Chapter 22: The Electric Field II:
Continuous Charge Distributions
Section 22-1: Calculating E from
Coulomb’s Law
A conducting circular disk has a uniform positive
surface charge density. Which of the following
diagrams best represents the electric field lines
from the disk? (The disk is drawn as a cross–
section.)
A. 1
B. 2
1
2
C. 3
D. 4
E. None of the diagrams.
3
4
A conducting circular disk has a uniform positive
surface charge density. Which of the following
diagrams best represents the electric field lines
from the disk? (The disk is drawn as a cross–
section.)
A. 1
B. 2
1
2
C. 3
D. 4
E. None of the diagrams.
3
4
An infinite plane lies in the yzplane and it
has a uniform surface charge density. The
electric field at a distance x from the plane
A. decreases linearly with x.
B. decreases as 1/x2.
C. is constant and does not depend on x.
D. increases linearly with x.
E. is undetermined.
An infinite plane lies in the yzplane and it
has a uniform surface charge density. The
electric field at a distance x from the plane
A. decreases linearly with x.
B. decreases as 1/x2.
C. is constant and does not depend on x.
D. increases linearly with x.
E. is undetermined.
A uniform circular ring has charge Q and radius r.
A uniformly charged disk also has charge Q and
radius r. Calculate the electric field due to the ring
at a distance of r along the axis of the ring divided
by the electric field due to the disk at a distance of
r along the axis of the disk.
A. 1.0
B. 0.60
C. 1.7
D. 0.50
E. 0.85
A uniform circular ring has charge Q and radius r.
A uniformly charged disk also has charge Q and
radius r. Calculate the electric field due to the ring
at a distance of r along the axis of the ring divided
by the electric field due to the disk at a distance of
r along the axis of the disk.
A. 1.0
B. 0.60
C. 1.7
D. 0.50
E. 0.85
Chapter 22: The Electric Field II:
Continuous Charge Distributions
Section 22-2: Gauss’s Law
A cubical surface with no charge enclosed and with sides
2.0 m long is oriented with right and left faces
perpendicular to a uniform electric field E of (1.6  105 N/C)
in the +x direction. The net electric flux fE through this
surface is approximately
A. zero
B. 6.4  105 N · m2/C
C. 13  105 N · m2/C
D. 25  105 N · m2/C
E. 38  105 N · m2/C
A cubical surface with no charge enclosed and with sides
2.0 m long is oriented with right and left faces
perpendicular to a uniform electric field E of (1.6  105 N/C)
in the +x direction. The net electric flux fE through this
surface is approximately
A. zero
B. 6.4  105 N · m2/C
C. 13  105 N · m2/C
D. 25  105 N · m2/C
E. 38  105 N · m2/C
A surface is so constructed that, at all points
on the surface, the E vector points inward.
Therefore, it can be said that
A. the surface encloses a net positive
charge.
B. the surface encloses a net negative
charge.
C. the surface encloses no net charge.
A surface is so constructed that, at all points
on the surface, the E vector points inward.
Therefore, it can be said that
A. the surface encloses a net positive
charge.
B. the surface encloses a net negative
charge.
C. the surface encloses no net charge.
A surface is so constructed that, at all points
on the surface, the E vector points outward.
Therefore, it can be said that
A. the surface encloses a net positive
charge.
B. the surface encloses a net negative
charge.
C. the surface encloses no net charge.
A surface is so constructed that, at all points
on the surface, the E vector points outward.
Therefore, it can be said that
A. the surface encloses a net positive
charge.
B. the surface encloses a net negative
charge.
C. the surface encloses no net charge.
The figure shows a surface enclosing the
charges q and –q. The net flux through the
surface surrounding the two charges is
A. q/0
B. 2q/0
C. –q/0
D. zero
E. –2q/0
The figure shows a surface enclosing the
charges q and –q. The net flux through the
surface surrounding the two charges is
A. q/0
B. 2q/0
C. –q/0
D. zero
E. –2q/0
The figure shows a surface enclosing
the charges 2q and –q. The net flux
through the surface surrounding the two A. q
0
charges is
2q
B. 
ε0
C. 
q
0
D. zero
3q
E.
0
The figure shows a surface enclosing
the charges 2q and –q. The net flux
through the surface surrounding the two A. q
0
charges is
2q
B. 
ε0
C. 
q
0
D. zero
3q
E.
0
The figure shows a surface, S, with two
charges q and –2q. The net flux through
the surface is
A.
q
0
2q
B. 
ε0
s
+q
C. 
2q
q
0
D. zero
3q
E.
0
The figure shows a surface, S, with two
charges q and –2q. The net flux through
the surface is
A.
q
0
2q
B. 
ε0
s
+q
C. 
2q
q
0
D. zero
3q
E.
0
A hollow spherical shell of radius 5.36 cm
has a charge of 1.91 mC placed at its center.
Calculate the electric flux through a portion
of the shell with an area of 1.20  10–2 m2.
A. 6.48  105 N.m2/C
B. 2.16  105 N.m2/C
C. 7.20  104 N.m2/C
D. 2.16  101 N.m2/C
E. None of the above.
A hollow spherical shell of radius 5.36 cm
has a charge of 1.91 mC placed at its center.
Calculate the electric flux through a portion
of the shell with an area of 1.20  10–2 m2.
A. 6.48  105 N.m2/C
B. 2.16  105 N.m2/C
C. 7.20  104 N.m2/C
D. 2.16  101 N.m2/C
E. None of the above.
A horizontal surface of area 0.321 m2 has an
electric flux of 123 N.m2/C passing through it
at an angle of 25° to the horizontal. If the
flux is due to a uniform electric field,
calculate the magnitude of the electric field.
A. 907 N/C
B. 423 N/C
C. 1.10  10–3 N/C
D. 2.36  10–3 N/C
E. 383 N/C
A horizontal surface of area 0.321 m2 has an
electric flux of 123 N.m2/C passing through it
at an angle of 25° to the horizontal. If the
flux is due to a uniform electric field,
calculate the magnitude of the electric field.
A. 907 N/C
B. 423 N/C
C. 1.10  10–3 N/C
D. 2.36  10–3 N/C
E. 383 N/C
Chapter 22: The Electric Field II:
Continuous Charge Distributions
Section 22-3: Using Symmetry to
Calculate E with Guass’s Law, and
Concept Check 22-1
The electric field E in Gauss’s Law is
A. only that part of the electric field due to
the charges inside the surface.
B. only that part of the electric field due to
the charges outside the surface.
C. the total electric field due to all the
charges both inside and outside the
surface.
The electric field E in Gauss’s Law is
A. only that part of the electric field due to
the charges inside the surface.
B. only that part of the electric field due to
the charges outside the surface.
C. the total electric field due to all the
charges both inside and outside the
surface.
A rod of infinite length has a charge per unit length
of l (= q/l). Gauss's Law makes it easy to determine
that the electric field strength at a perpendicular
distance r from the rod is, in terms of k = (40)–1,
k
A.
r2
k
B.
r
4k
C.
r
2k
D.
r
E. zero
A rod of infinite length has a charge per unit length
of l (= q/l). Gauss's Law makes it easy to determine
that the electric field strength at a perpendicular
distance r from the rod is, in terms of k = (40)–1,
k
A.
r2
k
B.
r
4k
C.
r
2k
D.
r
E. zero
A solid sphere of radius a is concentric with a hollow sphere of
radius b, where b > a. If the solid sphere has a uniform charge
distribution totaling +Q and the hollow sphere a charge of –Q,
the electric field magnitude at radius r, where r < a, is which
of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
kQr
a3
kQ
a2
kQ
b2
zero
A solid sphere of radius a is concentric with a hollow sphere of
radius b, where b > a. If the solid sphere has a uniform charge
distribution totaling +Q and the hollow sphere a charge of –Q,
the electric field magnitude at radius r, where r < a, is which
of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
kQr
a3
kQ
a2
kQ
b2
zero
A solid sphere of radius a is concentric with a hollow sphere
of radius b, where b > a. If the solid sphere has a uniform
charge distribution totaling +Q and the hollow sphere a
charge of –Q, the electric field magnitude at radius r, where
a < r < b, is which of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
2kQ
r2
kQ
a2
kQ
b2
kQ
(b  a ) 2
A solid sphere of radius a is concentric with a hollow sphere
of radius b, where b > a. If the solid sphere has a uniform
charge distribution totaling +Q and the hollow sphere a
charge of –Q, the electric field magnitude at radius r, where
a < r < b, is which of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
2kQ
r2
kQ
a2
kQ
b2
kQ
(b  a ) 2
A solid sphere of radius a is concentric with a hollow sphere
of radius b, where b > a. If the solid sphere has a uniform
charge distribution totaling +Q and the hollow sphere a
charge of –Q, the electric field magnitude at radius r, where
r > b, is which of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
2kQ
r2
kQ
a2
kQ
b2
zero
A solid sphere of radius a is concentric with a hollow sphere
of radius b, where b > a. If the solid sphere has a uniform
charge distribution totaling +Q and the hollow sphere a
charge of –Q, the electric field magnitude at radius r, where
r > b, is which of the following, in terms of k = (40)–1?
A.
B.
C.
D.
E.
kQ
r2
2kQ
r2
kQ
a2
kQ
b2
zero
A sphere of radius 8.0 cm carries a uniform volume
charge density r = 500 nC/m3. What is the electric
field magnitude at r = 8.1 cm?
A. 0.12 kN/C
B. 1.5 kN/C
C. 0.74 kN/C
D. 2.3 kN/C
E. 12 kN/C
A sphere of radius 8.0 cm carries a uniform volume
charge density r = 500 nC/m3. What is the electric
field magnitude at r = 8.1 cm?
A. 0.12 kN/C
B. 1.5 kN/C
C. 0.74 kN/C
D. 2.3 kN/C
E. 12 kN/C
A spherical shell of radius 9.0 cm
carries a uniform surface charge
density s = 9.0 nC/m2. The electric
field magnitude at r = 4.0 cm is
approximately
A. 0.13 kN/C
B. 1.0 kN/C
C. 0.32 kN/C
D. 0.75 kN/C
E. zero
A spherical shell of radius 9.0 cm
carries a uniform surface charge
density s = 9.0 nC/m2. The electric
field magnitude at r = 4.0 cm is
approximately
A. 0.13 kN/C
B. 1.0 kN/C
C. 0.32 kN/C
D. 0.75 kN/C
E. zero
A spherical shell of radius 9.0 cm
carries a uniform surface charge
density s = 9.0 nC/m2. The electric
field magnitude at r = 9.1 cm is
approximately
A. zero
B. 1.0 kN/C
C. 0.65 kN/C
D. 0.32 kN/C
E. 0.13 kN/C
A spherical shell of radius 9.0 cm
carries a uniform surface charge
density s = 9.0 nC/m2. The electric
field magnitude at r = 9.1 cm is
approximately
A. zero
B. 1.0 kN/C
C. 0.65 kN/C
D. 0.32 kN/C
E. 0.13 kN/C
An infinite plane of surface charge density s = +8.00 nC/m2
lies in the yz plane at the origin, and a second infinite
plane of surface charge density s = –8.00 nC/m2 lies in a
plane parallel to the yz plane at x = 4.00 m. The electric
field magnitude at x = 3.50 m is approximately
A. 226 N/C
B. 339 N/C
C. 904 N/C
D. 452 N/C
E. zero
An infinite plane of surface charge density s = +8.00 nC/m2
lies in the yz plane at the origin, and a second infinite
plane of surface charge density s = –8.00 nC/m2 lies in a
plane parallel to the yz plane at x = 4.00 m. The electric
field magnitude at x = 3.50 m is approximately
A. 226 N/C
B. 339 N/C
C. 904 N/C
D. 452 N/C
E. zero
An infinite plane of surface charge density s = +8.00
nC/m2 lies in the yz plane at the origin, and a second
infinite plane of surface charge density s = –8.00 nC/m2
lies in a plane parallel to the yz plane at x =4.00 m. The
electric field magnitude at x = 5.00 m is approximately
A. 226 N/C
B. 339 N/C
C. 904 N/C
D. 452 N/C
E. zero
An infinite plane of surface charge density s = +8.00
nC/m2 lies in the yz plane at the origin, and a second
infinite plane of surface charge density s = –8.00 nC/m2
lies in a plane parallel to the yz plane at x =4.00 m. The
electric field magnitude at x = 5.00 m is approximately
A. 226 N/C
B. 339 N/C
C. 904 N/C
D. 452 N/C
E. zero
An infinite slab of thickness 2d lies in the
xz–plane. The slab has a uniform volume
charge density r. The electric field
magnitude at y = b where 0 < b < d is
A. 4πkρb
z
B. 2πkρb
d d
4πkρ
C.
b
2πkρ
D.
b
4πkρ
x
E.
b2
y
An infinite slab of thickness 2d lies in the
xz–plane. The slab has a uniform volume
charge density r. The electric field
magnitude at y = b where 0 < b < d is
A. 4πkρb
z
B. 2πkρb
d d
4πkρ
C.
b
2πkρ
D.
b
4πkρ
x
E.
b2
y
An infinite slab of thickness 2d lies in the
xz–plane. The slab has a uniform volume
charge density r. The electric field
magnitude at y = b where b > d is
4kr
A.
b
4kr
B.
d2
C. 4krd
D. 2krd
4kr
E.
d
z
d d
y
x
An infinite slab of thickness 2d lies in the
xz–plane. The slab has a uniform volume
charge density r. The electric field
magnitude at y = b where b > d is
4kr
A.
b
4kr
B.
d2
C. 4krd
D. 2krd
4kr
E.
d
z
d d
y
x
An infinite slab of thickness 2d
lies in the xz–plane. The slab has
a uniform volume charge density
r. Which diagram best
represents the electric field along
the y–axis?
z
d d
y
x
E. None of the diagrams.
An infinite slab of thickness 2d
lies in the xz–plane. The slab has
a uniform volume charge density
r. Which diagram best
represents the electric field along
the y–axis?
z
d d
y
x
E. None of the diagrams.
Chapter 22: The Electric Field II:
Continuous Charge Distributions
Section 22-4: Discontinuity of En
A thin conducting plane with surface charge
density s is exposed to an external electric
Eext. The difference in the electric field
between one surface of the plane to the
other surface is
A. s/0
B. s/0  Eext
C. s/0  Eext
D. 2s/0  Eext
E. s/20  Eext
Eext
s
A thin conducting plane with surface charge
density s is exposed to an external electric
Eext. The difference in the electric field
between one surface of the plane to the
other surface is
A. s/0
B. s/0  Eext
C. s/0  Eext
D. 2s/0  Eext
E. s/20  Eext
Eext
s
Chapter 22: The Electric Field II:
Continuous Charge Distributions
Section 22-5: Charge and Field at
Conductor Surfaces
Electrical conductors contain
A. only free electrons.
B. only bound electrons.
C. both free and bound electrons.
D. neither bound nor free electrons.
E. only protons and neutrons.
Electrical conductors contain
A. only free electrons.
B. only bound electrons.
C. both free and bound electrons.
D. neither bound nor free electrons.
E. only protons and neutrons.
The electric field at the surface of a
conductor
A. is parallel to the surface.
B. depends only on the total charge on the
conductor.
C. depends only on the area of the
conductor.
D. depends only on the curvature of the
surface.
E. depends on the area and curvature of the
conductor and on its total charge.
The electric field at the surface of a
conductor
A. is parallel to the surface.
B. depends only on the total charge on the
conductor.
C. depends only on the area of the
conductor.
D. depends only on the curvature of the
surface.
E. depends on the area and curvature of
the conductor and on its total charge.
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of inner
radius rb1 and outer radius rb2. The inner sphere carries a
charge Q while the outer sphere does not carry any net
charge. The electric field for ra  r  rb1 is
A.
B.
C.
D.
E.
kQ
 2 rˆ
r
kQ
rˆ
2
r
2kQ

rˆ
r
2kQ
rˆ
r
zero
ra
Q
rb1
rb2
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of inner
radius rb1 and outer radius rb2. The inner sphere carries a
charge Q while the outer sphere does not carry any net
charge. The electric field for ra  r  rb1 is
A.
B.
C.
D.
E.
kQ
 2 rˆ
r
kQ
rˆ
2
r
2kQ

rˆ
r
2kQ
rˆ
r
zero
ra
Q
rb1
rb2
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of
inner radius rb1 and outer radius rb2. The inner sphere
carries a charge Q while the outer sphere does not carry
any net charge. The electric field for rb1  r  rb2 is
kQ
A.  2 rˆ
r
kQ
B.
rˆ
2
r
ra
2kQ
C. 
rˆ
Q
rb1
r
2kQ
D.
rˆ
r
rb2
E. zero
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of
inner radius rb1 and outer radius rb2. The inner sphere
carries a charge Q while the outer sphere does not carry
any net charge. The electric field for rb1  r  rb2 is
kQ
A.  2 rˆ
r
kQ
B.
rˆ
2
r
ra
2kQ
C. 
rˆ
Q
rb1
r
2kQ
D.
rˆ
r
rb2
E. zero
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of
inner radius rb1 and outer radius rb2. The inner sphere
carries a charge Q while the outer sphere does not carry
any net charge. The electric field for r  rb1 is
kQ
A.  2 rˆ
r
kQ
B.
rˆ
2
r
ra
2kQ
Q
rb1
C. 
rˆ
r
2kQ
rb2
D.
rˆ
r
E. zero
A solid conducting sphere of radius ra is placed
concentrically inside a conducting spherical shell of
inner radius rb1 and outer radius rb2. The inner sphere
carries a charge Q while the outer sphere does not carry
any net charge. The electric field for r  rb1 is
kQ
A.  2 rˆ
r
kQ
B.
rˆ
2
r
ra
2kQ
Q
rb1
C. 
rˆ
r
2kQ
rb2
D.
rˆ
r
E. zero
The charge on an originally
uncharged insulated conductor is
separated by induction from a
positively charged rod brought near
the conductor. For which of the
various Gaussian surfaces
represented by the dashed lines
 
does  E  ds  0 ?
A.
S1
B.
S2
C.
S3
D.
S4
E.
S5
The charge on an originally
uncharged insulated conductor is
separated by induction from a
positively charged rod brought near
the conductor. For which of the
various Gaussian surfaces
represented by the dashed lines
 
does  E  ds  0 ?
A.
S1
B.
S2
C.
S3
D.
S4
E.
S5