase, decrease
or stay the same? Explain your answer in terms of energy and ignore the negligible losses
of energy to the air and the lens.
1. Increases. I = P/A so if you put the same amount of power into a smaller
area the I increases.
2. Decreases. The beam must be losing energy as it propagates since the distance
traveled increases.
3. Same. Energy is conserved in this case.
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210
Electromagnetic Waves: Slides
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211
Electromagnetic Wave Propagation Along One Line
Electromagnetic wave propagating along +x direction.
Red indicates the electric field, blue the magnetic field.
y
x
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212
Electromagnetic Wave Propagation Along Several Directions
Electromagnetic waves produced by charge oscillating up and down the y axis.
Red indicates the electric field.
y
x
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213
Linearly Polarized Electromagnetic Waves
Electromagnetic wave propagating along +x direction. Only the electric field is indicated.
Horizontally Polarized
x
Vertically Polarized
x
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214
More Linearly Polarized Electromagnetic Waves
Electromagnetic wave propagating along +x direction. Only the electric field is indicated.
x
x
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215
Unpolarized Electromagnetic Waves
Electromagnetic wave propagating along +x direction. Only the electric field is indicated.
x
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216
Wave Optics
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217
Question 180
A beam of light propagates toward a
screen. The beam and the envelope of the
electric field are as illustrated. The screen
is labeled with a vertical scale.
E
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4
3
2
1
0
-1
-2
-3
-4
Which of the following is true regarding the
appearance of the light at the screen?
1. A constant vertical stripe from −3 to 3.
2. A constant vertical stripe from 0 to 3.
3. A flickering vertical stripe from −3 to 3.
4. A constant vertical stripe from −1.5 to 1.5.
5. A spot in the vicinity of 0.
218
Question 181
Light passes from air (n = 1.00) into glass
(n = 1.5). Which of the following most
correctly represents the light wave in this
case?
Case 1
Air
Case 2
Glass
Air
Glass
Glass
Case 3
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Air
219
Question 182
Two pulses approach each other on a string.
At an initial instant the string is as illustrated
and the pulses travel with speed 1 unit per
second.
Which of the following is an accurate
depiction of the entire string at an instant 2
seconds later?
Case 1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Case 2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Case 3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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220
Question 183
Two pulses approach each other on a string.
At an initial instant the string is as illustrated
and the pulses travel with speed 1 unit per
second.
Which of the following is an accurate
depiction of the entire string at an instant 2
seconds later?
Case 1
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Case 2
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Case 3
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
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221
Question 184
Two light waves propagate through different
combinations of media as illustrated.
Ez
In vacuum
Determine the index of refraction of the glass.
1. nglass = 0.5
2. nglass = 0.67
3. nglass = 1
Ez
In glass and vacuum
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4. nglass = 1.5
5. nglass = 1.33
222
Question 185
Two light waves propagate through different
combinations of media as illustrated.
Ez
The phase difference between the emerging
waves is:
In vacuum
1. 0
π
2.
2
3. π
Ez
In glass and vacuum
4.
3π
2
5. 2π
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223
Question 186
Two light waves propagate through different
combinations of media as illustrated.
Ez
The phase difference between the emerging
waves is:
In vacuum
1. 0
π
2.
2
3. π
Ez
In glass and vacuum
4.
3π
2
5. 2π
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224
Question 187
Snapshots of two waves at t = 0 s in the
same medium are illustrated.
y1
Determine the phase difference between the
waves.
Wave 1
1. ∆φ = 0
π
4
π
3. ∆φ =
2
2. ∆φ =
y2
Wave 2
4. ∆φ = π
5. ∆φ =
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3π
2
225
Question 188
Snapshots of two waves at t = 0 s in the
same medium are illustrated.
y1
Determine the phase difference between the
waves.
Wave 1
1. ∆φ = 0
π
4
π
3. ∆φ =
2
2. ∆φ =
y2
Wave 2
4. ∆φ = π
5. ∆φ =
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3π
2
226
Question 189
Snapshots of two waves in the same medium
are as illustrated.
By how far is wave 2 shifted from wave 1?
1. 4λ
Wave 1
2. 2λ
3. λ
Wave 2
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4.
λ
2
5.
λ
4
227
Question 190
Snapshots of two waves in the same medium
are as illustrated.
By how far is wave 2 shifted from wave 1?
1. 4λ
Wave 1
2. 2λ
3. λ
Wave 2
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4.
λ
2
5.
λ
4
228
Question 191
Monochromatic light (of just one wavelength)
is incident upon a double slit.
Which of the following describes the intensity
of the light at point P, which is located at
the midpoint of the double-slit arrangement?
1. There is a dark spot, since the light is
obstructed by the barrier.
b
P
2. There is a dark spot, since waves from
the slits interfere destructively.
3. There is a bright spot, since waves from
the slits interfere constructively.
Light
Barrier
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4. There is a spot of intermediate brightness.
Screen
229
Question 192
Monochromatic light (of just one wavelength)
is incident upon a double slit.
The wavelength of the light increases. Which
of the following describes what happens to
the bright fringes?
1. Stay the same.
2. Spread out.
3. Squash together.
4. Stay in the same location but diminish in
brightness.
Light
Barrier
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5. Stay in the same location but increase in
brightness.
Screen
230
Question 193
Monochromatic light (of just one wavelength)
is incident upon a double slit.
A piece of glass is placed in front of one
slit. The glass absorbs negligible light and
shifts the phase of the light passing through
it by exactly one half wavelength. Which of
the following describes what happens to the
pattern?
1. The pattern disappears.
2. The bright spots are closer together.
3. The bright spots are further apart.
Light
Barrier
4. The bright
interchanged.
and
dark
spots
are
Screen
5. There are no changes.
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231
Question 194
Red light and blue light are incident upon
double slits with the same slit spacing. The
distance from the slits to the screen is the
same for both. The wavelength of red light
is larger than that for blue light.
Which of the following is/are true?
1. In both cases there is a bright fringe at
the center.
2. There is a bright fringe at the center only
for the blue light.
3. The locations of the bright fringes are the
same for red and blue.
4. Red fringes are further apart than blue.
5. Red fringes are closer together than blue.
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232
Question 195
White light is a combination of
light waves of many different
frequencies. The wavelengths of
the light range from largest for
red to smallest for blue. A beam
of white light is incident upon a
double-slit.
Which of the following is true?
1. There is a white central bright fringe.
2. There is a bright blue fringe at the center.
3. There are only red fringes to the left of center and
blue fringes to the right of center.
4. Outer bright fringes contain a range of color bands
- red are further out than blue.
5. Outer bright fringes contain a range of color bands
- blue are further out than red.
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233
Question 196
Red light of wavelength 632 nm is incident
on a pair of narrow slits. A pattern of bright
and dark fringes is observed on a screen
placed beyond the slits.
The separation between the slits is decreased.
Which of the following describes the effect
on the pattern on the screen?
1. Bright and dark fringes are interchanged.
2. Distances between adjacent dark fringes
increase.
3. Distances between adjacent dark fringes
decrease.
4. There is no change.
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234
Question 197
Consider four equally spaced slits and
consider light waves that travel to one
particular screen location.
Suppose that
the discrepancy in the distance traveled by
the waves between adjacent slits is one
wavelength.
Which of the following is true regarding the
difference in the distance traveled between
the waves emanating from slit 1 and slit 4?
1. 2λ
2. 2.5λ
3. 3λ
Slit 1
Slit 2
4. 3.5λ
5. 4λ
Slit 3
Slit 4
Barrier
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235
Question 198
Consider four equally spaced slits and
consider light waves that travel to one
particular screen location. Suppose that the
discrepancy in the distance traveled by the
λ
waves between adjacent slits is .
2
Slit 1
Slit 2
Slit 3
Which of the following is true?
(Hint:
consider combinations of various pairs of
waves)
1. The waves interfere destructively ⇒ dark
fringe.
2. The waves interfere constructively ⇒
bright fringe.
3. Some waves interfere destructively others
constructively ⇒ intermediate fringe.
Slit 4
Barrier
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236
Question 199
Consider four equally spaced slits and
consider light waves that travel to one
particular screen location. Suppose that the
discrepancy in the distance traveled by the
λ
waves between adjacent slits is .
4
Slit 1
Slit 2
Slit 3
Which of the following is true?
(Hint:
consider combinations of various pairs of
waves)
1. The waves interfere destructively ⇒ dark
fringe.
2. The waves interfere constructively ⇒
bright fringe.
3. Some waves interfere destructively others
constructively ⇒ intermediate fringe.
Slit 4
Barrier
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237
Question 200
A narrow beam of white light is viewed
through a diffraction grating whose slits are
vertical. Wavelengths of light are typically
650 nm for red light 480 nm for violet.
Which of the following is true in the vicinity
of the region immediately opposite the beam
of light?
1. The light will split into a rainbow pattern
with the violet on the left and red on the
right.
2. The light will split into a rainbow pattern
with the violet on the right and red on
the left.
3. The light will split into a rainbow pattern
with the violet further from the center
than red.
4. The light will split into a rainbow pattern
with the violet closer to the center than
red.
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238
Question 201
A diffraction grating is illuminated with yellow
light at normal incidence. The pattern seen
on a screen behind the grating consists
of three yellow spots, one at 0◦ (straight
through) and one each at ±45◦.
You now add red light of equal intensity,
coming in the same direction as the yellow
light. The new pattern consists of:
1. red spots at 0◦ and 45◦.
2. yellow spots at 0◦ and 45◦.
3. orange spots at 0◦ and 45◦.
4. an orange spot at 0◦, yellow spots at 45◦ ,
and red spots slightly farther out.
5. an orange spot at 0◦, yellow spots at 45◦ ,
and red spots slightly closer in.
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239
Question 202
Light of wavelength 500 nm passes through
a single slit of width 1800 nm.
How many dark spots will appear in the
diffraction pattern?
1. 3
2. 4
3. 6
4. 7
5. Infinite
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240
Question 203
Monochromatic light is incident on a small
disk-shaped barrier.
The disk will produce a shadow. The center
of this area (marked by an arrow) is:
1. a bright spot,
2. darker than the rest of the shadow,
3. slightly lighter than the rest of the shadow,
4. bright or dark depending on the distance
between the screen and the disk.
Light
Screen
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241
Question 204
Light of wavelength 600 nm strikes a thin
film of thickness 200 nm perpendicularly and
a wave passes through the film as illustrated
(with the angles exaggerated). The index of
refraction of the film is nfilm = 1.5.
Which of the following represents the shift
resulting only from the distance which the
wave travels through the film?
1. 0 wavelengths
1
2.
wavelengths
2
3. 1 wavelength
4.
3
wavelengths
2
5. 2 wavelengths
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242
Question 205
Light of one wavelength is incident on a thin
film, whose index of refraction is 1.33. The
thickness of the film is such that when the
film is surrounded by air (index of refraction
1.00), the intensity of the reflected light is
zero.
Film
Which of the following is a possible phase
shift (in numbers of wavelengths) between
the two reflected light waves?
1. 0 wavelengths.
1
2.
wavelength.
2
3.
1
wavelength.
4
4. 1 wavelength.
5. 2 wavelengths.
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243
Question 206
Light of wavelength 600 nm strikes a thin
film of thickness 200 nm perpendicularly and
a waves travel as illustrated (with the angles
exaggerated). The index of refraction of the
film is nfilm = 1.5. The index of refraction
of the surrounding medium is 1.0.
Which of the following represents the shift
between the two waves that emerge from the
left edge of the film and travel leftwards?
1. 0 wavelengths
1
2.
wavelengths
2
3. 1 wavelength
4.
3
wavelengths
2
5. 2 wavelengths
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244
Question 207
Light of wavelength 600 nm strikes a thin
film of thickness 200 nm perpendicularly and
a waves travel as illustrated (with the angles
exaggerated). The index of refraction of the
film is nfilm = 1.5. The index of refraction
of the surrounding medium left of the film is
1.0 and to the right of the film 1.83.
Which of the following represents the shift
between the two waves that emerge from the
left edge of the film and travel leftwards?
1. 0 wavelengths
1
2.
wavelengths
2
3. 1 wavelength
4.
3
wavelengths
2
5. 2 wavelengths
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245
Question 208
Light is incident on a thin film of oil on
water. Assume that the film of oil has a
uniform thickness. The index of refraction of
the oil is 1.20 and of water 1.33. Red light
has a longer wavelength than blue light.
Consider light that is incident in a narrow
range of angles. Which of the following
is true regarding the distances traveled by
light through the oil that results in strongly
reflected red light and strongly reflected blue
light?
1. Shorter for red than blue.
Oil
2. Longer for red than blue.
3. Same for red as blue.
Water
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246
Question 209
White light is incident on a thin film of oil
on water. Assume that the film of oil has a
uniform thickness.
Oil
Water
The index of refraction of the oil is 1.20
and of water 1.33. Red light has a longer
wavelength than blue light. Which of the
following is true?
1. Red and blue light will be reflected at the
same angle.
2. Red light will be strongly reflected at a
greater angle than blue.
3. Blue light will be reflected at a greater
angle than red.
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247
Question 210
Light of one wavelength is incident on a thin
film, whose index of refraction is 1.33. The
thickness of the film is such that when the
film is surrounded by air (index of refraction
1.00), the intensity of the reflected light is
zero.
Film Glass
A sheet of glass (index of refraction 1.50) is
placed immediately to the right of the film.
Which of the following is true?
1. The intensity of the reflected light is zero
because the two reflected waves interfere
destructively.
2. The intensity of the reflected light is
brighter because the two reflected waves
interfere constructively.
3. The intensity of the reflected light is
brighter because there is now only one
reflected wave.
4. None of the above.
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248
Question 211
Two microscope slides are held together as
illustrated. Light is incident on the slides
from above. The slides are coated (black
line) to prevent reflections.
The upper slide is rotated away from the
lower slide so that the angle of the wedge
increases. What happens to the pattern of
fringes?
1. Stays the same.
2. Fringes are further apart.
3. Fringes are closer together.
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249
Question 212
Light passes through a single slit whose width
can be varied.
As the slit width is decreased, what happens.
1. The central maximum narrows.
2. The central maximum widens.
3. The central maximum stays the same
width but more dark fringes appear.
4. The central maximum stays the same
width but fewer dark fringes appear.
5. Nothing changes except for the brightness
of the central maximum.
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250
Warm Up Question 27
Fig 17.6 illustrates diffraction, the spreading of light as it passes through an opening.
Would the double-slit experiment of Fig 17.7 display bright and dark fringes if light did
NOT spread as it passed through the slits? Explain your answer.
1. Yes. The pattern would just be concentrated opposite each slit.
2. Yes. There would just be two bands opposite the slits.
3. No. The two waves are not overlapping after they pass through the slits. The
overlapping of waves causes interference which is what makes the light and dark
fringes. If the light does’t spread after the slits there is no interference and thus
no light and dark fringes.
4. No. The spreading of the light as it passes splits it into dark and light waves.
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251
Warm Up Question 28
Suppose that two different light sources are used to produce light that is incident upon
a double slit as shown in Fig 17.7. The sources produce light with distinct frequencies
(distinct colors). Will the resulting interference patterns for the two colors overlap perfectly
(i.e. each bright fringe for one color coincides with a bright fringe for the other color)?
Explain your answer.
1. Yes. The colors fringes will over lap and produce a new color.
2. Yes. They pass through the same slits and so the patterns produced will be the
same.
3. No. The waves have different wavelengths and so a crest of one will not
generally meet a crest of another.
4. No. frequency changes it alters wavelength and hence alters the position
(mλL/d) for positions of brightness for fringes .
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252
Warm Up Question 29
Red light of one particular wavelength is incident upon a single slit. The diffraction pattern
is observed while the intensity of the intensity of the light is reduced. Describe whether
the locations of the bright and dark fringes changes as the intensity is reduced. If they do,
describe whether they move closer or further apart. Explain your answer.
1. Closer together. The wavelength decreases as the intensity decreases and so
fringe locations are nearer the central fringe.
2. Further apart. The wavelengths increase, spacing everything further out.
3. No change. Neither a nor L change and so the locations of the dark fringes
stay the same.
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253
Warm Up Question 30
Two radio waves are broadcast into a gap between two hills. One is from an AM station
whose frequency is about 1000 kHz and the other from an FM radio station whose
frequency is about 100 MHz. Which wave is more likely to propagate to a town that is
behind one of the hills but not directly behind the gap between the hills? Explain your
answer.
1. AM. AM has longer wavelength meaning that the waves travel further.
2. AM. The AM waves are larger and will travel further.
3. AM. A bigger frequency means that the waves will be stronger.
4. FM. Larger wavelength means a larger diffraction pattern.
5. FM. The larger frequency means that the signal is stronger.
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254
Wave Optics: Slides
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255
Phase Shift I
Two waves overlap initially. Two crests that
initially align are marked.
Waves shift by different distances.
Ez
b
Ez
b
Ez
b
Ez
b
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256
Phase Shift II
One possible relative shift by a whole
wavelength.
Ez
A different but equivalent relative shift by a
whole number of wavelengths.
Ez
b
Ez
b
b
Ez
– Typeset by FoilTEX –
b
257
Phase Shift III
One possible
wavelength.
relative
Ez
shift
by
a
half
A different but equivalent relative shift by a
half wavelength.
Ez
b
Ez
b
b
Ez
– Typeset by FoilTEX –
b
258
Interference of Pulses
A snapshot of a string at t = 0 s displays
two pulses traveling toward each other. The
horizontal units are cm. Suppose that the
pulses travel with speed 1 cm/s.
At t = 1 s the pulses appear as:
x
x
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259
Interference of Pulses
A snapshot of a string at t = 1 s is as follows.
At t = 2.5 s the individual pulses and their
superposition appear as:
x
x
Add to give:
x
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260
General Interference I
Snapshots of two waves at t = 0 s in the
same medium are illustrated whose phase
difference is ∆φ = 0.
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
261
General Interference II
Snapshots of two waves at t = 0 s in the
same medium are illustrated whose phase
difference is ∆φ = π4 .
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
262
General Interference III
Snapshots of two waves at t = 0 s in the
same medium are illustrated whose phase
difference is ∆φ = π2 .
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
263
General Interference IV
Snapshots of two waves at t = 0 s in the
same medium are illustrated whose phase
difference is ∆φ = 3π
4 .
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
264
General Interference V
Snapshots of two waves at t = 0 s in the
same medium are illustrated whose phase
difference is ∆φ = π .
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
265
Constructive Interference
Snapshots of two waves at on instant in the
same medium.
y1
y2
Wave 1
The superposition of the two waves is:
y
Superposition
Wave 2
– Typeset by FoilTEX –
Individual waves
ytot
266
Destructive Interference
Snapshots of two waves at one instant in the
same medium.
y1
y2
Wave 1
The superposition of the two waves is:
y
Superposition
Wave 2
– Typeset by FoilTEX –
Individual waves
ytot
267
March 2006
Mach-Zehnder Interferometer
Detector
Beam Splitter
Mirror
Beam Splitter
– Typeset by FoilTEX –
Mirror
268
Waves from Two Sources
Sources coincide. Constructive interference
results.
Sources
offset
by
one
wavelength.
Constructive interference results.
λ
Source 1
b
Source 2
b
Source 1
Superposition
– Typeset by FoilTEX –
b
Source 2
b
Superposition
269
Waves from Two Sources
Sources offset by two wavelengths.
Constructive interference results.
Sources offset by two wavelengths.
Constructive interference results.
2λ
Source 1
b
2λ
Source 1
Source 2
Superposition
– Typeset by FoilTEX –
b
b
Source 2
b
Superposition
270
Waves from Two Sources
Sources offset by a half wavelength.
Destructive interference results.
Sources offset by one and a half wavelengths.
Destructive interference results.
λ/2
Source 1
b
Source 2
Superposition
– Typeset by FoilTEX –
3λ/2
b
Source 1
b
Source 2
b
Superposition
271
Waves from Two Sources: Constructive Interference
Sources offset by one wavelength.
Sources offset by two wavelengths.
λ
Source 1
λ
Source 1
b
Source 2
∆l
Superposition
– Typeset by FoilTEX –
b
λ
b
Source 2
b
∆l
Superposition
272
Waves from Two Sources: Constructive Interference
Sources offset by one wavelength.
Sources offset by two wavelengths.
λ
Source 1
λ λ
Source 1
b
Source 2
b
b
Source 2
∆l
∆l
Superposition
Superposition
– Typeset by FoilTEX –
b
273
Waves from Two Sources: Destructive Interference
Sources offset by one half wavelength.
Sources offset by one and a half wavelengths.
λ
Source 1
λ
Source 1
b
Source 2
b
∆l
Superposition
– Typeset by FoilTEX –
λ
b
Source 2
b
∆l
Superposition
274
Waves from Two Sources: Destructive Interference
Sources offset by half wavelength.
Sources offset by one and a half wavelengths.
λ
Source 1
Source 1
b
Source 2
∆l
Superposition
– Typeset by FoilTEX –
λ
b
λ
b
Source 2
b
∆l
Superposition
275
Overlapping Waves from a Double Slit
Light Intensity
Light
Barrier
– Typeset by FoilTEX –
Screen
276
Single Slit Interference I
Snapshots of two waves at t = 0 s in the
same medium are illustrated. The shift of
one relative to the other is λ/12.
y1
The superposition of the two waves is:
y
Individual waves
Wave 1
Superposition
y2
Wave 2
– Typeset by FoilTEX –
ytot
277
Single Slit Interference II
Interference of two waves at t = 0 s in the
same medium whose successive shifts are
λ/12.
y
Individual waves
Interference of four waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Superposition
ytot
– Typeset by FoilTEX –
Individual waves
Superposition
ytot
278
Single Slit Interference III
Interference of four waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Individual waves
Interference of eight waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Superposition
ytot
– Typeset by FoilTEX –
Individual waves
Superposition
ytot
279
Single Slit Interference IV
Interference of eight waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Individual waves
Interference of ten waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Superposition
ytot
– Typeset by FoilTEX –
Individual waves
Superposition
ytot
280
Single Slit Interference V
Interference of ten waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Individual waves
Interference of twelve waves at t = 0 s in
the same medium whose successive whose
successive shifts are λ/12.
y
Superposition
ytot
– Typeset by FoilTEX –
Individual waves
Superposition
ytot
281
Double Slit Pattern
Double slit interference
pattern for two slits of
negligible width.
Intensity
I = I max cos2 β
0
where
β=
θ
πd
sin θ.
λ
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282
Single Slit Pattern
Single slit interference
pattern.
I =I
max
sin α
α
0
where
α=
Intensity
2
θ
πa
sin θ.
λ
– Typeset by FoilTEX –
283
Double Slit Pattern: Width Included
Double slit interference
pattern including width
features.
I = I max
sin α
α
2
cos2 β
0
θ
where
α=
πa
sin θ
λ
β=
πd
sin θ.
λ
and
– Typeset by FoilTEX –
284
Double Slit Pattern: Width Included
Double slit interference
pattern including width
features.
I =I
max
sin α
α
2
2
cos β
where
α=
πa
sin θ
λ
and
πd
β=
sin θ.
λ
– Typeset by FoilTEX –
0
θ
285
Double Slit Pattern: Narrower Width
Double slit interference
pattern with a narrower
width.
I =I
max
sin α
α
2
2
cos β
where
α=
πa
sin θ
λ
and
πd
β=
sin θ.
λ
– Typeset by FoilTEX –
0
θ
286
Title
Question
1. Response
2. Response
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287
Geometric Optics
– Typeset by FoilTEX –
288
Question 213
A narrow beam of light rays is incident on a
perfectly flat mirror as indicated.
1
2
4
b
b
b
Which observer(s) can see the reflected light?
5
b
3
b
– Typeset by FoilTEX –
289
Question 214
A light ray is incident on a smooth curved
surface as illustrated. Which of the following
indicates the reflected light ray correctly?
Case 3
Case 1
– Typeset by FoilTEX –
Case 4
Case 2
290
Question 215
A light ray is incident on a smooth curved
surface as illustrated. Which of the following
indicates the reflected light ray correctly?
Case 3
Case 1
– Typeset by FoilTEX –
Case 4
Case 2
291
Question 216
An observer labeled O, faces a mirror and
observes a point light source S. Where is the
image of S located, according to O?
Where is the image of S located according to
O?
1. A
O
C
b
b
2. B
3. C
A
S
– Typeset by FoilTEX –
b
4. D
b
B
b
D
b
5. O cannot see an image of S.
292
Question 217
Three observers, A, B and C, and an object,
labeled S, are placed in front of a mirror as
illustrated.
Which of the observers can see the image of
the object?
1. Only C
C
b
B
b
2. Only B
3. Only B and C
4. Only A and C
S
A
b
5. Only A and B
b
– Typeset by FoilTEX –
293
Question 218
An object is placed between two parallel
mirrors as illustrated. The horizontal units
are marked in meters.
The images produced by the mirrors are
located at:
1. x = 2 m, 3 m, . . .
b
x
2. x = ±2 m, ±3 m, ±4 m, . . .
3. x = ±2 m, ±4 m, ±6 m, . . .
4. x = ±2 m
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294
Question 219
Case 4
Plane
Plane
Plane
Case 5
Plane
– Typeset by FoilTEX –
Case 2
Plane
Case 1
Case 3
Two mirrors are parallel to each other as
illustrated. A toy plane is placed between
the mirrors. Various possibilities for some of
the reflected images are illustrated. Which of
these is correct?
295
Question 220
Sections of convex spherical mirrors are
illustrated below.
Mirror A
Mirror B
Which of the following best represents the
rank of the radii of curvatures of the mirrors?
1. A > C > B
2. A = B > C
3. A = B < C
4. A < B = C
Mirror C
– Typeset by FoilTEX –
5. A < C < B
296
Question 221
Sections of convex spherical mirrors are
illustrated below.
Mirror A
Mirror B
The answer:
A=B<C
Mirror C
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297
Question 222
Various convex mirrors are used to
produce images of the same object.
Which of the following is true?
1. Convex mirrors always produce upright images.
2. Convex mirrors can produce upright or inverted
images depending on the location of the object.
3. Convex mirrors always produce inverted images.
4. Convex mirrors always produce reduced size
images.
5. Convex mirrors can produce enlarged or
reduced images depending on the object
location.
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298
Question 223
Light passes from air into water. Light
travels at a smaller speed in water than in
air. Which of the following is possible for the
waves?
Case 3
Case 1
– Typeset by FoilTEX –
Case 2
299
Question 224
Light passes from air (n = 1.00) into
glass (n = 1.52) and then into water
(n = 1.33).
Which of the following
indicates a possible trajectory of the light ray?
Case 3
Case 1
Case 4
Case 2
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300
Question 225
The indices of refraction for various
substances are given below:
Air
1.00
Water
1.33
Benzene
1.50
Which of the following is/are true?
1. Total internal reflection is possible for light passing
from any of the materials listed to any other one
listed.
2. Total internal reflection is possible for light passing
from benzene to air but not water to air.
3. Total internal reflection is possible for light passing
from benzene to air and water to air.
4. Total internal reflection is possible for light passing
from air to benzene but not air to water.
5. Total internal reflection is possible for light passing
from air to benzene and air to water.
– Typeset by FoilTEX –
301
Question 226
The indices of refraction for various
substances are given below:
Air
1.00
Water
1.33
Benzene
1.50
Which of the following is/are true?
1. Total internal reflection is possible for light passing
from any of the materials listed to any other one
listed.
2. Total internal reflection is possible for light passing
from benzene to air but not water to air.
3. Total internal reflection is possible for light passing
from benzene to air and water to air.
4. θc for the air/benzene combination is larger than
that for the air/water combination.
5. θc for the air/benzene combination is smaller than
that for the air/water combination.
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302
Question 227
White light enters a prism as illustrated.
The light is broken into distinct colors after
emerging.
Which of the following is true for the index
of refraction for light in glass?
1. It is the same for red and blue.
2. It is larger for red.
3.
4. It is larger for blue.
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303
Question 228
A lens focuses incoming parallel light rays in
air as illustrated. The lens is then immersed
in water a parallel light rays enter it. The
index of refraction of water is 1.33 and for
this glass 1.50.
Inside the water, the rays are focused:
1. closer to the lens
2. further from the lens
3. at the same point as in the air.
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304
Question 229
An object is placed to the left of a convex
lens with focal point as illustrated. Several
rays are traced from the tip of the object
through the lens.
Which of the rays is drawn correctly?
Object
Fb
b
F
1
2
3
4
– Typeset by FoilTEX –
305
Question 230
An object is placed to the left of a convex
lens with focal point as illustrated. Two
rays are traced from the tip of the object
through the lens and indicate the location of
the image.
As the object is shifted closer toward the
left focal point, which of the following is true?
1. The location and height of the image
remain fixed.
2. The image gets closer to the lens and its
height decreases.
Object
3. The image gets closer to the lens and its
height stays constant.
Fb
Fb
4. The image gets further from the lens and
its height increases.
5. The image gets further from the lens and
its height decreases.
– Typeset by FoilTEX –
306
Question 231
An object is placed between a convex lens
and its focal point.
Object
Fb
Provided that the object is somewhere
between the lens and its focal point, which
of the following is true is regarding the size
of the image?
1. Smaller than the object regardless of
object position.
Fb
2. Same as the object regardless of object
position.
3. Larger than the object regardless of object
position.
4. Larger than the object for certain object
positions, smaller for others.
– Typeset by FoilTEX –
307
Question 232
An object is placed to the left of a convex
lens with focal point as illustrated. Two
rays are traced from the tip of the object
through the lens and indicate the location of
the image.
As the object is shifted closer toward the
left focal point, which of the following is true?
1. The magnification stays constant.
2. The magnification decreases.
3. The magnification increases.
Object
Fb
– Typeset by FoilTEX –
Fb
308
Question 233
An object is placed to the left of a concave
lens with focal point as illustrated. Two
rays are traced from the tip of the object
through the lens and indicate the location of
the image.
As the object is shifted closer toward the
lens, which of the following is true?
1. The location and height of the image
remain fixed.
2. The image is produced at the focal point
and its height increases.
Object
3. The image gets closer to the lens and its
height decreases.
Fb
Fb
4. The image gets closer to the lens and its
height increases.
5. The image gets further from the lens and
its height increases.
– Typeset by FoilTEX –
309
Question 234
An object is placed to the left of a convex
lens with focal point as illustrated.
As the object is shifted closer toward the
left focal point, which of the following is true?
1. The location and height of the image
remain fixed.
Object
2. The image gets closer to the lens and its
height decreases.
Fb
Fb
3. The image gets closer to the lens and its
height increases.
4. The image gets further from the lens and
its height increases.
5. The image gets further from the lens and
its height decreases.
– Typeset by FoilTEX –
310
Question 235
An object is placed to the left of a convex
lens with focal length of 1 m. The distance
from the object to the lens is more than 2 m.
Which of the following is true of the image
location?
1. di is exactly equal to do.
2. di is not equal to do but is more than
2 m.
Object
3. di is less than 2 m.
F
b
– Typeset by FoilTEX –
F
b
311
Question 236
An object is placed to the left of a convex
lens with focal point as illustrated. The
distance from the object to the lens is less
than 2f.
Which of the following is true of the size of
the magnification?
1. m = 1
2. m > 1
3. m < 1
Object
F
b
– Typeset by FoilTEX –
F
b
312
Question 237
An object is placed to the left of a convex lens
with focal point as illustrated. The distance
from the object to the lens is greater than 2f.
Which of the following is true of the size of
the magnification?
1. m = 1
2. m > 1
Object
3. m < 1
F
b
– Typeset by FoilTEX –
F
b
313
Question 238
A simple model of the eye without any lens
mechanism is illustrated below. Two tiny
light sources are located to the left of the
eye opening.
Which of the following best illustrates the
image produced on the ”retina?”
Case 1
b
Case 2
b
b
b
b
b
Case 3
– Typeset by FoilTEX –
Case 4
314
Question 239
The eye always produces a clear image on
the retina provided that the object is beyond
the near point.
As the object moves closer to the eye, which
of the following is true?
1. The focal length of the lens stays constant;
the image size stays constant.
Object
Retina
Fb
Fb
2. The focal length of the lens stays constant;
the image size stays increases.
3. The focal length of the lens increases; the
image size increases.
4. The focal length of the lens decreases;
the image size increases.
5. The focal length of the lens decreases;
the image size decreases.
– Typeset by FoilTEX –
315
Question 240
A person who is nearsighted needs to observe
a tree which is beyond that person’s far point.
This can be accomplished by placing a lens in
front of the eye. The lens must produce an
image of the tree which is upright and closer
to the lens that the tree.
Which arrangement will accomplish this?
1. A concave lens placed so that the tree is
beyond the focal point of the lens.
2. A concave lens placed so that the tree is
between the lens and its focal point.
3. A convex lens placed so that the tree is
beyond the focal point of the lens.
4. A convex lens placed so that the tree is
between the lens and its focal point.
– Typeset by FoilTEX –
316
Question 241
A person who is farsighted needs to observe
an ant which is closer that person’s near
point. This can be accomplished by placing
a lens in front of the eye. The lens must
produce an image of the ant which is upright
and further from the lens than the ant.
Which arrangement will accomplish this?
1. A concave lens placed so that the ant is
beyond the focal point of the lens.
2. A concave lens placed so that the ant is
between the lens and its focal point.
3. A convex lens placed so that the ant is
beyond the focal point of the lens.
4. A convex lens placed so that the ant is
between the lens and its focal point.
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317
Question 242
Two people, Alex and Xela, have different
near points; Alex’s near point is twice as far
from his eye as Xela’s (25 cm). Their far
points are both at infinity. They both use
identical magnifying glass to observe identical
ants, each of which is 10 cm from their eyes.
They situate the magnifying glass so that the
ant is at the focal point of the magnifying
glass.
Which of the following is true?
1. Only Alex can see a clear image of the
ant.
2. Only Xela can see a clear image of the
ant.
3. Both Alex and Xela can see a clear image
of the ant.
4. Neither can see a clear image of the ant.
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318
Question 243
Two people, Alex and Xela, have different
near points; Alex’s near point is twice as far
from his eye as Xela’s (25 cm). Their far
points are both at infinity. They both use
identical magnifying glass to observe identical
ants, each of which is 10 cm from their eyes.
They situate the magnifying glass so that the
ant is at the focal point of the magnifying
glass.
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Which of the following is true regarding the
sizes of the images of the ant produced by
the magnifier?
1. The image is larger for Alex.
2. The image is larger for Xela
3. The image sizes are the same.
4. The images are infinitely tall.
319
Question 244
Two people, Alex and Xela, have different
near points; Alex’s near point is twice as far
from his eye as Xela’s (25 cm). Their far
points are both at infinity. They both use
identical magnifying glass to observe identical
ants, each of which is 10 cm from their eyes.
They situate the magnifying glass so that the
ant is at the focal point of the magnifying
glass.
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Which of the following is true regarding
angular magnifications attained using the
magnifier?
1. Larger for Alex.
2. Larger for Xela.
3. The same.
4. Both infinite.
320
Question 245
A person looks toward a full moon and
initially holds a quarter out in such a way
that the quarter exactly obscures the moon.
The person brings the quarter closer to his
eye.
Which of the following is true after the
person has brought the quarter closer to his
eye?
1. The angular size of the quarter is larger
than that of the moon.
2. The angular size of the quarter is smaller
than that of the moon.
3. The angular size of the quarter is the
same as that of the moon.
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321
Question 246
Two objects have the indicated
heights and distances from an eye:
Which of the following is true?
1. Angular size of blue same as angular size of red.
Red arrow
Blue arrow
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Height
Distance
10 cm
2.0 m
20 cm
6.0 m
2. Angular size of blue larger than angular size of
red.
3. Angular size of blue smaller than angular size of
red.
322
Question 247
A microscope is adjusted so that the
intermediate image is located at the focal
point of the eyepiece. When this is true the
total angular magnification is given by
M =−
dintN
dofeyepiece
where dint is the distance from the objective
to the intermediate image, N the eye’s near
point, do the distance from the objective to
the object, and feyepiece the focal length of
the eyepiece.
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Which of the following is true as the object
is brought closer to the objective?
1. The eyepiece must be moved closer to the
object. Magnification decreases.
2. The eyepiece must be moved closer to the
object. Magnification increases.
3. The eyepiece must be moved further from
the object. Magnification decreases.
4. The eyepiece must be moved further from
the object. Magnification increases.
323
Question 248
A telescope is used to view a star that is
infinitely far away. The eyepiece is situated
so that its focal point is located at the image
produced by the objective.
Which of the following represents the
distance between the lenses?
1. fobjective
2. fobjective − feyepiece
3. feyepiece
4. fobjective + feyepiece
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324
Warm Up Question 31
Someone states that, “The image formed by a lens is located at the focal point of the
lens, regardless of the location of the object” Is this statement true or not? Explain your
answer (you can refer to diagrams in the text if necessary).
1. True. Rays entering the lens in a parallel fashion pass through the focal point.
This produces an image at the focal point.
2. True for a converging lens. This always bends light rays through the focal point.
3. False. Diagram 18.30 shows an image that is not located at the focal point of
the lens.
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325
Warm Up Question 32
An arrow is placed to the left of a concave lens. Are there any locations where the arrow
can be placed so that the lens produces a sharp image of the arrow on a piece of paper?
If so, describe where these locations are. Explain your answers.
1. No (locations). It’s a diverging lens and the light rays cannot converge on a
screen.
2. Yes. At the focal point.
3. Yes. At a point on the opposite side of the lens.
4. Yes. Place the arrow at the center of the lens.
5. Yes. Place the arrow in the image plane.
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326
Warm Up Question 33
A magnifying glass provides a certain angular magnification, when the object is located
near to the focal point of the lens. In order to attain a larger angular magnification, would
one use a lens with a larger or smaller focal length? Explain your answer.
1. Focal length does not matter.
2. Larger. A bigger focal length implies that the image is produced further away
and is larger.
25 cm
3. Smaller.
According to M =
smaller focal length gives larger
f
magnification.
4. Smaller. Since the focal point is smaller, the angle from the lens to the focal
point is steeper, so this would make a larger angular magnification.
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327
Warm Up Question 34
Consider the image produced by a microscope. Is this image real or virtual? Upright or
inverted? Provide reasons for your answers.
1. Real and upright. First produces real and inverted. Second produces real and
re-inverts, giving upright.
2. Real and inverted. The first lens produces a real image. The minus sign in M
indicates that it is inverted.
3. Real and inverted. Microscopes produce inverted images. Inverted images are
always real.
4. Virtual and upright. The eyepiece acts like a magnifying glass which produces a
virtual and upright image.
5. Virtual and inverted. Virtual because the image is on the same side of the lens
as the object and it appears upside down after ray tracing.
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328
Warm Up Question 35
A telescope contains two lenses. That closer to the eye is called the eyepiece and
that closer to the object, the objective. A particular telescope produces an angular
magnification of 3. Describe as precisely as possible how the focal length of the objective
is related to the focal length of the eyepiece for this telescope.
1. The focal length of the objective is shorter than that of the eyepiece since the
magnification is only 3.
2. The focal length depends on the distance to the object, since the object’s
location will affect where any images are produced.
3. The focal length of the eyepiece is the same as that of the objective, since the
eyepiece focal point is placed at the location of the image produced by the
objective.
4. fobjective = 3feyepiece since this is the ratio given by the magnification.
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329
Warm Up Question 36
In many microscopes it is possible to switch between different objective lenses, having
different focal lengths. Suppose that one switches to an objective lens with a smaller focal
length. How will the position of the eyepiece lens have to be adjusted (no change, closer
or further from object) to produce the correct image? Explain your answer.
1. Closer. The image produced by the objective is closer to the object. The
eyepiece must be moved closer so that its focal point is at this image.
2. Further. The image produced by the objective lens is further from the object
than before. The eyepiece must be moved further so that its focal point is at
this image.
3. Further. The magnification equation predicts a larger objective magnification.
The eyepiece magnification must be smaller to compensate.
4. No change. When focusing one does not move the eyepiece.
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330
Quantum Physics
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331
Question 249
A Xenon lamp equipped with a filter that
transmits light of wavelength 400 nm.
The power (total energy per second) emitted by
the light is increased. Which of the following is
true?
1. The energy of each photon is unchanged and
the rate of photon emission is unchanged.
2. The energy of each photon is unchanged and
the rate of photon emission increases.
3. The energy of each photon increases and the
rate of photon emission is unchanged.
4. The energy of each photon increases and the
rate of photon emission increases.
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332
Question 250
A Xenon lamp equipped with a filter that
transmits light of wavelength 400 nm.
This light is incident upon a metal and
electrons are ejected.
The filter is adjusted so that the frequency of the
emitted light is increased and the power stays
constant. Which of the following is true regarding
the emitted electrons?
1. The rate of electron emission is unchanged.
2. The rate of electron emission decreases.
3. The rate of electron emission increases.
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333
Question 251
A Xenon lamp equipped with a filter that
transmits light of wavelength 400 nm.
This light is incident upon a metal and
electrons are ejected.
The filter is adjusted so that the frequency of the
emitted light is increased and the power stays
constant. Which of the following is true regarding
the emitted electrons?
1. The energy of each electron is unchanged.
2. The energy of each electron increases.
3. The energy of each electron decreases.
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334
Question 252
Two lasers each emit red light of
wavelength 632 nm. The power of laser
A is 1 mW and that of laser B is 5 mW.
Which of the following is/are true?
1. Each photon from laser A has the same energy
as that of laser B.
2. Each photon from laser A has smaller energy
than that of laser B.
3. Laser B emits more photons per second than
laser A.
4. Laser B emits the same number of photons per
second as laser A.
5. The frequency of light from laser B is larger
than that of laser A.
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335
Question 253
Photons are fired toward a screen. The
probability distribution for arrival at various
locations is as illustrated. Consider the two
illustrated locations.
Which of the following is true?
1. Photons will never arrive at A but will
sometimes arrive at B.
2. Photons will never arrive at B but will
sometimes arrive at A.
Screen
A
B
3. Photons could arrive at either A or B;
they are more likely to arrive at A.
4. Photons could arrive at either A or B;
they are more likely to arrive at B.
5. Photons will always arrive at B.
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336
Question 254
Photons are fired toward a screen. The
probability distribution for arrival at various
locations is as illustrated. Consider the two
illustrated locations.
Which of the following is true?
1. Photons will never arrive at A but will
sometimes arrive at B.
2. Photons will never arrive at B but will
sometimes arrive at A.
Screen
A
B
3. Photons could arrive at either A or B;
they are more likely to arrive at A.
4. Photons could arrive at either A or B;
they are more likely to arrive at B.
5. Photons will always arrive at B.
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337
Question 255
Neutrons are fired toward a barrier/slit
arrangement and arrive at a screen.
The probability distribution for arrival
at various locations depends on the
barrier/slit arrangement. A double slit
produces the solid dark blue probability
distribution. A single slit produces the
dashed dark red distribution.
Screen
Which of the following is true?
1. Single slit ⇒ neutron definitely arrives at A.
Double slit ⇒ neutron definitely arrives at A.
2. Single slit ⇒ neutron could arrive at A.
Double slit ⇒ neutron could arrive at A.
3. Single slit ⇒ neutron never arrives at A.
Double slit ⇒ neutron never arrives at A.
4. Single slit ⇒ neutron could arrive at A.
Double slit ⇒ neutron never arrives at A.
A
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338
Question 256
Many neutrons are fired toward a
barrier/slit arrangement and arrive at
a screen. The probability distribution
for arrival at various locations depends
on the barrier/slit arrangement. A
double slit produces the solid dark
blue probability distribution. A single
slit produces the dashed dark red
distribution.
Which of the following is true?
1. Single slit ⇒ more arrive at A than B.
Double slit ⇒ more arrive at A than B.
2. Single slit ⇒ more arrive at B than A.
Double slit ⇒ more arrive at A than B.
3. Single slit ⇒ more arrive at B than A.
Double slit ⇒ more arrive at B than A.
4. Single slit ⇒ more arrive at A than B.
Double slit ⇒ more arrive at B than A.
Screen
A
B
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339
Question 257
A particle of mass m is contained in a box
of length L. The energy of the particle is
measured.
Which of the following is/are a possible
outcome of the energy measurement?
h2
1.
8mL2
h2
2. 2
8mL2
h2
3. 4
8mL2
h2
4. 6
8mL2
h2
5. 10
8mL2
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340
Question 258
A partial energy level diagram for a system is
as illustrated. The energies are in units of
10−19 J.
E3 = 8.0
Which transition results in emission of light
with the largest wavelength (based only on
the illustrated energy levels)?
1. 1 → 2
2. 2 → 1
3. 3 → 1
E2 = 4.0
E1 = 2.0
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4. 1 → 3
5. 3 → 2
341
Question 259
Certain manufactured “artificial atoms”
have exactly two energy levels.
The
artificial atoms are initially in the lowest
energy state in each case.
Atom A
Light is incident upon the artificial atoms.
Which of the following is true regarding the
wavelengths of light required to excite the
atoms from the lower to higher energy states?
Atom B
5.0 eV
1. Wavelength for A equals wavelength for B.
4.0 eV
2. Wavelength for A is larger than wavelength
for B.
2.0 eV
3. Wavelength for A is smaller than wavelength
for B.
1.0 eV
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342
Question 260
The Balmer series lines satisfy
λ=
91.1 nm
.
1
1
− 2
22
n
The red line in the hydrogen spectrum has a
longer wavelength than the blue line. Which
of the following must be true?
1. The value of n for red is the same as that
for blue.
2. The value of n for red is larger than that
for blue.
3. The value of n for red is smaller than
that for blue.
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343
Question 261
The total energy of an electron that orbits a
proton at radius r is
1 e2
E=−
8πǫ0 r
If
the
electron emits energy via
electromagnetic radiation as it orbits, then as
time passes, which of the following is true?
1. The radius of orbit stays constant.
2. The radius of orbit decreases.
3. The radius of orbit increases.
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344
Question 262
In the Bohr model, the energy levels can
be labeled with an integer n.
Visible
light is emitted when the atom undergoes a
transition from a level with n > 2 into one
with n = 2.
−0.85 eV
n=4
−1.51 eV
n=3
−3.40 eV
n=2
The frequency of blue light is larger than
the frequency of red light. Which of the
following is true?
1. Blue light and red light are each produced
from a transition involving the same
energy level to the n = 2 level.
2. Blue light is produced from a transition
from a level that is closer in energy (than
for red light) to the n = 2 level.
3. Red light is produced from a transition
from a level that is closer in energy (than
for blue light) to the n = 2 level.
−13.6 eV
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n=1
345
Question 263
In the Bohr model, it turns out that visible
light is emitted when an electron makes a
transition from an orbital with n > 2 into
the orbital with n = 2.
The frequency of blue light is larger than
the frequency of red light. Which of the
following is true?
1. Blue light and red light are each produced
from a transition involving the same
orbital to the n = 2 orbital.
2. Blue light is produced from a transition
from an orbital that is closer in energy
(than for red light) to the n = 2 orbital.
3. Red light is produced from a transition
from an orbital that is closer in energy
(than for blue light) to the n = 2 orbital.
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346
Question 264
The ground state energy of the Bohr model
hydrogen atom is −13.6 eV.
Which of the following best represents the
energy of the n = 3 level?
1. −1.51 eV
2. +1.51 eV
3. −4.53 eV
4. +4.53 eV
5. −10.6 eV
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347
Question 265
For the f states of the hydrogen atom l = 3.
Which of the following is the number of f
energy states?
1. 3
2. 5
3. 7
4. 10
5. 14
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348
Question 266
A hydrogen atom is initially in its ground
state (n = 1). A free electron is fired
toward the hydrogen atom and collides with
the atom. The lowest energy levels for
hydrogen are as illustrated.
What is the minimum energy that the
electron must have in order for it to stop
after the collision (and all the energy be
absorbed by the atom)?
1. 0.85 eV
−0.85 eV
n=4
−1.51 eV
n=3
−3.40 eV
n=2
2. 1.0 eV
3. 10.2 eV
4. 12.8 eV
5. 13.6 eV
−13.6 eV
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n=1
349
Warm Up Question 37
Two beams of electromagnetic radiation (similar to beams of light), one ultraviolet light
and the other infrared light, have the same power. Each of these are incident upon
the same type of molecule, whose atoms will be separated if the energy supplied by any
incident radiation is large enough. Which beam of light (ultraviolet or infrared) is more
likely to be able to split the molecule? Explain your answer.
1. Ultraviolet. Infrared light has a longer wavelength and thus a lower frequency so
the energy of it is less than the energy of a photon from ultraviolet light. The
ultraviolet light beam will be more likely to split the molecule because it has
more energy.
2. Ultraviolet. This has a longer wavelength and therefore larger intensity.
3. Infrared. Infrared light has a longer wavelength and a higher frequency. Thus it
has a larger energy.
4. Infrared. Infrared has a larger wavelength and this means it is stronger.
5. Infrared. There are more photons per second. They are more likely to split the
molecule.
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350
Warm Up Question 38
Electrons and neutrons are each fired, with the same speed, through a barrier with two
slits. The particles strike a screen which produces a pattern such as that of Fig 28.14.
This pattern is identical to that produced by light passing through a similar barrier and
the locations of the bright bands are found by using a equation 17.8 (this works for any
kind of wave). For which type of particle are the bright bands spread out more? Explain
your answer.
1. Electrons. Wavelength = h/p = h/mv. Neutrons have larger mass than
electrons, so the wavelength of the neutron must be shorter than that of the
electron. If the wavelength is shorter the spacing should also be shorter for the
neutron, and larger for the electron.
2. Electrons. These have a higher energy and will spread out more.
3. Neutrons. Larger mass means a greater effect at the screen and spread out
more.
4. Neutrons. These have a larger wavelength and so are more spread out.
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351
Warm Up Question 39
The Bohr model and quantum physics predict the possible energies for a hydrogen atom
and these depend on an integer, n. Is the following statement true: ”As n increases, the
energy approaches infinity?” Explain your answer.
1. Not true. As n increases the energy increases to the ionization limit where
E = 0 eV.
2. Not true. As n increases, the energy decreases.
3. True. Clearly as n increases, the energy increases and so it will approach infinity.
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352
Warm Up Question 40
The total angular momentum, L, of the hydrogen atom can, in various circumstances, be
zero. Suppose that L = 0. Does this imply that the energy of the hydrogen atom must
also be zero? Explain your answer.
1. Yes. Since L = n~, it follows that n = 0 so the energy is zero.
2. Yes. If angular momentum is zero but radius is not zero then the speed must be
zero. So the kinetic energy will be zero.
3. No. Its l = 0 therefore making L zero. l has nothing to do with energy.
4. No. When n = 1 then l (orbital quantum number) is equal to zero. This means
the L (angular momentum) is zero. But at n = 1 the energy is not zero.
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353
Question 267
here
1.
2.
3.
4.
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354
Warm Up Question 41
Question
1. Response
2. Response
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355
Title
Question
1. Response
2. Response
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356
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