page 1 of 15
Practice Final A
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Signature_____________________________________________________
Student ID #__________________________________________________
Circle TA’s Name:
Circle START TIME of your recitation: 8am 9am 10am 11am Noon 1pm 2pm 3pm 4pm 5pm
Please do not open the exam until you are told to.
Your exam should have 15 pages, numbered 1 thru 15. The last sheet is for scratch paper. This exam consists of
42 questions, weighted equally. Fill in the bubble sheet with a #2 pencil.
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Check each box as you complete the instructions.
Please circle your TA's name and the start time of your recitation section.
Print and bubble in your name on the bubble sheet.
Print and bubble in your 9-digit student Identification Number.
Bubble in your exam version, A or B.
On your bubble sheet, erase mistakes thoroughly, and make no extraneous marks
As you take the exam, show all your work on the exam and circle the correct answers on your exam.
Your circled exam answers and bubbled answers must agree.
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unauthorized assistance on this exam.
Signature______________________________________________
Try to relax. Budget your time. All your neighbors also think this is a long, hard exam.
vers. A
page 2 of 15
Possibly useful information:
e = 16
.  10−19 C ,  o = 8.85  10−12 (SI units) , k = 1/(4o) = 9.0  109 (SI units), o = 4  10-7 (SI units)
I
B-field magnitude at distance r from infinitely long straight wire: B = o
2r
B-field magnitude at center of current loop of radius R: B =
o I
2R
1.
Three point charges are on the x-axis, separated by distance d, as shown. A charge +Q/2 is midway
between a –2Q charge on the left, and a –Q charge on the right. What is the MAGNITUDE of the net
electric force on the –2Q charge on the far left?
+Q/2
−2Q
−Q
d
A)
k Q2
d2
B)
d
k Q2
2 d2
C)
x
2k Q 2
d2
D) zero
E) None of these is correct
.
2. A box of mass m is on a frictionless, horizontal surface. The
box has net positive charge +q. There is a constant, uniform
electric field E at an angle  below the horizontal, as shown.
What is the correct expression for the magnitude of the normal
force on the box from the floor? (Hint: Draw a free-body
diagram)
A) zero
3.
B) mg
C)
qE cos 
m
E
D) mg + qE sin 

g
m, +q
E) None of these
Recall that ˆi, ˆj, and kˆ are the unit vectors along the +x-, +y-, and +z- directions.
ˆ (ˆj  ˆi) ? [k-hat dot (j-hat cross i-hat)?]
What is k
A) zero
vers. A
B) +1
C) −1
D) the vector −k̂
E) None of these.
No
friction
page 3 of 15
4. Two positively charged particles, labeled 1 and 2, with the masses and charges shown in the figure,
are placed a distance apart in empty space as shown and released from rest. Each particle feels only the
electrostatic force due to the other particle (ignore any other forces like gravity). How do the magnitudes
of the initial forces on the two particles compare, and how do the magnitudes of the initial accelerations
compare? F1 is the magnitude of the force on 1 due to 2; F2 is the magnitude of the force on 2 due to 1.
A) F1 > F2, a1 > a2
Particle 1
m, +q
B) F1 < F2, a1 = a2
C) F1 = F2, a1 = a2
Particle 2
2m, +2q
D) F1 = F2, a1 > a2
E) F1 = F2, a1 < a2
5. Two charges, +Q and –Q, a fixed distance apart, form an
electric dipole. A metal cube, with no net charge on it, is
brought to the left of the left charge, as shown in the diagram.
What happens to the magnitudes of the net electric forces on
the two charges when the cube is brought near as shown?
Before:
−Q
+Q
A) The net electric force on each charge remains unchanged.
B) The net electric force on each charge increases.
C) The net electric force on each charge decreases.
After:
D) The net electric force on one of the charges increases and
the net electric force on the other charge decreases.
−Q
+Q
6. A
negative charge –Q is located on the y-axis at position y = h. What is the
correct expression for the y-component Ey of the electric field on the x-axis at
position x = a ?
A)
kQh
(a + h 2 )3/2
2
kQ
C) 2
a + h2
vers. A
B)
kQa
(a + h 2 )3/2
−Q
h
2
−k Q h
D) 2
a + h2
y
Ey = ?
a
E) None of these
x
page 4 of 15
The following three questions refer to this situation. Four point charges
+2Q, +2Q, +Q , and −Q are each located a distance r from the origin as
shown.
+2Q
r
7. The magnitude of the electric field at the origin is..
kQ
A) 2 2 2
r
kQ
B) 10 2
r
D) zero
E) None of these.
C)
r
–Q
kQ
5 2
r
r
+2Q
r
+Q
8. What is the (approximate) direction of the electric field at the origin?
A) upper right
B) upper left
C) lower left
D) lower right
B
A
E) the E-field points along a direction parallel to the x- or y-axes.
C
D
Note: this question is not asking for the exact direction. For instance, if the
E-field direction is anywhere in the first quadrant, so that the E-field makes
any angle with the +x direction greater than 0o and less than 90o , then the answer is: upper right.
9. What is the value of the voltage at the origin?
A) 4
kQ
r
B) 6
kQ
r
C)
5
kQ
r
D) zero
E) None of these.
10. A charge +Q is at a fixed location in space, and a small negative charge –q, starting close to +Q, is
carried farther away at constant speed.by an external agent
−q
+Q
As the –q charge is carried away, what is the sign of the work done by the external agent, and what is
the sign of the change in electrostatic potential energy of this two charge system?
A) Wext < 0, U < 0
B) Wext > 0, U > 0
D) Wext > 0, U < 0
E) Wext = 0, U = 0
vers. A
C) Wext < 0, U > 0
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11. A positive point charge +Q is placed outside a closed cylindrical surface as shown.
The closed
surface consists of the flat end caps (labeled A and C) and the curved side surface (B). What is the sign
of the flux through surface B? Recall that for closed surfaces, the direction of the surface vector is the
r r
direction of the outward normal. ò E ×dA is ..
B
A) positive
B) negative
C) zero
D) not enough information given to decide
A
+Q
+Q
B
C
(side view)
12.
At a particular instant of time, a negatively charged particle (charge –q) is
moving to the right with speed v, in a region where there is a constant, uniform
electric field upward, and a constant, uniform magnetic field into the page, as
shown. What is the direction of the net force on the particle due to the electric
and magnetic fields?
A) up 
B) down 
C) into the page
E
B(in)
v
D) lower right
E) impossible to tell without knowing the relative size of E and vB.
13. A circuit has a light bulb in series with a switch and a battery. The
A
switch is open. What is the magnitude of the voltage difference VAB (where
points A and B are on opposite sides of the switch)?
A) 2V
B) zero
C) V/2
D) V
B
switch
V
E) Impossible to tell from the information given
bulb
vers. A
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14.
A very large (effectively infinite) plastic slab of thickness t has a uniform positive charge density
 (charge per volume). A student wishes to compute the magnitude E of the electric field at a distance d
Q
from the center of the slab (d > t/2). She writes down Gauss’s Law  E  dA = enc and sketches the
o
s
centered, cylindrical Gaussian surface S shown. The cylinder has length 2d and end caps each of area A
=  r2. What is the correct expression for the integral  E  dA in this case?
s

t
area A = r2
r
2d
perspective
view
side view
A) 2 E A
B)  A t
C) 4  r d E
D) 2 d A E
E) None of these
15.
In two different regions of space (labeled I and II), the
electric fields are accurately indicated by the electric field
lines shown. The distance from point a to point b is the same
in both regions. In which region is the average magnitude of
the E-field |E| the largest, and in which region is the magnitude
of the voltage difference Vab the largest?
a
b
a
b
A) |E| largest in region I and Vab largest in region II
B) |E| largest in region II and Vab largest in region I
C) both |E| and Vab largest in region I
D) both |E| and Vab largest in region II
E) impossible to tell from the information given
vers. A
region I
region II
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16. Consider two identical small seeds, each with a permanent dipole moment (each has net charge
zero, with equal positive and negative charges separated, as shown.) One seed sits in a uniform electric
field I, the other sits in field II. The fields are as shown by the field line diagrams. At the instant shown,
what is the direction of the net force on each seed?
Field I
Field II
A) Down  for both fields
B) Up for field I, Fnet = zero for Field II
C) Fnet = zero for both fields
D) Fnet = zero for field I, up for Field II
E) Fnet = zero for field I, down for Field II
17. A battery is attached to 2 identical resistors as shown.
How do the magnitudes of the currents flowing in the wire at
the fours points A, B, C, and D compare?
A
A) IA > IB > IC > ID
B) IA > IB = IC > ID
C
B
V
R
R
C) IA > IB = IC = ID
D
D) IA = IB > IC = ID
E) None of these.
18.
Two particles, labeled 1 and 2, are observed to travel through a constant,
uniform magnetic field along the paths shown. The B-field is everywhere into
the page, and the trajectories of both particles are in the plane of the page.
What can you say about the charges of the two particles?
A) Nothing. The particles’ charges cannot be determined from this information.
B) Both particles are negative.
C) Both particles are positive.
D) Particle 1 is positive and 2 is negative.
E) Particle 1 is negative and 2 is positive.
vers. A
B(in)
1
2
page 8 of 15
19.
Two identical light bulbs, labeled A and B, and a
capacitor are connected to an ideal battery of voltage V, as
shown. Initially, the switch is open and the capacitor is
uncharged. The switch is then closed. A long time after
the switch is closed (long compared to RC for this
circuit), the voltage across Bulb B is..
(Hint: what is the current through the capacitor after a long
time?)
A) zero
B) V
C) 2V
V
switch
Bulb A
C
D) V/2
E) None of these
Bulb B
Vinit = ?
20.
Which one of the following equations is correct, given
I2
the choice of current directions in this circuit?
A) V1 – V2 + I2R2 – I3R3 = 0
B) V2 – I2R2 – I3R3 = 0
R2
V1
I1
R1
C) V1 + I1R1 + I3R3 = 0
D) V1 – V2 + I1R1 – I3R3 = 0
V2
R3
E) V2 – I1R1 + I2R2 = 0
I3
21. An electron and a proton are both accelerated from rest through a potential difference of 1000 V.
How do the final kinetic energies and the final speeds of the two particles compare?
A) KEelectron > KEproton and velectron > vproton
B) KEelectron < KEproton and velectron < vproton
C) KEelectron = KEproton and velectron > vproton
D) KEelectron < KEproton and velectron = vproton
E) None of these
vers. A
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22. A hand-cranked electrical generator is attached at to a resistor of resistance R.
The generator is
turned at a constant rate which causes an AC current to flow in the resistor. Suddenly, the value of the
resistance R decreases. Does the generator get easier or harder to turn?
A) easier
B) harder
C) no change in difficulty
The following two questions refer to the circuit shown which has three identical light bulbs, each with
resistance R.
23. How do the brightness’s of the bulbs compare? (P1 =
power dissipated in bulb 1, etc.)
A) P1 = P2 =P3 (i.e. they are all equally bright)
V
3
2
B) P1 < P2 = P3
C) P1 > P2 = P3
D) P1 > P2 > P3
1
E) None of the above is correct.
24. What is the total equivalent resistance of the three bulbs (each with resistance R); that is, what is the
total resistance which the battery sees?
A) 3R
B) R
C) 0.5 R
D) 1.5 R
E) None of these.
25. A wire with a square cross-section and resistance R1 is cut into four equal length pieces, and a new
resistor R2 is made by pressing the four pieces side by side as shown. What is the ratio
R2
R1
A) 4
vers. A
B) 16
C) 1/4
D) 1/16
E) None of these
R2
?
R1
page 10 of 15
26. An imaginary rectangular loop L, with edge lengths a and b, is in a
b
magnetic field B that is uniform in space and constant in time As shown, the
magnetic field is into the page, perpendicular to the plane of the loop L.
Consider the following two statements:
I. The line integral of B around the loop L is zero,
 B  dl = 0
a
.
B = constant
L
II. The current through the loop L is zero: Ithru = 0.
Loop L
Which of these statements is true?
A) I is true and II is false.
B) II is true and I is false
C) Both are true
D) Both are false.
27. A field line forms a closed loop as shown in the diagram. Is it possible
that this could be a magnetic field line or an electric field line?
A) This could be a magnetic field line, but could not be an electric field line.
B) This could be an electric field line, but could not be a magnetic field line.
C) This could be either a magnetic field line or an electric field line.
D) This could neither a magnetic field line nor an electric field line.
28.
Two separate wires, each carrying a current I, and each
forming a semicircle, are put side-by-side to form a circular
loop in the middle of long straight portions, as shown. What is
the direction of the B-field in the center of the circular loop?
[Hint: Biot-Savart ]
A) out of the page 
B) into the page 
D) right →
E) left 
right, is located above a moving rectangular wire loop. The straight wire
and loop are in the same plane, and the wire loop is moving upward,
toward the straight wire, as shown. The current induced in the
rectangular loop is ..
vers. A
B) counter-clockwise
B=?
I
_
C) No direction, B = 0
29. A long, straight, stationary wire, carrying a steady current I to the
A) clockwise
I
_
C) zero
I
v
page 11 of 15
30.
A solid homogeneous wire of radius R carries a uniform current I,
so the current density is J = I/(R2) . Consider the (imaginary) circular
loop L of radius r within the wire and oriented with its plane
perpendicular to the current flow, as shown. Consider the following two
statements about the value of  B d l :
I
L
r
r 
= o I  2 
II.  B d l =  o J r 2
R
L
L


Which of these statements is true?
I.
2
 B dl
A) Both are true
B) Neither are true
C) I is true and II is false.
D) II is true and I is false.
2R
31. A keyboard button consists of a capacitor with an
adjustable distance d between the plates. Suppose that this
capacitor is charged to a voltage V by hooking it to a
battery. Then the capacitor is disconnected from the battery,
so that it is isolated. The plates are then pushed together (by
pressing on the key). As the plate separation decreases, the
voltage across the capacitor
A) increases
B) decreases
C) remains constant
D) impossible to determine from the information given.
32. In the LR circuit shown, the switch has been closed for a
0.1 H
long time. Then, at t = 0, the switch is opened.
What is the current through the inductor, immediately after the
switch is opened (at t = 0+)?
A) zero
B) 1 A
D) 0.5 A
E) None of these
vers. A
C) 2 A
10 V
switch
10 
10 
page 12 of 15
33. A metal loop is attached to an axle with a
handle as shown. The north pole of a magnet is
placed below the loop and the handle turned so that
the loop rotates at a constant rate. At which of the
two times shown does an induced current flow in the
loop? (At time t1 the loop is vertical, and at t2 the
loop is horizontal.)
A) Current flows at t1 but there is no current at t2.
B) Current flows at t2 but there is no current at t1.
C) Current flows at both t1 and t2.
D) Current flows at neither t1 nor t2.
34. The primary coil of an ideal transformer has 100 turns
and the secondary coil has 300 turns and is connected to a
10 ohm resistor. The power supplied to the primary coil is
30 W. What is the power consumed by the resistor in the
secondary?
A) 30W
B) 10 W
C) 90W
D) 2700 W
E) 3.33 W

35. An electromagnetic plane wave, given by E ( x, y, z) = Eo yˆ sin( kx − t ) , propagates to the right. The
figure represents this wave at a particular instant in time. Four antennas are oriented parallel to the yaxis (labeled 1-4). Which is the best ranking of the time-averaged signals received by each antenna?
(That is, if the antennas were attached to radios, what is the ranking of the loudness of the radios?)
A) 1=2>4>3
vers. A
B) 2=3>4>1
C) 1=2=3=4
D) 1=2>3=4
E) None of these
page 13 of 15
36. Light traveling through a medium with index of refraction n1 is
refracted as it enters a medium with index of refraction n2 as shown.
Based on this figure, what can you infer about the index of refraction
of the two materials?
medium 1
n1
medium 2
n2
A) n1 > n2
B) n1 = n2
C) n1 < n2
D) Not enough information determine the relative size of n1 and n2.
37. The pass axes of three ideal polaroid filters, labeled 1, 2, and 3, are at angles of 0o, 45o, and 90o
relative to the vertical. Initially, the three filters are placed in order 1, 2, 3, between a source of
unpolarized light and an observer. Then, filters 2 and 3 are switched, as shown. What does the observer
report?
Situation I
light source
(unpolarized)
1
2
observer
3
Situation II
light source
(unpolarized) polarizer 1
2
3
A) Some light in Situation I, and no light in situation II.
B) Some light in Situation I, and the same amount of light in situation II.
C) Some light in both Situations I and II, but different amounts.
D) No light in Situation I, and no light in situation II.
E) No light in Situation I, and some light in situation II.
vers. A
observer
page 14 of 15
38. A bright point source and a lens are used to make a perfectly collimated circular beam of light of
constant diameter d. The intensity I of the light is measured at two points in the beam: Point A, a
distance R from the source, and point B, a distance 2R from the source. The ratio of the intensities,
is …
A) 4
B) 2
C) 1/4
D) 4
IB
,
IA
E) 1
2R
R
A
B
d
source
39. A converging lens projects an image of an arrow onto a screen as shown. What happens to the
image of the arrow on the screen when the top half of the lens is covered up?
cover
object
lens
image
A) The top half of the image on the screen disappears; the bottom half is unaffected.
B) The bottom half of the image on the screen disappears; the top half is unaffected.
C) The entire image remains in place on the screen, but it is dimmer.
D) The entire image remains on the screen, but it is shifted down.
E) The entire image remains on the screen but it is shifted up.
40. NASA’s Juno spacecraft is now orbiting the planet Jupiter. Juno radios information back to earth at
a frequency of 8 GHz (8109 Hz). If the spacecraft were to half the frequency of its transmission to
4 GHz, the time required for a radio signal to travel from Jupiter to Earth would
A) increase
B) decrease
C) remain constant
D) not enough information is given to answer the question
vers. A
page 15 of 15
41. Two lenses, labeled 1 and 2, have focal lengths f1 and f2, respectively.
They are positioned a
distance f1+f2 apart, as shown A screen is a distance twice f2 from lens 2. Both lenses have the same
diameter d and a collimated beam of light (a parallel bundle of rays) with the same diameter d enters
lens 1 from the left, as shown. What appears on the screen?
2
1
d
f1
f2
2f2
screen
A) a point of light in sharp focus
B) a disk of light with diameter d
C) a disk of light with diameter greater than d
D) a disk of light with diameter smaller than d, but larger than a sharply-focused point of light.
E) the screen is completely dark because no light reaches it
42. An object is placed to the left of a converging lens at a location further from the lens than the focal
length, as shown in the figures below. The focal points of the lens are labeled F in the figures. Which of
the following choices shows correct ray tracing?
END OF EXAM. HAVE A GREAT BREAK!
vers. A