SP212 Spring 2016
Practice Final Exam
This practice exam and its attached equation sheet are provided so that you can get a feel for the upcoming
final. The practice test was written at the same time as the actual final and so it has the same general theme
and goals even if the problems are different.
In addition to this practice exam, you can also find the 2004 and 2005 exams on the course website. They can
be helpful, but this practice exam looks and feels much more like the upcoming final exam. It was written at
the same time as the actual final and has the same goals and problem types.
About the upcoming final exam:
• What to bring? One calculator and writing utensils. You may not use two calculators.
• With the TI-NSpire, make sure you know your settings, and if you change them make sure you select
Make Default.
• The equation sheet will be provided with your exam. Do not bring your own copy.
• There are 50 questions. The test has one question drawn from each of the 40 days of material on the
syllabus. Each chapter has at least two questions from it. There are five questions that would be relevant
to the labs.
• Most problems report answers to two significant figures, a few use three.
• There is no penalty for guessing.
• Your instructor can not answer questions about the exam or aid in interpretation.
• Write directly on the exam itself and clearly circle your answers. Use extra blank paper whenever needed.
Turn in any extra pages with your exam.
• Many problems are variations on problems you have solved before. Even if a problem looks familiar, make
sure you read the problem statement carefully.
• During the actual exam, You will fill out a Scantron form only after you have completed the entire exam.
Instructions for filling out the Scantron form will appear at the end of the exam after the last problem.
• It is common for students to mismark problems resulting in one question having two responses and a
neighboring question left blank. Review your Scantron form (it is likely that no one else will!) for
mismarks.
• After reviewing for mismarks, review for neatness of entered answers and for the clean up of stray marks.
• The practice exam gives the chapter and section from which the problem was drawn. The actual final will
not.
• This exam uses five copyrighted images from Halliday and Resnick, 10th edition (John Wiley and Sons).
The specific images used were from Chapters 23 (Fig22), 31 (Fig. 19), 32 (Fig. 21), 33 (Fig. 32) and 35
(Fig. 28).
1. Complete the following sentence: An electrical insulator has...
A. the ability to let charge move freely, but does not easily conduct heat.
B. the ability to let charge move freely but says nothing about its ability to easily conduct heat.
C. the ability to easily conduct both electricity and heat.
D. the property that charge cannot move freely.
E. many intrinsic conducting paths inside of it.
Sections Covered: Chapter 21, 1-3
2. Two identical particles are separated by a distance of 0.0010 meter. You measure a repulsive force of
3.0 × 10−14 N between them. What is the charge on each particle?
A. +3.3 × 10−30 C
B. Could be either +3.3 × 10−30 C or −3.3 × 10−30 C
C. −3.3 × 10−30 C
D. +1.8 × 10−15 C
E. Could be either +1.8 × 10−15 C or −1.8 × 10−15 C
Sections Covered: Chapter 21, 1-3
3. As shown in the figure, charge 13.0 µC sits at the origin and charge of -13.0 µC sits at the point
(0, 4.00 m). The net electric field at point P at (3.00 m, 2.00 m) is most nearly:
y(m)
A. 16600 î N/C
−13.0 µC
B. 16600 ĵ N/C
C. (−7500 î + 5890 ĵ) N/C
D. 9970 ĵ N/C
P
E. (+3330 î + 4500 ĵ) N/C
+13.0 µC
Sections Covered: Chapter 22, 1-3
x(m)
4. A thin rod has been bent into a half-circle with a radius of 3.00 meters. It carries a charge density of
+10.0 µC/m. The net electric field at point P (the origin) is most nearly:
y(m)
A. 60000 î N/C
B. −130000 ĵ N/C
+10µC/m
C. 0
D. 30000 ĵ N/C
P
E. −60000 ĵ N/C
x(m)
Sections Covered: Chapter 22, 4-5
5. An electric dipole consists of a positive charge of 5.0 µC located at the point (x, y) = (0, 1.0 cm) and a
negative charge of −5.0 µC located at (x, y) = (0, −1.0 cm). What is the torque on the dipole from the electric
~ = 2.0 × 106 N/C î?
field E
A. 0.2 N·m k̂
B. −0.2 N·m k̂
C. 0.0 N·m k̂
D. 0.4 N·m ĵ
E. −0.4 N·m ĵ
Sections Covered: Chapter 22, 6-7
6. What is the difference between “charging by conduction” and “charging by induction?”
A. Charging by conduction involves physically transferring electrons between the objects through contact while
charging by induction means using the electric field of two objects in proximity to move charge.
B. Charging by induction involves physically transferring electrons between the objects through contact while
charging by conduction means using the electric field of two objects in proximity to move charge.
C. Charging by conduction means using an external source of EMF, like a battery, to place charge on the object
while charging by induction means using a magnetic force to charge the object.
D. Charging by induction means using an external source of EMF, like a battery, to place charge on the object
while charging by conduction means using a magnetic force to charge the object.
E. The only difference is in the types of material used. The location of the object on the Triboelectric Series
determines whether it would charge by conduction or induction.
Sections Covered: ELECTROSTATICS LAB
3
7. The area vector for a flat surface that has the shape of a square...
A. is perpendicular to the surface and has a magnitude equal to the length of one side of the surface.
B. is tangent to the surface and has a magnitude equal to the length of one side of the surface.
C. is tangent to the surface and has a magnitude equal to the length of one side squared.
D. is perpendicular to the surface and has a magnitude equal to the length of one side squared.
E. is tangent to the radial vector directed from the center of the cube created by six of these flat surfaces.
Sections Covered: Chapter 23, 1-2
8. A point particle with charge q is exactly at the center of a Gaussian surface in the form of a cube. The
electric flux through any one face of that cube is:
A. Cannot be determined due to the charge location in the cube.
B.
C.
D.
E.
q
ǫ0
q
4πǫ0
q
4ǫ0
q
6ǫ0
Sections Covered: Chapter 23, 3-6
9. The figure shows, in cross section, three infinitely long solid cylinders, each of length L and uniform charge Q.
Concentric with each cylinder is a cylindrical Gaussian surface, with all three surfaces having the same radius.
Rank the Gaussian surfaces according to the electric field at any point on their surfaces, greatest first.
A. a > b > c
B. c > b > a
C. b > c > a
D. a = b > c
E. a = b = c
Sections Covered: Chapter 23, 3-6
10. The total work required to carry a particle with a charge of 6.95 µC from a 5.00 V equipotential surface to
a 6.00 V equipotential surface and back to the 5.00 V equipotential surface is:
A. 0 J
B. 6.95 µJ
C. -6.95 µJ
D. −1.00 J
E. 1.00 J
Sections Covered: Chapter 24, 1-3
4
11. The potential difference between the ends of a 2.00 meter stick that is parallel to a uniform electric field is
550 V. The magnitude of the electric field is:
A. 1100 N/C
B. 275 N/C
C. 2200 N/C
D. 130 N/C
E. 0 N/C
Sections Covered: ELECTRIC POTENTIAL LAB
~ = Cx4 î where C is a positive constant, then the associated electric potential along
12. If the electric field is E
the x-axis is given by the expression:
A. − Cx
3
3
B. − Cx
5
5
C.
Cx3
3
D. −4Cx3
E. 4Cx3
Sections Covered: Chapter 24, 4-5
13. Which of the following units are the SI units for the electric potential?
A. ampere (A)
B. newton/coulomb (N/C)
C. joule (J)
D. volt (V)
E. gauss (G)
Sections Covered: Chapter 24, 6-8
14. An air-filled parallel-plate capacitor has a capacitance of 1.0 pF. The plate separation is doubled and a
wax dielectric is inserted, completely filling the space between the plates. As a result, the capacitance becomes
2.0 pF. The dielectric constant of the wax is
A. 8.0
B. 4.0
C. 2.0
D. 0.5
E. 0.25
Sections Covered: Chapter 25, 1-3
5
15. A 2 µF and a 1 µF capacitor are connected in series and a potential difference is applied across the combination. The 2 µF has:
2 µF
1 µF
A. half the potential difference of the 1 µF capacitor.
B. none of the other choices are correct.
C. twice the charge of the 1 µF capacitor.
D. twice the potential difference of the 1 µF capacitor.
E. half the charge of the 1 µF capacitor.
Sections Covered: Chapter 25, 4-5
16. Which one of the following statements concerning the conventional direction of current is true?
A. The conventional direction of current is the hypothetical direction of movement of positive charges through
the wires of an electric circuit.
B. The conventional direction of current is the direction of movement of electrons through the wires of an
electric circuit.
C. The conventional direction of current is equal to the electromotive force of the battery in an electric circuit.
D. The conventional direction of current is always a clockwise movement around the circuit.
E. The conventional current is the one that moves in a dc circuit and an unconventional current is one that
moves in an ac circuit.
Sections Covered: Chapter 26, 1-3
17. A resistor to be used near a steam main has a resistance of 100. Ω at 20.0o C. When the temperature is
increased to 25.0o C, the resistance increases to 105. Ω. If the initial temperature is doubled, from 20.0o C to
40.0o C, how much resistance will this object have at the final 40.0o C temperature?
A. 240 Ω
B. 120 Ω
C. 110 Ω
D. 200 Ω
E. 220 Ω
Sections Covered: Chapter 26, 1-3
18. Thermal energy is produced in a resistor at a rate of 100 W when the current is 3.00 A. What is the
resistance?
A. 11.1 Ohms
B. 33.3 Ohms
C. 300 Ohms
D. 900 Ohms
E. 77.3 Ohms
Sections Covered: Chapter 26, 4-5
6
19. A 10.0 Volt battery is providing current to three resistors, each 3.0 Ω, connected in parallel. In total, how
much current does the battery provide?
A. 1.11 Amp
B. 90 Amps
C. 30 Amps
D. 10 Amps
E. 3.33 Amps
Sections Covered: Chapter 27, 1
20. In the illustrated circuit all batteries are ideal. The current through the 20 Ω resistor is:
20.0 V
20.0 Ω
A. 0.71 A to the left
B. 0.71 A to the right
C. 1.07 A to the left
D. 0.99 A to the right
30.0 V
E. 1.07 A to the right
5.00 V
Sections Covered: Chapter 27, 2-3
40.0 Ω
10.0 Ω
21. You have been tasked with procuring a supply of 20 Ω resistors for your command. The contractor says the
resistors meet the specifications, but you feel that they may be mislabelled. You quickly grab some available
meters and arrange an impromptu test, using a battery and one of the provided resistors arranged as shown
in the figure. Your meters tell you that for a 9.00 ± 0.30 V potential the current is 0.50 ± 0.05 A. Using the
method of uncertainties taught in lab calculate the resistance and its uncertainty and make a conclusion about
whether your test shows the resistors are actually 20 Ω resistors.
A. R = 18 ± 3 Ω, The resistors are likely 20 Ω.
B. R = 18 ± 1 Ω, The resistors are likely not 20 Ω.
V
C. R = 18 ± 2 Ω, The resistors are likely 20 Ω.
R
D. R = 18 ± 1 Ω, The resistors are likely 20 Ω.
E. R = 18 ± 3 Ω, The resistors are likely not 20 Ω.
Sections Covered: KIRCHOFF’S LAW LAB
22. A circuit includes a capacitor that charges over time. If the resistance of the circuit is 5.00 Ω, the capacitance
is 0.200 F and the potential charging circuit is 6.00 V, what is the potential across the capacitor after a time of
2 seconds, assuming the capacitor was initially uncharged?
A. 5.19 V
B. 2.00 V
C. 4.00 V
D. 0.81 V
E. 1.19 V
Sections Covered: Chapter 27, 4
7
23. A charged particle is moving in a field measured in millitesla. What is the direction of the force on the
particle due to this field?
A. in the direction of the field
B. in the direction that is perpendicular to both the field and the velocity
C. in the direction opposite to which the particle is moving
D. in the direction of motion
E. in the same plane as the field and the velocity, but not in either of those two directions
Sections Covered: Chapter 28, 1
24. A uniform magnetic field of 0.50 T is directed out of the page. A capacitor with no dielectric is then placed
in the field in order to generate an electric field. The capacitor has a plate area of 4.0 × 10−1 m2 and a plate
separation of 1.6 × 10−3 m. An ion, whose charge is +3.2 × 10−19 C, is projected into the capacitor in the −ĵ
direction with a speed of 4.0 × 105 m/s. If we desire the ion to be completely undeflected as it passes through
the region the potential across the capacitor, Va − Vb should be:
q⊕
A. +320 V
B. -320 V
C. +640 V
A
D. -640 V
B
E. Any value but 0 V would make this happen.
Sections Covered: Chapter 28, 2-3
B = 0.5 T
25. A proton (charge e), traveling perpendicular to a magnetic field, experiences the same force as an alpha
v
particle (charge 2e) which is also traveling perpendicular to the same field. The ratio of their speeds, vproton
is:
alpha
A. 0.5
B. 1.0
C. 2.0
D. 4.0
E. 8.0
Sections Covered: Chapter 28, 4 and 6
8
26. At what orientation angle relative to the magnetic field direction does the torque of a magnetic dipole have
its largest value?
A. 0◦
B. 45◦
C. 90◦
D. 135◦
E. 180◦
Sections Covered: Chapter 28, 7-8
27. How far away from a long, straight wire carrying a current of 4.5 A is the magnetic field 0.32 µT?
A. 8.8 m
B. 1.4 m
C. 2.8 m
D. 17 m
E. 7.5 m
Sections Covered: Chapter 29, 1-2
28. The figure shows the cross section of a long cylindrical conductor of radius a=0.080 meters. The current in
the cylinder is 3.0.0.0.0.0.0.0.0 A and it is uniformly distributed through the cross section. What is the current
enclosed by the Amperian loop of radius r=0.054 m?
A. 410 A
a
B. 2.7 A
r
C. 0.68 A
D. 1.4 A
E. 5.4 A
Sections Covered: Chapter 29, 3
29. A rectangular coil is fed a current of 6.00 A. The dimensions of each rectangular loop in the coil are 0.040
m by 0.080 m. The magnetic moment of the loop is determined to be 12.0 A · m2 . The number of turns in the
loop is most nearly:
A. 50
B. 630
C. 100
D. 7800
E. 26
Sections Covered: Chapter 29, 4-5
9
30. A circular wire loop with an initial radius of 0.088 m undergoes thermal contraction and shrinks to a final
radius of 0.044 m over a time period of 0.25 s. The loop is in a uniform magnetic field of 3.5 T that is directed
out of the page. What was the magnitude and direction of the average induced emf in the loop while it was
shrinking?
A. 0.26 V, clockwise
~
B
B. 0.26 V, counter-clockwise
C. 8.5×10−2 V, clockwise
D. 8.5×10−2 V, counter-clockwise
E. 6.8×10−2 V, clockwise
Sections Covered: Chapter 30, 1
31. The rectangular wire loop shown below lies partly in a region with a uniform magnetic field of 5.6 T directed
into the page. What force is required to pull the loop to the right at a constant speed of 1.2 m/s?
A. 0.81 N
B. 0.10 N
1.2 m/s
C. 6.8×10−2 N
~
B
×
D. 6.5 N
0.12 m
8.0 Ω
E. 8.1×10−2 N
Sections Covered: Chapter 30-2
32. A 0.25 H inductor is placed in a circuit where the current varies with time as i(t) = −2.5t2 + 3.0t, where i
has units of amperes when t has units of seconds. What is the magnitude and direction of the induced emf in
this inductor at time t=0.90 s?
A. 0.17 V, opposite direction from the current
B. 0.19 V, opposite direction from the current
C. 0.19 V, same direction as the current
D. 0.38 V, opposite direction from the current
E. 0.38 V, same direction as the current
Sections Covered: Chapter 30, 4-5
10
33. The figure shows three circuits with identical ideal batteries, identical resistors, and identical inductors.
Rank the circuits according to the current running through the battery a very long time after the switch is
closed, greatest first.
A. 3, 2, 1
B. All three tie
C. 2 and 3 tie, then 1
D. 2, 3, 1
(1)
E. 1, 3, 2
(2)
(3)
Sections Covered: Chapter 30, 6
34. Which of the following phrases best describes the term magnetic flux?
A. The direction of the magnetic field relative to a surface.
B. The amount of magnetic field that passes through a surface.
C. the number of magnetic dipoles moving through a wire.
D. the flow of magnetons in space.
E. (A) and (B) together are correct.
Sections Covered: Chapter 30, 7-8
35. There are two separate situations shown in the picture. In Situation 1, resistor Ra has been connected to
a coil. A magnet is being moved towards the coil with the North pole oriented as shown in the picture. In
Situation 2, resistor Rb has been connected to a loop of wire. The loop is sitting in a magnetic field which is
oriented as shown but decreasing in strength. The directions of the current in each resistor as they are shown
are:
S
N
v
Ra
Rb
Situation 1 – Magnet is approaching coil
Situation 2 – B is decreasing
A. The current in Ra is down, the current in Rb is left.
B. The current in Ra is down, the current in Rb is right.
C. The current in Ra is up, the current in Rb is left.
D. The current in Ra is up, the current in Rb is right.
E. No currents are generated in either case. That would require an applied electric field instead.
Sections Covered: FARADAY LAW LAB
11
36. The figure shows three oscillating LC circuits with identical inductors and capacitors. Rank the circuits
according to the time taken to fully discharge the capacitors during oscillations, greatest first.
A. b > a > c
B. a = b = c
C. c > b > a
D. b > c > a
E. a > b = c
Sections Covered: Chapter 31, 1
37. A charged capacitor and an inductor are connected in series. At time t=0, the current is zero but the
capacitor is fully charged. If T is the period of the resulting oscillations in the LC circuit, the next time after
T=0 where the energy stored in the magnetic field of the inductor will be a maximum is:
A. 3T/2
B. T/4
C. 2T
D. T/2
E. T
Sections Covered: Chapter 31, 1
38. A magnet is placed inside of a small cube which is then placed inside of a larger cube which has 8 times
the volume of the small cube. How does the net magnetic flux through the large cube compare with the net
magnetic flux through the smaller cube.
A. The net magnetic flux through the larger cube is half that through the smaller cube.
B. The net magnetic flux through the larger cube is twice that through the smaller cube.
C. There is no net magnetic flux through either cube.
D. The net magnetic flux through the larger cube is eight times that through the smaller cube.
E. The net magnetic flux through the larger cube is one-eighth that through the smaller cube.
Sections Covered: Chapter 32, 1-3
~ and an induced magnetic field line. In each
39. The figure shows, in two situations, an electric field vector E
~ increasing, decreasing or static?
of the two situations, (a) and (b), is the magnitude of E
A. (a) is decreasing, (b) is decreasing
B. (a) is decreasing, (b) is increasing
C. (a) is increasing, (b) is decreasing
D. (a) is increasing, (b) is increasing
E. (a) is static, (b) is static
Sections Covered: Chapter 32, 1-3
12
40. A transmitter for a Navy search radar consists of an LC circuit containing an inductance of 3.1 pH and a
capacitance of 23 pF. What is the wavelength of the electromagetic wave created by the radar?
A. 220 cm
B. 1.6 cm
C. 35 cm
D. 29 mm
E. 65 mm
Sections Covered: Chapter 33, 1-3
41. The diagram shows the passage of a ray of light from air into an unknown substance X. The index of
refraction for substance X must be:
A. 0.53
B. 3.0
Air
40◦
C. 1.9
50◦
D. 0.82
E. 1.2
70◦
Substance X
20◦
Sections Covered: Chapter 33, 4-5
42. The figure shows four long horizontal layers A-D of different materials, with air above and below them. The
index of refraction of each material is given. Rays of light are sent into the left end of each layer as shown. In
which layer would there be a possibility of totally trapping the light in that layer so that, after many reflections,
all of the light reaches the right end of the layer?
A. A
B. B
C. C
D. D
E. None of the layers will allow the light to reach the right end.
Sections Covered: Chapter 33, 6-7
13
43. A concave mirror forms a real image which is half the size of the object. If the image is 20 cm from the
mirror, the radius of curvature of the mirror must be about:
A. 20 cm
B. 27 cm
C. 40 cm
D. 13 cm
E. 10 cm
Sections Covered: Chapter 34, 1-2
44. In a cinema, a picture 2.0 cm wide on the film is projected to an image 1.3 meters wide on a screen which
is 24 meters away. The focal length of the lens is about:
A. 24 cm
B. 12 cm
C. 36 cm
D. 4.8 cm
E. 2.4 cm
Sections Covered: Chapter 34, 3-4
45. An object is 20 cm to the left of a lens with focal length +10 cm. A second lens, of focal length +15 cm, is
50 cm to the right of the first lens. The distance between the original object and the final image is:
A. 20 cm
B. 100 cm
C. 40 cm
D. 130 cm
E. 60 cm
Sections Covered: THIN LENSES LAB
46. In a Young’s double slit experiement to measure the wavelength of a monochromatic light source, we found
that the fringes are too close together to easily count or measure. If our goal is to spread out the fringe pattern
on the screen, we could:
A. Do something different, because nothing on this list works.
B. Double the slit separation.
C. Halve the width of each slit.
D. Double the width of each slit.
E. halve the slit separation.
Sections Covered: Chapter 35, 1-2
14
47. The figure shows four situations in which light reflects perpendicularly from a thin film of thickness L
sandwiched between much thickermaterials.
The indexes of refraction are given for each layer. In which
1 λ
situations does the equation 2L = m +
, m = 0, 1, 2, ... correspond to the reflections yielding maxima
2 n2
(that is, a bright film for some wavelength of light)?
A. a
B. b
C. c and d
D. d
E. a and b
Sections Covered: Chapter 35, 4-5
48. A soap film is illuminated by white light arriving normal to its surface. The index of the refraction of the
soap film is 1.33. We find that wavelengths of both 479 nm and 798 nm (and no wavelengths between them)
are enhanced in the reflected beam. The thickness of the film is:
A. 600 nm
B. 450 nm
C. 479 nm
D. 360 nm
E. 240 nm
Sections Covered: Chapter 35, 4-5
49. Light of wavelength 520 nm is incident on a diffraction grating with a slit spacing of 2.20 µm, what is the
angle from the axis for the third order maximum?
A. 13.7◦
B. 45.2◦
C. 28.2◦
D. 23.6◦
E. 17.4◦
Sections Covered: Chapter 36, 1,3
50. How many lines/cm must a diffraction grading have in order to produce the first order maximum for 720 nm
at 25◦ ?
A. 11,800 lines/cm
B. 5,900 lines/cm
C. 3,400 lines/cm
D. 1,700 lines/cm
E. 23,600 lines/cm
Sections Covered: Chapter 36, 5
15