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Physics 1120 Final Exam (May 4, 2002) 10:30AM - 1 PM
Exam version 0001
SOLUTIONS
Before:
F
1. Two small objects each with a net charge of +Q
initially exert a force of magnitude F on each other.
Then we replace one of those objects with a
different one whose net charge is -3Q, AND we move
them apart, so that the distance between them is twice
what it was before.
What is the magnitude of the force on the -3Q charge now?
A) F
B) 3F
C) 3F/2
D) 3F/4
+Q
+Q
F
After:
+Q
-3Q
E) F/4
2. A hollow metal conducting sphere is electrically neutral (There are no excess charges on it, and none
nearby either). A small amount of negative charge is suddenly placed at one point P on this metal
sphere. If we check on this excess negative charge a few seconds later, what will we find?
A) All of the excess charge remains right around P
B) The excess charge has distributed itself evenly over the outside surface of the sphere.
C) The excess charge has distributed itself evenly over the inside and outside surfaces of the sphere
D) Most of the charge is still at point P, but some will have spread over the sphere
E) There will be no excess charge left
3. You have three charges arranged on 3 corners of a
square, as shown. (Note the signs of the charges!)
QA =+1 C QB =+1 C
A
B
(B is equally distant from A, and from C.)
What is the direction of the electric force on charge B?
A)
B)
Exam 0001 Page 1 of 11
C)
D)
FBC
C
QC =-1 C
FBA
Ftot
E) None of these is correct
4. You have two objects (labelled #1 and #2), with charges +Q and -Q respectively, fixed on the x-axis
at x=-d and x=+d respectively. (Define voltage to be zero off at infinity)
There are no other charges anywhere. At the origin, halfway between the charges, what can you say
about the magnitude of the electric field, and the voltage?
x=0
+Q
#1
A)
B)
C)
D)
E)
d
-Q
x
d
#2
|E| = 0, V = 0
|E| is not zero, V = 0
|E| = 0, V is not 0
|E| is not zero, V is not 0
Not enough information to decide.
For the next three questions: an electron is placed at rest in the center of a three-dimensional region of
space in which there is a uniform electric field. (A uniform field is one whose strength and direction
are the same at all points in the region)
There are no other forces in this problem besides the electric force.
a
c
Points a, b, c, and d are simply names for points in space, there are no
charges at those points!
\
5. When the electron is released from rest in the uniform E field,
what will its subsequent motion be?
E
-e
b
d
A) It will remain at rest in its initial position.
B) It will move at a constant velocity.
C) It will move with a constant acceleration.
D) It will move with a linearly changing acceleration .
E) It will move in a circle with constant speed.
6. Rank the value of electrical potential (i.e. voltage) at the four points (a,b,c, and d)
from highest to lowest. (Assume the electron is not present.)
A) V(a) > V(b) > V(c) = V(d)
B) V(c) = V(d) > V(b) > V(a)
C) V(a) = V(c) > V(b) = V(d)
D) V(a) > V(c) > V(b) > V(d)
E) V(b) = V(d) > V(a) = V(c)
7. Suppose you could put the electron either at point a, or at d, and compare the force it feels.
How does the electric force on an electron at those two positions compare?
A) Force is greater on a charge at point a
B) Force is greater on a charge at point d
C) Force is zero at both places
D) Force is the same at both places, but is NOT zero
E) Force has the same magnitude at both places, but is in different directions.
8. The figure shows a solid conducting metal sphere which is
electrically neutral. The sphere is held fixed in space.
A large positive charge +Q is placed near the sphere as shown.
Exam 0001 Page 2 of 11
P
+Q
What is the direction of the electric field at point P, inside the sphere, halfway between the center and
the edge of the sphere?
(P is just a point in space, there is no charge there)
A) Left
B) Right
C) Up
D) Some other direction, but NOT zero.
E) Zero field
+y
9. Two charges, -Q and +2Q are fixed on the y-axis, a distance “a”
apart, as shown.
Point P is on the +x axis, a distance "x" away.
There is no charge at point P; it’s empty space.
q1= -Q
a
What is the value of the voltage at point P (assume voltage is zero
at infinity)
kQ
A)
x
C)
2kQ
kQ
2 + 2
x
x + a2
2kQ
!
B)
x
kQ
x 2 + a2
2kQ
!
x
kQ
x 2 + a2
D)
x
x + a2
2
E)
q2= +2Q
2kQ
kQ
2 ! 2
x
x + a2
x
P
+x
x
x + a2
2
10. The figure shows 3 circuits with the same voltage battery, V, and identical light bulbs,
all of resistance R.
V
#1
V
#2
R
Rank the bulbs in order of
brightness, from dimmest to
brightest.
V
#5
R
R
#3
#4
R
R
A) #1 = #2 = #3 = #4 = #5 (all the same)
B) (#4= #5), but they are each dimmer than (#1 =#2 = #3)
C) (#1 = #4 = #5), but they are all dimmer than (#2=#3)
D) (#1 = #2 = #3), but they are all dimmer than (#4 = #5 )
E) (#2 = #3 ) , but they are each dimmer than (#1 = #4 = #5)
11. In the circuit shown to the right, a current I1 flows through R1.
At t=0, you break R2 (so R2 goes to infinity). Describe I1 before and after t=0.
A) Before, I1 is downward.
After, I1 is completely unchanged.
B) Before, I1 is downward.
After, I1 is downward, and increased in magnitude.
C) Before, I1 is downward.
After, I1 is downward, and decreased in magnitude.
V1
R1
I3
V2
I1
I2
R2
Exam 0001 Page 3 of 11
D) Before, I1 is zero.
After, I1 is downward.
E) Before, I1 is upward.
After, I1 is downward.
12. You have 2 identical bulbs (#1 and #2) connected in series to a
power supply. They are both glowing equally.
Then you add a resistor R in parallel to bulb #2, exactly as shown
in the figure.
What happens after "R" is connected?
R
#1
V
A) #1 gets brighter than it was before, #2 gets dimmer than
before.
B) #1 gets dimmer than it was before, #2 gets brighter than before.
C) #1 and #2 both get dimmer than they were before.
D) #1 and #2 both get brighter than they were before.
E) #1 and #2 stay just the same as they were.
(Attach this
resistor...)
#2
13. An electron (which has negative charge) initially moves horizontally to the right, towards a screen.
There are no electric fields in the problem (and no gravity or
screen
friction), but there is a magnetic field, B.
The electron moves along the dashed path shown.
In what direction does the B field point?
-e
A) Toward the top of the page (in the plane of the page)
B) Towards the right of the page (in the plane of the page).
C) Into the page.
D) Out of the page.
E) The magnetic field is in the direction of the curved path.
14. Wire 1 has a large current i flowing out of the page, as
shown in the figure.
Wire 2 has the same large current i flowing into the page.
In what direction does the magnetic field point at position P,
midway between them?
A) Up
B) Left
D) Down
C) Right
B??
v0
Point
P
#1
#2
i (out of
page)
i (into
page)
E) B is zero there.
15. Two parallel wires I and II that are near each other carry currents
i and 3i both in the same direction.
3i
i
Compare the forces that the two wires exert on each other.
Exam 0001 Page 4 of 11
I
II
A) Wire I exerts a larger force on wire II than II exerts on I.
B) Wire II exerts a larger force on wire I than wire I exerts on II.
C) The wires exert equal magnitude attractive forces on each other.
D) The wires exert equal magnitude repulsive forces on each other.
E) The wires exert no forces on each other.
16. The figures below represent positively charged particles moving in the same uniform magnetic
field. The B field is shown, dashed: it points from left to right. It is the same in all three figures.
All of the particles have the same charge and the same speed v.
I
II
III
+
+
v
v
+
B
B
B
v
Rank the three situations acording to the magnitude of the force exerted by the B field on the moving
charge, from greatest force to smallest force.
A) I > II > III
B) III > II > I
C) II > I > III
D) III > I > II
E) The force is the same in all three figures.
17. Two identical circular current loops are both perfectly horizontal.
One of them is placed directly above the other.
Parallel currents flow in the direction shown by the arrows.
(Each is CCW as seen from above)
What can you say about the direction of the magnetic field at the point P midway
between the loops?
A) Down
B) Right
D) Out of the page
P
C) Up
E) Zero
18. A circular loop of wire has 10 turns, an area of 0.5 m^2. There is an external magnetic field
perpendicular to the area.
The magnitude of the external B field is changing with time, according to the formula
B(t) = (5 ! 1000 " t) Tesla. (with t in seconds).
What is the magnitude of the induced EMF around the loop at t=1.0 msec?
A) 5 kV
B) 20 V
C) 20 kV
D) 25 V
E) 4 V
19. The four separate figures below involve a tiny light bulb connected to the ends of a loop of copper
wire, and a bar magnet. The plane of the wire loop is perpendicular to the axis shown in all cases.
The motion of the magnet, or the loop, are indicated in the figures.
Exam 0001 Page 5 of 11
v
I)
bulb
S
axis
N
Magnet moves left
bulb
II)
S
N
Magnet stationary
III)
S
axis
loop is
collapsing (shrinking)
bulb rotates around
axis
the axis.
N
Magnet stationary
IV)
S
bulb moves
left
N
axis
v
Magnet stationary
(Note: In figure III, the loop is rotating CCW around the axis, when viewed from the magnet.
The motion is like someone twisting a ring around their finger.)
In which of the above figures will the light bulb be glowing?
A) I, III, and IV only
B) I and IV only
C) I, II, and IV only
D) IV only
E) II only.
20. A conducting loop sits flat on a table. There is a large external magnetic field which initially points
down into the table (perpendicular to the plane of the loop).
Initial B
Final B
Over a period of a few seconds, the external field is smoothly
reversed, so that it ends up pointing up (out of the table).
During those few seconds while the B field is changing from
"down" to "up", you watch the loop from above, looking down
on it. Which way will current flow?
A) Counterclockwise
B) Clockwise
C) No current will flow
D) It starts off clockwise, but as the B field passes through 0 (on its way from "down" to "up"),
the current flips, ending up counter-clockwise.
E) It starts off counterclockwise, but as the B field passes through 0 (on its way from "down" to "up"),
the current flips, ending up clockwise.
21. In the previous problem, the B field ends up pointing up (out of the table, through the loop).
Assume B is now held constant.
As you look from above, down onto the loop, which way will current flow now?
A) No current will flow if the B field is held constant.
B) Counterclockwise
C) Clockwise
D) It alternates, CW to CCW, back and forth with time.
switch
22. A circuit has a 12 V battery, two 4 Ω resistors, and a 2 H
inductor.
BOTH switches have been open, as shown, for a long time.
Exam 0001 Page 6 of 11
a
12 V
R1 =4 !
L
(2 H)
switch
b
R2
(4 !)
At t=0, switch "a" (only) is suddenly closed.
(Switch "b" is left open!) Just afterwards, at t=0+, what is the approximate current through the
inductor?
A) 1.5 A
B) 2 A
C) 3 A
D) 6 A
E) 0 A
23. The previous circuit is left to sit for a long time, with switch "a" CLOSED and switch "b" OPEN.
Then, at time t=1000 sec, switch "b" is suddenly CLOSED too.
Just afterwards, at t=1000+ sec, what is the approximate current through the inductor?
A) 1.5 A
B) 2 A
C) 3 A
D) 6 A
E) 0 A
24. A radio antenna broadcasts a power P0 uniformly in all directions.
I live a distance R from the broadcast station, and I have a dish receiver of radius r.
You live a distance 3 R away from the broadcast station, and you have a dish receiver of radius 3r.
Which statement is correct? (Note: each statement has two parts, one about power, one about flux)
By "flux", I mean intensity, i.e. energy/(area*time)
A) Your dish receives 3 times the power, but the same flux, as mine.
B) Your dish receives 9 times the power, but the same flux, as mine
C) Your dish receives the same power, and the same flux, as mine
D) Your dish receives the same power, but 1/3 the flux, as mine
E) Your dish receives the same power, but 1/9 the flux, as mine
25. You have two solenoids. Number 1 has twice as many windings, is twice as long, and has twice the
diameter, as number 2. What is the ratio of the self inductances, L(1) / L (2)
(Hint: Recall, self inductance L = Φ(total) / I)
A) 1
B) 2
C) 4
D) 8
E) 16
26. If you double the period, T of an electromagnetic wave in vacuum, what happens to the wavelength?
A) wavelength is the same, it is independent of period.
B) wavelength decreases by a factor of 2
C) wavelength decreases by a factor of 4.
D) wavelength increases by a factor of 2.
E) wavelength increases by a factor of 4
The next two problems refer to this situation: a transformer at a power station is designed to step up the
voltage from 120 V (RMS, AC) to 12,000 V (RMS). The voltage oscillates with a frequency of 60 Hz.
27. If the primary (input) side is a coil with 100 turns, how many turns should the secondary (output)
side have?
A) 1 turn
B) 100 turns
Exam 0001 Page 7 of 11
C) 200 turns
D) 10,000 turns
E) 12,000 turns
28. If the station delivers an average power of 100 MW, what is the maximum instantaneous current
flowing out of the secondary side?
A) 8.3 kA
B) 3.1 MA
C) 12 kA
D) 5.9 kA
E) 17 kA
For the next two problems: an electromagnetic plane wave travels in vacuum with an E-field given by
E(x,t) = 10 sin(2x ! 6"108 t) (with E in V/m, x in meters, and t in seconds)
29. What is the wavelength of this wave?
A) 2 m
B) 1 m
C) 10 m
D) 0.1 m
E) 3.14 m
D) 2 m/s
E) 0 m/s
30. The speed of this wave is
A) 6E8 m/s
B) 3E8 m/s
C) 0.3E8 m/s
31. You look at a light source through two polarizers as shown in the side view diagram below.
Polarizer A is oriented in the vertical direction
Unpolarized
(straight up and down) Unpolarized light
Observer
Light source
(intensity I0) comes from the source.
The axis of Polarizer B is oriented 30 degrees from
the horizontal. (Recall, polarizer A is vertical.)
Polarizer B
Polarizer A
Head on view
What is the intensity of the light reaching your eyes?
A) 0, no light reaches the observer.
B) (1/2)I0
300
C) (1/2) I0 * cos(30 deg) = (0.43) I0
60
0
Incident light axis
D) (1/2) I0 * cos 2 (30 deg) = (0.38)I0
E) (1/2) I0 * cos 2 (60 deg) = (0.13)I0
300
Polarizer B
32. In lectures, you have seen a time varying voltage on the oscilloscope screen like this:
1 div
Voltage
The volts/div setting on the 'scope is 10 V/div and the
"3
time/div setting is 5 msec/div ( 5 !10 sec/div)
Which of the following is the best conclusion?
A) frequency = 60 Hz, Vrms = 23 V
B) frequency = 60 Hz, Vrms = 33 V
C) frequency = 40 Hz, Vrms = 23 V
D) frequency = 40 Hz, Vrms = 33 V
E) frequency = 60 Hz, Vrms = 47 V
(Please note that I'm asking for "rms" voltage)
Exam 0001 Page 8 of 11
V=0
1 div
time
33. A variable power supply is connected to the input side of a transformer, and an ammeter which
measures current.
Power
supply
The ammeter reading is shown in the graph below:
Voltmeter
Amps
Ammeter
+
time
Which one of the following graphs could show the time dependence of the voltmeter reading?
Volts
(A)
Volts
(B)
Volts
+
time
time
Volts
(C) is correct
(D)
Volts
time
time
(E)
+
time
Exam 0001 Page 9 of 11