15. The table below gives the electric flux in N ·m2/C through the ends and round surfaces of four
Gaussian surfaces in the form of cylinders. Rank the cylinders according to the charge inside,
from the most negative to the most positive.
left end right end rounded surface
cylinder 1: +2 ×10−9+4 ×10−9−6×10−9
cylinder 2: +3 ×10−9−2×10−9+6 ×10−9
cylinder 3: −2×10−9−5×10−9+3 ×10−9
cylinder 4: +2 ×10−9−5×10−9−3×10−9
A. 1, 2, 3, 4
B. 4, 3, 2, 1
C. 3, 4, 2, 1
D. 3, 1, 4, 2
E. 4, 3, 1, 2
ans: E
16. A conducting sphere of radius 0.01 m has a charge of 1.0×10−9C deposited on it. The
magnitude of the electric field in N/C just outside the surface of the sphere is:
A. 0
B. 450
C. 900
D. 4500
E. 90,000
ans: C
17. A round wastepaper basket with a 0.15-m radius opening is in a uniform electric field of
300 N/C, perpendicular to the opening. The total flux through the sides and bottom, in
N·m2C, is:
A. 0
B. 4.2
C. 21
D. 280
E. can not tell without knowing the areas of the sides and bottom
ans: C
18. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of −3C is
placed at the center of the cavity. The net charge on the inner surface of the shell is:
A. −7C
B. −3C
C. 0 C
D. +3 C
E. +7 C
ans: D
346 Chapter 23: GAUSS’ LAW
Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com
19. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of −3C is
placed at the center of the cavity. The net charge on the outer surface of the shell is:
A. −7C
B. −3C
C. 0 C
D. +3 C
E. +7 C
ans: E
20. A 30-N/C uniform electric field points perpendicularly toward the left face of a large neutral
conducting sheet. The surface charge density in C/m2on the left and right faces, respectively,
are:
A. −2.7×10−9C/m2;+2.7×10−9C/m2
B. +2.7×10−9C/m2;−2.7×10−9C/m2
C. −5.3×10−9C/m2;+5.3×10−9C/m2
D. +5.3×10−9C/m2;−5.3×10−9C/m2
E. 0; 0
ans: A
21. A solid insulating sphere of radius Rcontains positive charge that is distributed with a volume
charge density that does not depend on angle but does increase with distance from the sphere
center. Which of the graphs below might give the magnitude Eof the electric field as a function
of the distance rfrom the center of the sphere?
r
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R
E
ans: D
Chapter 23: GAUSS’ LAW 347
Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com
22. Which of the following graphs represents the magnitude of the electric field as a function of
the distance from the center of a solid charged conducting sphere of radius R?
r
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R
E
ans: E
23. Charge Qis distributed uniformly throughout an insulating sphere of radius R. The magnitude
of the electric field at a point R/2 from the center is:
A. Q/4π0R2
B. Q/π0R2
C. 3Q/4π0R2
D. Q/8π0R2
E. none of these
ans: D
24. Positive charge Qis distributed uniformly throughout an insulating sphere of radius R, centered
at the origin. A particle with positive charge Qis placed at x=2Ron the xaxis. The
magnitude of the electric field at x=R/2 on the xaxis is:
A. Q/4π0R2
B. Q/8π0R2
C. Q/72π0R2
D. 17Q/72π0R2
E. none of these
ans: C
25. Charge Qis distributed uniformly throughout a spherical insulating shell. The net electric flux
in N ·m2/C through the inner surface of the shell is:
A. 0
B. Q/0
C. 2Q/0
D. Q/4π0
E. Q/2π0
ans: A
348 Chapter 23: GAUSS’ LAW
Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com
26. Charge Qis distributed uniformly throughout a spherical insulating shell. The net electric flux
in N ·m2/C through the outer surface of the shell is:
A. 0
B. Q/0
C. 2Q/0
D. Q/40
E. Q/2π0
ans: B
27. A 3.5-cm radius hemisphere contains a total charge of 6.6×10−7C. The flux through the
rounded portion of the surface is 9.8×104N·m2/C. The flux through the flat base is:
A. 0
B. +2.3×104N·m2/C
C. −2.3×104N·m2/C
D. −9.8×104N·m2/C
E. +9.8×104N·m2/C
ans: C
28. Charge is distributed uniformly along a long straight wire. The electric field 2 cm from the
wire is 20 N/C. The electric field 4 cm from the wire is:
A. 120 N/C
B. 80 N/C
C. 40 N/C
D. 10 N/C
E. 5 N/C
ans: D
29. Positive charge Qis placed on a conducting spherical shell with inner radius R1and outer
radius R2. A particle with charge qis placed at the center of the cavity. The magnitude of the
electric field at a point in the cavity, a distance rfrom the center, is:
A. zero
B. Q/4π0R2
1
C. q/4π0r2
D. (q+Q)/4π0r2
E. (q+Q)/4π0(R2
1−r2)
ans: C
30. Positive charge Qis placed on a conducting spherical shell with inner radius R1and outer
radius R2. A point charge qis placed at the center of the cavity. The magnitude of the electric
field at a point outside the shell, a distance rfrom the center, is:
A. zero
B. Q/4π0r2
C. q/4π0r2
D. (q+Q)/4π0r2
E. (q+Q)/4π0(R2
1−r2)
ans: D
Chapter 23: GAUSS’ LAW 349
Simpo PDF Merge and Split Unregistered Version - http://www.simpopdf.com
31. Positive charge Qis placed on a conducting spherical shell with inner radius R1and outer
radius R2. A point charge qis placed at the center of the cavity. The magnitude of the electric
field produced by the charge on the inner surface at a point in the interior of the conductor, a
distance rfrom the center, is:
A. 0
B. Q/4vπ0R2
1
C. Q/4π0R2
2
D. q/4π0r2
E. Q/4π0r2
ans: D
32. A long line of charge with λfcharge per unit length runs along the cylindrical axis of a cylin-
drical shell which carries a charge per unit length of λc. The charge per unit length on the
inner and outer surfaces of the shell, respectively are:
A. λfand λc
B. −λfand λc+λf
C. −λfand λc−λc
D. λf+λcand λc−λf
E. λf−λcand λc+λf
ans: B
33. Charge is distributed uniformly on the surface of a large flat plate. The electric field 2 cm from
the plate is 30 N/C. The electric field 4 cm from the plate is:
A. 120 N/C
B. 80 N/C
C. 30 N/C
D. 15 N/C
E. 7.5N/C
ans: C
34. Two large insulating parallel plates carry charge of equal magnitude, one positive and the other
negative, that is distributed uniformly over their inner surfaces. Rank the points 1 through 5
according to the magnitude of the electric field at the points, least to greatest.
+
+
+
+
+
+
+
−
−
−
−
−
−
−
••• ••
123 45
A. 1, 2, 3, 4, 5
B. 2, then 1, 3, and 4 tied, then 5
C. 1, 4, and 5 tie, then 2 and 3 tie
D. 2 and 3 tie, then 1 and 4 tie, then 5
E. 2 and 3 tie, then 1, 4, and 5 tie
ans: C
350 Chapter 23: GAUSS’ LAW
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