Name_____________________________________
Alpha
____________
Instructor_________________________________
Section
___________
USNA Physics Department
SP212 Final Exam
Version A
6 May 2006 0755 – 1055
Instructions and information:
1. Do not open this booklet until you are told to do so.
2. Please fill in the top of this sheet now.
3. You may use your calculator, instructor-supplied
scratch paper, and one 8.5  11-inch equation sheet
to help you work the exam. You may not use any
other test aids.
4. Your instructor may not answer any questions about
the exam or assist you in interpreting any questions
on the exam.
5. You may write in this exam booklet.
6. While working the exam, please record each of your
answers in the booklet by circling the letter that
corresponds to the best response.
7. There is no penalty for guessing.
8. After finishing the exam or at 1050 (whichever is
first), please obtain a SCANTRON answer form
from your instructor. Instructions for filling out the
answer form are found at the end of the exam. Fill
out the answer form and turn it in along with this
test booklet, your equation sheet and any scratch paper that you may have used by 1055.
9. All of the materials that you turn in represent your work on the exam and all of them are
subject to evaluation.
Some constants and prefixes:
12
2
2
0  8.85  10 C /N  m
e  1.60  10 19 C
p = pico =Ź1012
1
ke 
 8.99  10 9 N  m 2 /C2
4 0

me  9.11  10 31 kg
n = nano = 109
 = micro = 106
0  4  10 7 N/A 2
m = milli = 103
c  3.00  10 8 m/s
k = kilo = 103
Good Luck!
SP212 Final Exam
Version A
6 May 2006
1. The sphere on the right has three times the charge of the one on the left. The diagram that
best represents the magnitudes and directions of the electric forces on the two spheres is:
B.
A.
C.
E.
D.
2. Three point charges are arranged in a line as shown. If Q  80 nC and a  4.0 m , then the
magnitude of the electric field at point P is closest to:
A. 68 N/C
B. 135 N/C
C. 19 N/C
D. 45 N/C
E. 0
3. A uniformly charged insulating rod is bent into a semicircle with
radius r  10 cm as shown. If the rod carries a total charge
Q  1.5 C , then the magnitude of the electric field at point O is
closest to:
A. 1.3  10 6 N/C
B. 8.6  10 5 N/C
C. 1.3  10 7 N/C
D. 4.6  10 6 N/C
E. 5.7  10 7 N/C
SP212 Final Exam
Version A page 2
6 May 2006
4. A small object of mass m  0.025 kg has an electric charge q  1.3  10 5 C . When the
object is placed in an electric field near the earth’s surface, it hovers, without moving. If the
acceleration due to gravity is g  9.8 m/s2 , then the magnitude and direction of the electric field
are most nearly:
A. 1.4  10 4 N/C, upward
B. 1.9  10 4 N/C, upward
C. 1.4  10 4 N/C, downward
D. 1.9  10 4 N/C, downward
E. 2.5  10 4 N/C, downward
5. The dashed circle represents the cross section of a closed spherical Gaussian surface. There
are 7.0 C and 4.0 C charges inside the Gaussian surface and 2.0 C and 5.0 C outside the
surface. The net electric flux through the Gaussian surface is closest to:
A.  7.9  1011 V  m
B. 0
C. 7.9 1011 V  m
D.  4.5  1011 V  m
E. 3.4  1011 V  m
6. A cube that is 0.20 m on a side is oriented with its edges along
the axes of a Cartesian coordinate system. The cube is in an

electric field E  1.0 î - 2.0 ĵ  3.0 k̂ N/C . The electric flux

through the square surface at the top of the cube is closest to:


A. 0
B. 0.05 N  m 2 /C
C. 0.12 N  m 2 /C
D. 0.60 N  m 2 /C
E. 1.01 N  m 2 /C
SP212 Final Exam
Version A page 3
6 May 2006
7. A charge q is placed on a conducting sphere of radius r1 . This sphere is
then connected to an uncharged conducting sphere of smaller radius r2 by a
long conducting wire. After all charge motion has ceased, so that the spheres
are in electrostatic equilibrium, which of the following statements are true?
A. The electric fields at the surfaces of the two spheres are equal
B. Both spheres have an equal amount of charge
C. Both spheres are at the same electric potential
D. Both A. and B. above
E. Both B. and C. above
8. The electric field in a certain region of space is given by

E  3.0x î  2.0 ĵ N/C , where x is in meters. Points A and B

are on the x-axis at xA  2.0 m and xB  5.0 m , respectively.
The potential difference V  VB  VA is closest to:


A. 9.0 V
B. 6.0 V
C. 15 V
D. 32 V
E. 28 V
9. Three capacitors are connected together as shown.
The equivalent capacitance between points a and b for
this combination of capacitors is closest to:
6.0 F
a
A. 9.5 F
b
8.0 F
B. 16 F
2.0 F
C. 8.0 F
D. 4.0 F
E. 12 F
SP212 Final Exam
Version A page 4
6 May 2006
10. A parallel-plate capacitor has two square metal plates. The sides of each
plate are 3.0 cm long and the plates are separated by 5.0 mm . The space
between the plates is filled with Teflon, which has a dielectric constant   2.1.
The capacitance of this capacitor is closest to:
A. 1.6 pF
B. 33 pF
C. 14 pF
D. 2.1 pF
E. 3.3 pF
11. The resistance of a certain light bulb is 0.93  when the bulb is not glowing because its
filament is at room temperature. Its resistance is 9.8  when it is glowing because its filament
is hot. The filament is made of tungsten, which has a temperature coefficient of resistivity (  )
equal to 0.0045/ÞC . If room temperature is 20ÞC , then the temperature of the filament when it is
glowing is closest to:
A. 1900ÞC
B. 2400ÞC
C. 220ÞC
D. 2100ÞC
E. 4200ÞC
12. Two solid cylinders are made of nichrome. Cylinder A has radius r and length  . Cylinder
B has radius 2r and length 2 l . The ratio of the resistance of cylinder B to that of cylinder A is:
A. RB R A = 4
B. RB R A = 2
C. RB R A = 1
D. RB R A = 1/2
E. RB R A = 1/4
SP212 Final Exam
Version A page 5
6 May 2006
13. An R  5.60  load resistor is connected to a battery with
internal resistance r  0.250  , as shown. (The shaded
rectangle in the sketch represents the battery.) The terminal
voltage of the battery is V  Vb  Va  8.30 V . The emf E of
the battery is closest to:
A. 1.42 V
B. 8.67 V
C. 186 V
D. 8.30 V
E. 7.92 V
14. Three 162- resistors are connected as shown. The maximum power that can be delivered
to any resistor without melting it is
c  11.5 W . The maximum voltage
a
b
V  Vb  Va that can be applied across
points a and b without melting any of the
resistors is closest to:
A. 129 V
B. 64.7 V
C. 0.266 V
D. 43.2 V
E. 30.5 V
15. In the circuit shown, the current through the 5.00- resistor is
2.32 A directed from left to right. The current through the 7.00-
resistor is closest to:
7.00  15.0 V
A. 1.83 A
B. 5.14 A
5.00 
C. 2.32 A
2.00 
D. 1.07 A

E. 0.486 A
SP212 Final Exam
Version A page 6
6 May 2006
16. An initially charged, 2.53-nF capacitor is discharged by connecting a 156- resistor across
its terminals. Once the resistor is connected across the terminals of the capacitor, the time it
takes for the charge on the capacitor to reach one-fifth of its initial value is closest to:
A. 245 ns
B. 1270 ns
C. 635 ns
D. 316 ns
E. 568 ns
17. A proton moves between the poles of a permanent magnet as shown. When the proton’s
velocity is directed toward the bottom of the page, the magnetic force on the proton is directed:
A. out of the page
B. into the page
C. toward the top of the page
D. toward the left side of the page
E. toward the right side of the page
18. A 0.250-m long wire carrying an 8.75-A current is placed in a uniform magnetic field. If
the maximum magnetic force on the wire is 1.18 N , then the strength of the magnetic field is
closest to:
A. 1.85 T
B. 0.539 T
C. 0
D. 3.37  10 2 T
E. 41.3 T
SP212 Final Exam
Version A page 7
6 May 2006
19. A one-turn square loop, 1.25 m on a side, carries a 37.0-A
current as shown. The loop is hinged along the y-axis and is
oriented so that its plane makes a 30.0Þangle with respect to a

uniform magnetic field B  0.415 î T . The torque on the loop
around the hinge line is closest to:
A. 0
B. 20.8öj N  m
C. 20.8öj N  m
D. 12.0öi N  m
E. 12.0öi N  m
20. Two long straight parallel wires are perpendicular to the plane of the page as shown. Wire 1
carries a 6.5-A current into the page. The current that Wire 2 must carry to make the total
magnetic field at point P equal to zero is closest to:
A. 6.5 A, out of the page
B. 4.3 A, out of the page
C. 4.3 A, into the page
D. 2.2 A, into the page
E. 2.2 A, out of the page
21. Four long, straight conductors carry currents into or out of the page as indicated. The
v r
magnitude of —
B
 ds around the dashed-line path is closest to:

A. 2.0  10 5 T  m
B. 3.1  10 5 T  m
C. 3.8  10 6 T  m
D. 1.5  10 5 T  m
E. 9.7  10 6 T  m
SP212 Final Exam
Version A page 8
6 May 2006
22. A one-turn rectangular loop of wire with the dimensions shown is located so that part is
inside a region of uniform magnetic field B  0.555 T directed into the page, and part is outside
the field. The total resistance of the loop is R  0.812  . The loop moves to the right at a
constant speed v  3.23 m/s . The induced current in the loop is closest to:
A. 2.02 A
B. 0.947 A
C. 0.769 A
D. 1.64 A
E. 0
23. Two circular loops of wire lie on either side of a long straight wire. The current in the
straight wire is downward and increasing. The directions of the induced currents in the circular
loops are best described as:
A. clockwise in both
B. counterclockwise in both
C. clockwise in L and counterclockwise in R
D. counterclockwise in L and clockwise in R
E. no current in either loop
24. A long solenoid has a radius of 6.12  10 2 m . When a current is passed through its
windings, a uniform magnetic field is produced inside it, directed parallel to its axis. By
decreasing the current, the strength of the magnetic field inside the solenoid is made to decrease
at a rate of 6.50  10 3 T/s . The magnitude of the induced electric field at a distance of
8.12  10 2 m from the axis of the solenoid is closest to:
A. 7.50  10 5 V/m
B. 9.94  10 2 V/m
C. 3.75  10 5 V/m
D. 1.50  10 4 V/m
E. 3.25 V/m
SP212 Final Exam
Version A page 9
6 May 2006
25. An air-core solenoid with 300 turns is 0.25 m long and has a cross-sectional area of
4.00  10 4 m 2 . If a 15.0-mV self-induced emf exists at some instant across the solenoid, then
the time rate of change of the current in the solenoid at that instant is closest to:
A. 8300 A/s
B. 830 A/s
C. 83 A/s
D. 38 A/s
E. 450 A/s
26. A 15-H inductor and a 30- resistor are connected in
series with a 100-V battery as shown. At t  0 , the switch S
is closed, after having been open for a long time. The
magnitudes of the potential differences across the resistor and
inductor at t  0.80 s are closest to:
A. VR  20 V; VL  80 V
B. VR  33V; VL  66 V
C. VR  80 V; VL  80 V
D. VR  80 V; VL  20 V
E. VR  27 V; VL  63V
27. The switch in the circuit shown has been connected
to point a for a long time. At t  0 it is moved to point b.
The energy in the inductor at t  4.00 ms is closest to:
A. 4.9  10 7 J
B. 4.1  10 6 J
C. 3.5  10 6 J
D. 7.2  10 5 J
E. 1.2  10 5 J
SP212 Final Exam
Version A page 10
6 May 2006
28. A 10-kW radio station radiates spherical electromagnetic waves. The maximum value
(amplitude) of the wave’s oscillating electric field at a distance of 5.0 km from the station is
closest to:
A. 3.6 V/m
B. 0.16 V/m
C. 0.56 V/m
D. 1.6 V/m
E. 16 V/m
29. The intensity of sunlight in space, just outside the Earth’s atmosphere, is 1.40  103 W/m 2 .
A certain satellite has solar panels measuring 35.0 m  128 m that absorb all of the sunlight
striking them. The solar radiation pressure on each panel, when its surface is perpendicular to
the sun’s rays, is closest to:
A. 4.67  10 6 N/m 2
B. 9.34  10 6 N/m 2
C. 2.34  10 6 N/m 2
D. 2.09  10 2 N/m 2
E. 4.18  10 2 N/m 2
30. A 0.20-A current is charging a capacitor that has circular plates 0.10 m in radius. If the
plate separation is 4.0  103 m , then the magnetic field between the plates and 0.050 m from
the center has a magnitude that is closest to:
A. 2.0  10 7 T
B. 6.6  10 8 T
C. 6.0  10 7 T
D. 3.0  10 7 T
E. 6.0  10 6 T
SP212 Final Exam
Version A page 11
6 May 2006
31. A beam of light traveling in air strikes the surface of a
solution of corn syrup in water at an angle of 30ū to the vertical.
If the beam is refracted at an angle of 19ū to the vertical, then the
speed of the light in the corn syrup solution is closest to:
A. 1.5  10 8 m/s
B. 1.7  10 8 m/s
C. 2.0  10 8 m/s
D. 2.3  10 8 m/s
E. 2.6  10 8 m/s
32. A flat piece of glass (with index of refraction 1.50 ) has a layer of ethanol (with index of
refraction 1.36 ) floating on top of it. Light traveling in the glass strikes the glass-ethanol
surface. The critical angle for total internal reflection in the glass
is closest to:
A. 65ū
B. 59ū
C. 47ū
D. 55ū
E. 39ū
33. The figure shows an overhead view of two
people looking at a stone that is in front of a plane
mirror. Observer 1 sees the image of the stone at
point C. Observer 2 sees the image of the stone
at:
A. Point A.
B. Point B.
C. Point C.
D. Point D.
E. Point E.
SP212 Final Exam
Version A page 12
6 May 2006
34. An object is placed 0.800 m in front of a convex mirror with a 2.00-m radius of curvature.
The resulting image is:
A. Real, upright, and on the same side of the mirror as the object.
B. Virtual, inverted, and on the opposite side of the mirror as the object.
C. Real, inverted, and on the same side of the mirror as the object.
D. Virtual, inverted, and on the same side of the mirror as the object.
E. Virtual, upright, and on the opposite side of the mirror as the object.
35. An object located 32.0 cm in front of a thin lens forms an image on a screen located
8.00 cm behind the lens as shown. (The figure is not to
scale.) The focal length of the lens is closest to:
A. 6.40 cm
B. 20.0 cm
C. 10.7 cm
D. 40.0 cm
E. 24.0 cm
36. A Young’s two-slit experiment is performed with monochromatic
light. The separation between the two slits is 0.500 mm and the
interference pattern on a screen located 3.30 m away has its first
minimum at 1.70 mm from the center of the pattern. The wavelength
of the light is closest to:
A. 515 nm
B. 1030 nm
C. 258 nm
D. 633 nm
E. 532 nm
SP212 Final Exam
Version A page 13
6 May 2006
37. A thin layer of transparent Magnesium Fluoride (MgF2) is to be
applied to a glass camera lens so that reflection of 500-nm light is
eliminated. If the index of refraction of the MgF2 layer is 1.38 and
the index of refraction of the glass is 1.52, then the minimum
thickness of MgF2 that will accomplish this is closest to:
A. 125 nm
B. 82.2 nm
C. 45.3 nm
D. 181 nm
E. 90.6 nm
38. The Alvan Clark telescope in the USNA Class of 1941 observatory has an objective lens that
is 7.75 inches (19.7 cm) in diameter. The lens is a circular aperture that diffracts the light
passing through it. When observing two stars in light of wavelength 550 nm , the smallest
angular distance between the stars that can be resolved with this lens is closest to:
A. 3.41  10 6 rad
B. 2.78  10 6 rad
C. 3.58  10 6 rad
D. 1.71  10 6 rad
E. 8.67  10 6 rad
39. A laser produces unpolarized light with an intensity of 5.0 W/cm 2 . The light passes through
three sheets of Polaroid film as shown. The transmission axis of the second Polaroid makes a
30Þ angle with that of the first, and the axis of the third makes a 60Þ angle with that of the
second (and 90Þ angle with that of the first). The intensity of the light that emerges from the
third Polaroid is closest to:
A. 0
B. 1.4 W/cm 2
C. 1.1 W/cm 2
D. 0.16 W/cm 2
E. 0.47 W/cm 2
SP212 Final Exam
Version A page 14
6 May 2006
40. Light from a gas discharge lamp passes through the grating
of a spectroscope. The grating has 527 lines/mm . A bright
spectral line is observed in second order ( m  2 ) at an angle of
32.7ū with respect to the incident light. The wavelength of this
spectral line is closest to:
A. 1025 nm
B. 513 nm
C. 683 nm
D. 633 nm
E. 532 nm
Instructions for filling out the SCANTRON answer form
1. Please do not make any stray marks on the answer form.
2. Please make sure that your name, alpha code, section and test version are
entered in the appropriate spaces and that the corresponding bubbles are filled
in. Please be sure that your instructor’s name is in the appropriate space at the
bottom of the form.
3. Please make clean, dark marks that completely fill the spaces. If you must
erase, erase thoroughly so that there are no shadows or smudges. If you can’t
do this, then please get a new form from your instructor and start over.
Have a great summer!
SP212 Final Exam
Version A page 15
6 May 2006