Download PH2200 Exam I Spring 2004

PH2200 Practice Exam I
Summer 2004
INSTRUCTIONS
1. Write your name and student identification number on the answer sheet.
2. This a ninety minute exam.
3. Please cover your answer sheet at all times.
4. This is a closed book exam. You may use the PH2200 formula sheet that is included with the exam.
5. Equations may not be stored in calculators, nor may calculators be exchanged.
6. Record your answers in the form A, B, C, etc, on the answer sheet.
7. This exam consists of 10 concept questions worth five points each and five problems having a total of 20 parts.
The problem parts are equally weighted: each is worth five points. The total number of points on the exam is 150.
8. If you have any questions during the exam, please raise your hand and wait for assistance.
9. Turn-in only your answer sheet at the end of the exam.
PH2200 Practice Exam I
Summer 2004
Concept Questions: Each question has a single correct answer and is worth five points.
1. Only one of three identical conducting balls carries a net charge q. One of the uncharged balls can become charged by
touching it to the charged ball and then separating the two. This process of touching one ball to another and then
separating the two balls can be repeated over and over again, with the result that the three balls can take on a variety of
charges. Which one of the following charge distributions could not possibly be achieved in this fashion?
(A)
(B)
(C)
(D)
(E)
1/2, 1/2, 0 (one ball has 1/2 the charge, the second ball has 1/2 the charge, and the third ball has no charge)
1/2, 1/4, 1/4
3/8, 3/8, 1/8
3/8, 5/16, 5/16
11/32, 11/32, 5/16
2. Each of the pictures to the right shows a pair of small
electrically charged spheres. The sign and the magnitude
of the charge on each sphere may be the same or different.
The arrows represent the force on each sphere due to the
other sphere in that pair. Taking both the direction and
the length of the arrows into account, which pictures
are impossible?
(A) Picture I, only (B) Pictures I and II, only
(E) Pictures I, II, and III
I
II
III
(C) Pictures II and III, only
(D) Picture III, only
3. Shown in the figure to the right is the parabolic trajectory of a proton.
Assuming the electric force is the only force acting on the proton, which
electric field shown below is responsible for the motion of the proton?
parabola
+ proton
(A)
(B)
(C)
(D)
(E)
4. The spark created by a spark plug that ignites the gasoline in the engine in your car, boat or lawn mower results
from the
(A)
(B)
(C)
(D)
(E)
permittivity leakage
dielectric breakdown
flux concentration
potential instability
Van de Graaf oscillation
of the gas in the spark gap.
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PH2200 Practice Exam I
Summer 2004
The following information applies to questions 5 and 6.
In each arrangement shown below, three fixed electric charges and a point labeled P are identified. All charges are the
same size, but they can be positive or negative as indicated. The charges and point P all lie on a straight line. The
distances between adjacent items, either between two charges or between a charge and point P, are all the same. There
are no other charges in this region.
(A)
+
+
+
P
(B)
+
+
P
+
(C)
+
+
P
-
(D)
+
-
P
+
+
+
-
P
(E)
5. For which arrangement is the magnitude of the electric field greatest at point P?
6. For which arrangement is the magnitude of the electric potential greatest at point P, assuming the electric potential is
zero infinitely far from the charges?
7. As shown in the figure to the right, charges -Q and
+Q are uniformly distributed over adjacent rods of
equal length. Which vector most closely represents the
direction of the electric field at point P, located
along the perpendicular bisector of the rods?
B
A
P
C
D
(A)
(B)
(C)
(D)
(E)
A
B
C
D
none of the above - there is no electric field at P.
Q
8. A spherical balloon contains a positive charge at its center. As the balloon is
inflated to a greater volume while the charge remains at the center, does the
electric flux through the surface of the balloon increase, decrease, or remain
the same? What about the magnitude of the electric field on the surface
of the balloon?
(A)
(B)
(C)
(D)
(E)
(F)
Both the flux and field decrease.
The flux remains the same and the field decreases.
The flux decreases and the field remains the same.
Both the flux and field remain the same.
Both the flux and field increase.
The flux remains the same and the field increases.
Q
expanding
balloon
Q
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PH2200 Practice Exam I
Summer 2004
The following information applies to questions 9 and 10.
As shown in the figure to the right, a cone with base radius
R and height h is located in a horizontal uniform electric
field directed to the right and having magnitude E. There
are no electric charges in the region of space shown in the figure,
and the symmetry axis of the cone is parallel to the electric field.
As shown in the figure, the closed surface of the cone consists
of two surfaces, the circular base and the pointed cap.
pointed cap
R
circular
base
9. What is the flux of the electric field through the closed surface of the cone?
(A) 0
(B)  R 2 E
(C) 4 R 2 E
(D) 12 RhE
(E)  R  R 2  h2 
1/ 2
E
10. What is the flux of the electric field through the pointed cap of the cone?
(A) 0
(B)  R 2 E
(C) 4 R 2 E
(D) 12 RhE

(E)  R R 2  h2

1/ 2
E
4
h
E
PH2200 Practice Exam I
Summer 2004
Problems: Each part of each problem is worth five points.
y
1. Two point charges are arranged as shown in the figure
to the right.
(1-1) How many electrons are required to form a charge
of 6.00 109 C ?
(A)
(B)
(C)
(D)
(E)
P
6.00 109 C
0.300 m
1.29  1010
2.97 1010
3.75 1010
4.02 1010
4.98 1010
x = 0.400 m
y = 0.300 m
0.500 m
0.400 m
O
4.00 109 C
x
(1-2) What is the magnitude of the electric force exerted on one charge by the other?
(A)
(B)
(C)
(D)
(E)
8.00 107 N
8.17 107 N
8.30 107 N
8.42 107 N
8.63 107 N
(1-3) What is the magnitude of the electric field at point O, the origin of the coordinate system?
(A)
(B)
(C)
(D)
(E)
4.25 102 N/C
5.20 102 N/C
5.60 102 N/C
6.40 102 N/C
7.50 102 N/C
(1-4) What is the potential energy of the pair of point charges?
(A)
(B)
(C)
(D)
(E)
1.31107 J
2.31107 J
4.31107 J
5.31107 J
7.31107 J
(1-5) Suppose a third point charge is placed at point O, the origin of the coordinate system. If the electric potential
at point P equals zero, what is the charge of the point at the origin? Point P is located at x  0.400 m,
y = 0.300 m.
(A)
(B)
(C)
(D)
(E)
0.833 109 C
2.13 109 C
4.63 109 C
1.97 109 C
3.04 109 C
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PH2200 Practice Exam I
Summer 2004
2. A solid conducting sphere of radius 0.100 m bears a net charge
of Q1,net  5.50  106 C . Concentric with the sphere is a conducting
spherical shell having an inner radius of 0.400 m and an outer
radius of 0.500 m. The spherical shell bears a net charge of
Q2,net  7.50 106 C . A second conducting spherical shell
bearing an unknown charge surrounds the conductors previously
described and is concentric with them.
Q1,net

P1
(2-1) If point P1 is 0.0500 m from the center of the solid
conducting sphere, what is the magnitude of the electric
field at point P1 ?
(A)
(B)
(C)
(D)
(E)

P2
Q2,net
0
4.09 104 N/C
5.58 104 N/C
8.82 104 N/C
1.20 105 N/C
(2-2) If point P2 is 0.250 m from the center of the solid conducting sphere, what is the magnitude of the electric
field at point P2 ?
(A)
(B)
(C)
(D)
(E)
1.47 105
3.35 105
5.63 105
7.91105
9.37 105
N/C
N/C
N/C
N/C
N/C
(2-3) What is the surface charge density on the outer surface of the middle conductor, i.e., what is the surface
charge density on the sphere of radius 0.500 m?
(A)
(B)
(C)
(D)
(E)
3.26 107
2.24 107
1.99 107
4.45 107
6.37 107
C/m2
C/m2
C/m2
C/m2
C/m2
(2-4) Point P3 is an arbitrary point completely outside the solid conducting sphere as well both spherical shells.
If the electric field vanishes at point P3 , what is the net charge on the second (outermost) conducting spherical
shell?
(A)
(B)
(C)
(D)
(E)
1.50 106 C
2.00 106 C
6.50 106 C
9.00 106 C
13.0 106 C
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
P3
PH2200 Practice Exam I
Summer 2004
Problem 2 continued
(2-5) If the net charge on the second (outermost) conducting shell were doubled while Q1,net and Q2,net remain constant,
the magnitude of the electric field at point P2
(A)
(B)
(C)
(D)
(E)
doubles.
increases, but doesn't double.
is halved.
decreases, but isn't halved.
remains the same.
3. A continuous line of charge lies along the x-axis, extending from x   d to positive infinity. The line carries a
 d2
non-uniform linear charge density given by    o 2 where o is a positive constant.
x
y

x
d
(3-1) In terms of d, o and any necessary physical constants, find the magnitude of the electric field at the origin.
(A) o d 2 / 4 o
(B) o d / 4 o
(C) o /12 o d
(D) o / 2 o d 2
(E) o / 4 o d 4
(3-2) Which of the following expressions represents the total charge on the line extending from x   d to positive
infinity?
(B)
(C)
2
2
o
2
2
o
2

d x dx
 dx
d
d x
(D) o d 2
(E)
 dx
d x
 dx
d
0 x
 dx
1
 d d x
(A) o d 2
2
2
o
4
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PH2200 Practice Exam I
Summer 2004
4. In the figure below, two Gaussian surfaces have been drawn around an infinitely long, uniformly charged rod with
linear charge density +  . The first surface is a cube of side d. The second one is a cylinder with length d and base
radius d/2 whose axis is set along the rod.
d /2
+
right circular
end-cap
d
d
(4-1) Which one of the following statements correctly relates the magnitude of the net electric flux through each
closed surface?
(A)  E ,cylinder   E ,cube
(B)  E ,cylinder   E ,cube
(C)  E ,cylinder   E ,cube
(D) none of the above - Gauss's Law does not apply to the cube
(4-2) What is the flux of the electric field through the closed cylinder?
(A)  d
(B)  d 2 / 4 o
(C)  d 2 /  o
(D)  / 2 o
(E)  d /  o
(4-3) What is the flux of the electric field through the right circular end-cap identified in the figure?
(A) 0
(B)  d 2 /8 o
(C)  d 2 / 2 o
(D)  / 4 o
(E)  / 2 o
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PH2200 Practice Exam I
Summer 2004
5. Two square conducting plates 5.25 103 m apart carry equal but opposite
charges and produce a uniform electric field between the plates having
a magnitude of 2.00 105 N/C .
(5-1) What is the magnitude of the surface charge density of the
conducting plates?
(A)
(B)
(C)
(D)
(E)
q
1.19 106 C/m2
1.77 106 C/m2
2.17 106 C/m2
2.79 106 C/m2
3.03 106 C/m2
q
5.25 103 m
(5-2) What is the magnitude of the electric potential difference between the plates?
(A)
(B)
(C)
(D)
(E)
1050 V
1290 V
1430 V
1620 V
1770 V
Suppose the magnitude of the charge on each plate is increased so that the potential difference between the plates
becomes 2250 V. An electron, released at rest on the negative plate, accelerates as it travels to the positive plate.
The weight of the electron may be neglected.
(5-3) What is the speed of the electron just before it strikes the positive plate?
(A)
(B)
(C)
(D)
(E)
1.57 107 m/s
1.99 107 m/s
2.35 107 m/s
2.81107 m/s
2.98 107 m/s
(5-4) What is the magnitude of the acceleration of the electron as it moves between the plates?
(A)
(B)
(C)
(D)
(E)
1.29 1016 m/s2
3.19 1016 m/s2
5.45 1016 m/s2
7.54 1016 m/s2
9.46 1016 m/s2
(5-5) If each edge of the square plates is 0.150 m in length, what is the magnitude of the charge on each plate?
(A)
(B)
(C)
(D)
(E)
6.43 108 C
6.82 108 C
7.01108 C
7.79 108 C
8.54 108 C
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PH2200 Practice Exam I
Summer 2004
KEY
Name: ____________________________________
ID#
___________________________________________
Concept Questions
Problems
C
1. _______
C
1-1 _______
C
3-1 _______
E
2. _______
E
1-2 _______
A
3-2 _______
D
3. _______
D
1-3 _______
B
4-1 _______
B
4. _______
C
1-4 _______
E
4-2 _______
C
5. _______
A
1-5 _______
A
4-3 _______
B
6. _______
A
2-1 _______
B
5-1 _______
A
7. _______
D
2-2 _______
A
5-2 _______
B
8. _______
E
2-3 _______
D
5-3 _______
A
9. _______
B
2-4 _______
D
5-4 _______
B
10. _______
E
2-5 _______
E
5-5 _______
Subtotal 1 _______
Subtotal 2 _______
Subtotal 3 _______
Exam Score _______
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