Chapter 21 MCQs
1
X and Y are two uncharged metal spheres on insulating stands, and are in contact with each other. A
positively charged rod R is brought close to X as shown in Figure (a).
Sphere
is now moved away from
, as in Figure (b).
What are the final charge states of X and Y?
ANSWER:
X is neutral and Y is positive.
X is positive and Y is neutral.
X is negative and Y is positive.
Both X and Y are neutral.
Both X and Y are negative.
2
Two identical small charged spheres are a certain distance apart, and each one initially experiences an
electrostatic force of magnitude
due to the other. With time, charge gradually leaks off of both spheres.
When each of the spheres has lost half its initial charge, the magnitude of the electrostatic force will be
ANSWER:
1/8
.
1/4
.
1/2
.
1/16 F.
3
When two point charges are a distance
other has magnitude
be changed to
ANSWER:
part, the electric force that each one feels from the
. In order to make this force twice as strong, the distance would have to
2 .
/
.
/4.
/2.
4
A point charge
is located a short distance from a point charge 3 , and no other charges are present. If
the electrical force on
is
, what is the electrical force on 3 ?
ANSWER:
/
F/3
3
5
A positive point charge
is fixed on a very large horizontal frictionless tabletop. A second positive point
charge is released from rest near the stationary charge and is free to move. Which statement best
describes the motion of after it is released?
ANSWER:
As it moves farther and farther from
, its speed will decrease.
As it moves farther and farther from
increasing.
, its acceleration will keep
Its acceleration is zero just after it is released.
As it moves farther and farther from
, its speed will keep increasing.
Its speed will be greatest just after it is released.
6
One very small uniformly charged plastic ball is located directly above another such charge in a test tube
as shown in the figure. The balls are in equilibrium a distance apart. If the charge on each ball is
doubled, the distance between the balls in the test tube would become
ANSWER:
.
.
.
.
7
The figure shows two unequal point charges, q and Q, of opposite sign. Charge Q has greater magnitude
than charge q. In which of the regions X, Y, Z will there be a point at which the net electric field due to
these two charges is zero?
ANSWER:
only region X
only region Y
only regions X and Z
only region Z
all three regions
8
Two point charges Q 1 and Q 2 of equal magnitudes and opposite signs are positioned as shown in the
figure. Which of the arrows best represents the net electric field at point P due to these two charges?
ANSWER:
A
B
C
D
The field is equal to zero at point
.
9
Four equal negative point charges are located at the corners of a square, their positions in the
being
,
direction as
,
,
ANSWER:
.
.
.
. The electric field on the
-axis at
-plane
points in the same
.
10
Three equal negative point charges are placed at three of the corners of a square of side d as shown in
the figure. Which of the arrows represents the direction of the net electric field at the center of the
square?
ANSWER:
A
B
C
D
The field is equal to zero at point P.
11
The figure shows three electric charges labeled Q 1, Q 2, Q 3, and some electric field lines in the region
surrounding the charges. What are the signs of the three charges?
ANSWER:
Q 1 is positive, Q 2 is negative, Q 3 is positive.
Q 1 is negative, Q 2 is positive, Q 3 is negative.
Q 1 is positive, Q 2 is positive, Q 3 is negative.
All three charges are negative.
All three charges are positive.
12
Two large, flat, horizontally oriented plates are parallel to each other, a distance
apart. Half way
between the two plates the electric field has magnitude . If the separation of the plates is reduced to
/2 what is the magnitude of the electric field half way between the plates?
ANSWER:
4
/2
2
0
13
Two very large parallel sheets a distance d apart have their centers directly opposite each other. The
sheets carry equal but opposite uniform surface charge densities. A point charge that is placed near the
middle of the sheets a distance d/2 from each of them feels an electrical force F due to the sheets. If this
charge is now moved closer to one of the sheets so that it is a distanced/4 from that sheet, what force will
feel?
ANSWER:
F/2
F
F/4
4F
2F
14
An electron is initially moving to the right when it enters a uniform electric field directed upwards. Which
trajectory shown below will the electron follow?
ANSWER:
trajectory Z
trajectory Y
trajectory W
trajectory X
15
A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece
-19
of plastic have? (e = 1.60 × 10 C)
ANSWER:
1.25 × 1013
2.50 × 1013
1.25 × 1019
2.50 × 1019
16
A
-C point charge is
other is
m from a second point charge, and the electric force on one of them due to the
N. What is the magnitude of the second charge? (
ANSWER:
2
2
N · m /C )
C
C
nC
C
nC
17
When two point charges are 2.0 cm apart, each one experiences a 1.0-N electric force due to the other
charge. If they are moved to a new separation of 8.0 cm, the electric force on each of them is closest to
ANSWER:
0.25 N.
4.0 N.
16 N.
0.063 N.
1.0 N.
18
Two identical small conducting spheres are separated by 0.60 m. The spheres carry different amounts of
charge and each sphere experiences an attractive electric force of 10.8N. The total charge on the two
spheres is -24 μC. The two spheres are now connected by a slender conducting wire, which is then
removed. The electric force on each sphere is closest to
ANSWER:
zero.
3.6 N, repulsive.
5.4 N, attractive.
3.6 N, attractive.
5.4 N, repulsive.
19 A
Three point charges are placed on the -axis. A charge of
μC is placed at the
origin,
μC to the right at
cm, and
μC at the
cm mark. What is the
magnitude of the electrostatic force that acts on the charge at the origin? (
N · m2/C2)
ANSWER:
N
7.20×10
−2
B
What is the direction of the electrostatic force that acts on the charge at the origin?
ANSWER:
toward the left
toward the right
20 A
Charge
nC is at (
m, ), charge
charge
nC is at ( , ). What is the magnitude of the net electrostatic force on the
charge due to the other charges? (
ANSWER:
nC is at ( ,
m), and
-nC
N · m2/C2)
N
5.40×10
−6
Part B
What is the direction of the net electrostatic force on the
ANSWER:
-nC charge due to the other charges?
above -axis
56.0
21
Two small insulating spheres are attached to silk threads and aligned vertically as shown in the
figure. These spheres have equal masses of 40 g, and carry charges and of equal magnitude
2.0 μC but opposite sign.The spheres are brought into the positions shown in the figure, with a
vertical separation of 15 cm between them. Note that you cannot neglect gravity. (
N · m2/C2) The tension in the lower thread is closest to
ANSWER:
N.
N.
N.
N.
N.
22
In the figure, a small spherical insulator of mass
wire of negligible mass. A charge of
right of it, so the wire makes an angle
2
2
N · m /C )
ANSWER:
μC is held
kg and charge
μC is hung by a thin
m away from the sphere and directly to the
with the vertical, as shown. What is the angle
?(
23
An atomic nucleus has a charge of
of
. What is the magnitude of the electric field at a distance
2
m from the center of the nucleus? (
2
N · m /C ,
C)
ANSWER:
N/C
N/C
N/C
N/C
N/C
24
A metal sphere of radius
cm carries a charge of
μC uniformly distributed over its surface. What
is the magnitude of the electric field due to this sphere at a point
2
cm outside the sphere's surface? (
2
N · m /C )
ANSWER:
N/C
N/C
N/C
N/C
N/C
25
A small sphere with a mass of 441 g is moving upward along the vertical + -axis when it encounters an
electric field of 5.00 N/C . If, due to this field, the sphere suddenly acquires a horizontal acceleration of
2
13.0 m/s , what is the charge that it carries?
ANSWER:
-1150 C
1150 C
-1.15 C
1.15 C
26
A point charge Q of mass 8.50 g hangs from the horizontal ceiling by a light 25.0-cm thread. When a
horizontal electric field of magnitude 1750 N/C is turned on, the charge hangs away from the vertical as
shown in the figure. The magnitude of Q is closest to
ANSWER:
47.6 µC.
3.5 µC.
55.0 µC.
3.0 µC.
27.5 µC.
27
A point charge
= -500 nC and two unknown point charges,
figure. The electric field at the origin
closest to
ANSWER:
-76 nC.
76 nC.
130 nC.
-130 nC.
150 nC.
, due to charges
,
1
1
and
and
2,
2,
are placed as shown in the
is equal to zero. The charge
1
is
28
μC and
Two point charges,
2
2
N · m /C ) The
μC, are placed as shown in the figure. (
component of the electric field, at the origin
, is closest to
ANSWER:
N/C.
N/C.
N/C.
N/C.
N/C.
29
Three
-μC point charges are at the three corners of a square of side
occupied by a
m. The last corner is
-μC charge. Find the magnitude of the electric field at the center of the square. (
2
2
N · m /C )
ANSWER:
N/C
4.30×10
5
30
Three equal negative point charges are placed at three of the corners of a square of side
magnitude of the net electric field at the center of the square? (
Express your answer in terms of the variables
ANSWER:
=
, , and appropriate constants.
. What is the
)
31
A 5.0-μC point charge is placed at the 0.00 cm mark of a meter stick and a -4.0-μC point charge is placed
at the 50 cm mark. At what point on a line joining the two charges is the electric field due to these charges
equal to zero?
ANSWER:
m from 0.00-cm mark
4.70
32 A
Two thin 80.0-cm rods are oriented at right angles to each other. Each rod has one end at the
origin of the coordinates, and one of them extends along the
-axis while the other extends
along the
-axis. The rod along the
-axis carries a charge of
µC distributed
uniformly along its length, and the other rod carries
µC uniformly over its length. Find
the magnitude of the net electrical force that these two rods exert on an electron located at the
point (
cm,
ANSWER:
cm). (
C2/N · m2)
C,
N
1.35×10−13
Part B
Find the direction of the net electrical force that these two rods exert on an electron located at the
point (40.0 cm, 40.0 cm).
ANSWER:
with respect to the
-axis
135
33
A long, thin rod parallel to the
density of
-axis is located at
cm and carries a uniform linear charge
nC/m. A second long, thin rod parallel to the -axis is located at
carries a uniform linear charge density of
2
the origin? (
2
C /N · m )
ANSWER:
(
N/C)
(
N/C)
(
N/C)
cm and
nC/m. What is the net electric field due to these rods at
(
N/C)
zero
34
A thin, circular disk of radius
carries a total charge of
cm is oriented in the
-plane with its center at the origin. The disk
μC distributed uniformly over its surface. Calculate the magnitude of the
electric field due to the disk at the point
cm along the
2
-axis. (
2
C /N · m )
ANSWER:
N/C
N/C
N/C
N/C
N/C
35
In the figure, a ring 0.71 m in radius carries a charge of + 580 nC uniformly distributed over it. A point
charge
is placed at the center of the ring. The electric field is equal to zero at field point
the axis of the ring, and 0.73 m from its center. (
closest to
ANSWER:
2
2
, which is on
C /N · m ) The point charge
is
36
Two very large, flat plates are parallel to each other. Plate
, located at
cm, is along the
-
2
plane and carries a uniform surface charge density
μC/m . Plate B is located at
cm and
2
carries a uniform surface charge density +2.00 μC/m . What is the electric field vector at the point
having
,
, coordinates (
cm,
cm,
2
cm)? (
2
C /N · m )
ANSWER:
N/C)
N/C)
N/C)
N/C)
N/C)
37
An electric field is set up between two parallel plates, each of area
2
m , by putting
μC of charge on
one plate and
μC of charge on the other. The plates are separated by
mm with their centers
opposite each other, and the charges are distributed uniformly over the surface of the plates. What is the
magnitude of the electric field between the plates at a distance of
2
near the edges of the plates? (
mm from the positive plate, but not
2
C /N · m )
ANSWER:
N/C
N/C
N/C
N/C
N/C
38
A pair of charged conducting plates produces a uniform field of
N/C, directed to the right, between
the plates. The separation of the plates is 40 mm. An electron is projected from plate
plate
, with an initial velocity of
2
C,
closest to
, directly toward
m/s, as shown in the figure. (
2
C /N · m ,
kg) The velocity of the electron as it strikes plate
is
ANSWER:
m/s.
m/s.
m/s.
m/s.
m/s.
39
A pair of charged conducting plates produces a uniform field of
the plates. The separation of the plates is
plate
C,
to plate
, with an initial velocity of
2
2
C /N · m ,
is nearest to
N/C, directed to the right, between
mm. An electron is projected from plate
, directly toward
m/s, as shown in the figure. (
kg) The distance of closest approach of the electron
ANSWER:
mm.
mm.
mm.
mm.
mm.
40
An electric dipole is made of two charges of equal magnitudes and opposite signs. The positive
charge,
μC, is located at the point ( ,
charge is located at the point ( ,
by an electric field
ANSWER:
, )
N/C)
(
, )
(
cm,
cm,
cm,
cm,
cm), while the negative
cm). How much work will be done
to bring the dipole to its stable equilibrium position?
J
J
J
J
J
41
An initially-stationary electric dipole of dipole moment
field
(
N/C)
(
electric field exerts on the dipole?
N/C)
(
C · m)
placed in an electric
. What is the magnitude of the maximum torque that the
ANSWER:
N·m
N·m
N·m
N·m
N·m
42
An electric dipole consists of charges ±5.00 µC separated by 1.20 mm. It is placed in a vertical electric
field of magnitude 525 N/C oriented as shown in the figure. The magnitude of the net torque this field
exerts on the dipole is closest to
ANSWER:
1.21 × 10-6 N · m.
2.41 × 10-6 N · m.
3.15 × 10-6 N · m.
1.01 × 10-6 N · m.
2.02 × 10-6 N · m.
43
-6
-6
In the figure, charge q 1 = 2.4 × 10 C is placed at the origin and charge q 2 = -7.2 × 10 C is placed on
the x-axis, at x = -0.20 m. Where along the positive x-axis can a third charge Q = -8.3 µC be placed such
that the resultant force on this third charge is zero?
Express your answer using two significant figures.
ANSWER:
x =
m
0.27
44
A +4.00 μC point charge and -6.00 μC point charge are placed along the x-axis at x = 0.000 cm and x =
40.0 cm, respectively. Where must a third charge, q, be placed along the x-axis so that it does not
experience any net electric force due to the other two charges?
ANSWER:
-0.200 m
-0.180 m
0.180 m
1.78 m
-1.78 m
45
In the figure, all the charges are point charges and the charge in the middle is Q = -4.1 nC. For what
charge q 1 will charge q 2 be in static equilibrium?
ANSWER:
16 nC
33 nC
8.2 nC
4.1 nC
46
The figure shows two tiny 5.0-g spheres suspended from two very thin 1.0-m-long threads. The spheres
repel each other after being charged to +81 nC and hang at rest as shown. What is the angle θ? (k =
9
2
2
1/4πε 0 = 8.99 × 10 N · m /C )
ANSWER:
7.6°
11°
3.8°
15°
47
In the figure Q = 1.3 nC and all other quantities are accurate to 2 significant figures. What is the
9
2
2
magnitude of the force on the charge Q? (k = 1/4πε 0 = 8.99 × 10 N · m /C )
ANSWER:
2.7×10−4 N
4.1×10−4 N
2.3×10−4 N
2.0×10−4 N
48
A proton is placed in an electric field of intensity 400 N/C. What are the magnitude and direction of the
-27
-19
acceleration of this proton due to this field? (m proton = 1.67 × 10 kg, e = 1.60 × 10 C)
ANSWER:
3.83 × 1010 m/s2 in the direction of the electric field
3.83 × 109 m/s2 opposite to the electric field
38.3 × 1010 m/s2 in the direction of the electric field
38.3 × 1010 m/s2 opposite to the electric field
3.83 × 1010 m/s2 opposite to the electric field