Electrostatics Multiple-Choice Practice Questions | AP Physics C Electricity and Magnetism - Grade 9 PDF Download

 Page 1


Section I: Multiple Choice
1. What will happen to the magnitude of electric force between two particles if the distance
between them is doubled and each charge is tripled?
(A) It will be multiplied by a factor of .
(B) It will be multiplied by a factor of .
(C) It will be multiplied by a factor of .
(D) It will be multiplied by a factor of .
(E) It will be multiplied by a factor of .
2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does F
E
, the strength of the
electric force between the spheres, compare to F
G
, the strength of their gravitational
attraction?
(A) F
E
 < F
G
(B) F
E
 = F
G
(C) F
E
 > F
G
(D) If the charges on the spheres are of the same sign, then F
E
 > F
G
; but if the charges on the
spheres are of opposite sign, then F
E
 < F
G
.
(E) Cannot be determined without knowing the distance between the spheres
3. The particle shown above is initially at rest inside a uniform electric field E = 50 N/C toward
the left. The field area is a square with 1 m long sides. If the particle has a mass of 10
-10
 kg and
a charge of q = -5 × 10
-13
 C, how long will it take the particle to escape the electric field?
(A) 1.10 s
(B) 1.23 s
(C) 1.55 s
(D) 2.31 s
(E) 2.59 s
Page 2


Section I: Multiple Choice
1. What will happen to the magnitude of electric force between two particles if the distance
between them is doubled and each charge is tripled?
(A) It will be multiplied by a factor of .
(B) It will be multiplied by a factor of .
(C) It will be multiplied by a factor of .
(D) It will be multiplied by a factor of .
(E) It will be multiplied by a factor of .
2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does F
E
, the strength of the
electric force between the spheres, compare to F
G
, the strength of their gravitational
attraction?
(A) F
E
 < F
G
(B) F
E
 = F
G
(C) F
E
 > F
G
(D) If the charges on the spheres are of the same sign, then F
E
 > F
G
; but if the charges on the
spheres are of opposite sign, then F
E
 < F
G
.
(E) Cannot be determined without knowing the distance between the spheres
3. The particle shown above is initially at rest inside a uniform electric field E = 50 N/C toward
the left. The field area is a square with 1 m long sides. If the particle has a mass of 10
-10
 kg and
a charge of q = -5 × 10
-13
 C, how long will it take the particle to escape the electric field?
(A) 1.10 s
(B) 1.23 s
(C) 1.55 s
(D) 2.31 s
(E) 2.59 s
4. Points A and B are equidistant from point P. At point A, there is a particle of charge + Q. This
results in an electric field, E, at point P. If we want to triple the electric field at P, what charge
should be placed at point B?
(A) +3 Q
(B) +2 Q
(C)  -Q
(D) -2 Q
(E) -3 Q
5. A sphere of charge + Q is fixed in position. A smaller sphere of charge + q is placed near the
larger sphere and released from rest. The small sphere will move away from the large sphere
with
(A) decreasing velocity and decreasing acceleration
(B) decreasing velocity and increasing acceleration
(C) decreasing velocity and constant acceleration
(D) increasing velocity and decreasing acceleration
(E) increasing velocity and increasing acceleration
6. A particle of negligible mass and charge q = 1 µC is fixed in place. A small object of mass m =
10
-3
 kg and charge q = 1 µC is released from rest from a position 1 m directly above the
particle. How far does the object fall before the electric force manages to push it away?
(A) 0.1 m
(B) 0.3 m
(C) 0.5 m
(D) 0.7 m
(E) 0.9 m
7. A conducting sphere of radius R has a charge of + Q. If the electric field at a point 2 R from the
center has an electric field of E, what is the electric field at a point  from the center?
(A) 0
(B) E
(C) E
(D) 2 E
(E) 4 E
8. The figure below shows four point charges and the cross section of a Gaussian surface:
Page 3


Section I: Multiple Choice
1. What will happen to the magnitude of electric force between two particles if the distance
between them is doubled and each charge is tripled?
(A) It will be multiplied by a factor of .
(B) It will be multiplied by a factor of .
(C) It will be multiplied by a factor of .
(D) It will be multiplied by a factor of .
(E) It will be multiplied by a factor of .
2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does F
E
, the strength of the
electric force between the spheres, compare to F
G
, the strength of their gravitational
attraction?
(A) F
E
 < F
G
(B) F
E
 = F
G
(C) F
E
 > F
G
(D) If the charges on the spheres are of the same sign, then F
E
 > F
G
; but if the charges on the
spheres are of opposite sign, then F
E
 < F
G
.
(E) Cannot be determined without knowing the distance between the spheres
3. The particle shown above is initially at rest inside a uniform electric field E = 50 N/C toward
the left. The field area is a square with 1 m long sides. If the particle has a mass of 10
-10
 kg and
a charge of q = -5 × 10
-13
 C, how long will it take the particle to escape the electric field?
(A) 1.10 s
(B) 1.23 s
(C) 1.55 s
(D) 2.31 s
(E) 2.59 s
4. Points A and B are equidistant from point P. At point A, there is a particle of charge + Q. This
results in an electric field, E, at point P. If we want to triple the electric field at P, what charge
should be placed at point B?
(A) +3 Q
(B) +2 Q
(C)  -Q
(D) -2 Q
(E) -3 Q
5. A sphere of charge + Q is fixed in position. A smaller sphere of charge + q is placed near the
larger sphere and released from rest. The small sphere will move away from the large sphere
with
(A) decreasing velocity and decreasing acceleration
(B) decreasing velocity and increasing acceleration
(C) decreasing velocity and constant acceleration
(D) increasing velocity and decreasing acceleration
(E) increasing velocity and increasing acceleration
6. A particle of negligible mass and charge q = 1 µC is fixed in place. A small object of mass m =
10
-3
 kg and charge q = 1 µC is released from rest from a position 1 m directly above the
particle. How far does the object fall before the electric force manages to push it away?
(A) 0.1 m
(B) 0.3 m
(C) 0.5 m
(D) 0.7 m
(E) 0.9 m
7. A conducting sphere of radius R has a charge of + Q. If the electric field at a point 2 R from the
center has an electric field of E, what is the electric field at a point  from the center?
(A) 0
(B) E
(C) E
(D) 2 E
(E) 4 E
8. The figure below shows four point charges and the cross section of a Gaussian surface:
Which of the following statements is true concerning the situation depicted?
(A) The net electric flux through the Gaussian surface depends on all four charges shown, but
the electric field at point P depends only on charges Q
2
 and Q
3
.
(B) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, but
the electric field at point P depends on all four charges.
(C) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, and
the electric field at point P depends only on charges Q
2
, Q
3
, and Q
4
.
(D) The net electric flux through the Gaussian surface depends only on charges Q
1
 and Q
4
, and
the electric field at point P depends only on charges Q
2
 and Q
3
.
(E) Both the net electric flux through the Gaussian surface and the electric field at point P
depend on all four charges.
9. A nonconducting sphere of radius R contains a total charge of - Q distributed uniformly
throughout its volume (that is, the volume charge density, ? is constant).
The magnitude of the electric field at Point P, at a distance r < R from the sphere’s center, is
equal to
(A)
(B)
(C)
(D)
Page 4


Section I: Multiple Choice
1. What will happen to the magnitude of electric force between two particles if the distance
between them is doubled and each charge is tripled?
(A) It will be multiplied by a factor of .
(B) It will be multiplied by a factor of .
(C) It will be multiplied by a factor of .
(D) It will be multiplied by a factor of .
(E) It will be multiplied by a factor of .
2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does F
E
, the strength of the
electric force between the spheres, compare to F
G
, the strength of their gravitational
attraction?
(A) F
E
 < F
G
(B) F
E
 = F
G
(C) F
E
 > F
G
(D) If the charges on the spheres are of the same sign, then F
E
 > F
G
; but if the charges on the
spheres are of opposite sign, then F
E
 < F
G
.
(E) Cannot be determined without knowing the distance between the spheres
3. The particle shown above is initially at rest inside a uniform electric field E = 50 N/C toward
the left. The field area is a square with 1 m long sides. If the particle has a mass of 10
-10
 kg and
a charge of q = -5 × 10
-13
 C, how long will it take the particle to escape the electric field?
(A) 1.10 s
(B) 1.23 s
(C) 1.55 s
(D) 2.31 s
(E) 2.59 s
4. Points A and B are equidistant from point P. At point A, there is a particle of charge + Q. This
results in an electric field, E, at point P. If we want to triple the electric field at P, what charge
should be placed at point B?
(A) +3 Q
(B) +2 Q
(C)  -Q
(D) -2 Q
(E) -3 Q
5. A sphere of charge + Q is fixed in position. A smaller sphere of charge + q is placed near the
larger sphere and released from rest. The small sphere will move away from the large sphere
with
(A) decreasing velocity and decreasing acceleration
(B) decreasing velocity and increasing acceleration
(C) decreasing velocity and constant acceleration
(D) increasing velocity and decreasing acceleration
(E) increasing velocity and increasing acceleration
6. A particle of negligible mass and charge q = 1 µC is fixed in place. A small object of mass m =
10
-3
 kg and charge q = 1 µC is released from rest from a position 1 m directly above the
particle. How far does the object fall before the electric force manages to push it away?
(A) 0.1 m
(B) 0.3 m
(C) 0.5 m
(D) 0.7 m
(E) 0.9 m
7. A conducting sphere of radius R has a charge of + Q. If the electric field at a point 2 R from the
center has an electric field of E, what is the electric field at a point  from the center?
(A) 0
(B) E
(C) E
(D) 2 E
(E) 4 E
8. The figure below shows four point charges and the cross section of a Gaussian surface:
Which of the following statements is true concerning the situation depicted?
(A) The net electric flux through the Gaussian surface depends on all four charges shown, but
the electric field at point P depends only on charges Q
2
 and Q
3
.
(B) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, but
the electric field at point P depends on all four charges.
(C) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, and
the electric field at point P depends only on charges Q
2
, Q
3
, and Q
4
.
(D) The net electric flux through the Gaussian surface depends only on charges Q
1
 and Q
4
, and
the electric field at point P depends only on charges Q
2
 and Q
3
.
(E) Both the net electric flux through the Gaussian surface and the electric field at point P
depend on all four charges.
9. A nonconducting sphere of radius R contains a total charge of - Q distributed uniformly
throughout its volume (that is, the volume charge density, ? is constant).
The magnitude of the electric field at Point P, at a distance r < R from the sphere’s center, is
equal to
(A)
(B)
(C)
(D)
(E)
10. Calculate the electric flux through a Gaussian surface of area A enclosing an electric dipole
where each charge has magnitude q.
(A) 0
(B) Aq/(4pe
0
)
(C) Aq
2
/4pe
0
)
(D) Aq/(4pe
0
r)
(E) Aq/(4pe
0
r
2
)
Page 5


Section I: Multiple Choice
1. What will happen to the magnitude of electric force between two particles if the distance
between them is doubled and each charge is tripled?
(A) It will be multiplied by a factor of .
(B) It will be multiplied by a factor of .
(C) It will be multiplied by a factor of .
(D) It will be multiplied by a factor of .
(E) It will be multiplied by a factor of .
2. Two 1 kg spheres each carry a charge of magnitude 1 C. How does F
E
, the strength of the
electric force between the spheres, compare to F
G
, the strength of their gravitational
attraction?
(A) F
E
 < F
G
(B) F
E
 = F
G
(C) F
E
 > F
G
(D) If the charges on the spheres are of the same sign, then F
E
 > F
G
; but if the charges on the
spheres are of opposite sign, then F
E
 < F
G
.
(E) Cannot be determined without knowing the distance between the spheres
3. The particle shown above is initially at rest inside a uniform electric field E = 50 N/C toward
the left. The field area is a square with 1 m long sides. If the particle has a mass of 10
-10
 kg and
a charge of q = -5 × 10
-13
 C, how long will it take the particle to escape the electric field?
(A) 1.10 s
(B) 1.23 s
(C) 1.55 s
(D) 2.31 s
(E) 2.59 s
4. Points A and B are equidistant from point P. At point A, there is a particle of charge + Q. This
results in an electric field, E, at point P. If we want to triple the electric field at P, what charge
should be placed at point B?
(A) +3 Q
(B) +2 Q
(C)  -Q
(D) -2 Q
(E) -3 Q
5. A sphere of charge + Q is fixed in position. A smaller sphere of charge + q is placed near the
larger sphere and released from rest. The small sphere will move away from the large sphere
with
(A) decreasing velocity and decreasing acceleration
(B) decreasing velocity and increasing acceleration
(C) decreasing velocity and constant acceleration
(D) increasing velocity and decreasing acceleration
(E) increasing velocity and increasing acceleration
6. A particle of negligible mass and charge q = 1 µC is fixed in place. A small object of mass m =
10
-3
 kg and charge q = 1 µC is released from rest from a position 1 m directly above the
particle. How far does the object fall before the electric force manages to push it away?
(A) 0.1 m
(B) 0.3 m
(C) 0.5 m
(D) 0.7 m
(E) 0.9 m
7. A conducting sphere of radius R has a charge of + Q. If the electric field at a point 2 R from the
center has an electric field of E, what is the electric field at a point  from the center?
(A) 0
(B) E
(C) E
(D) 2 E
(E) 4 E
8. The figure below shows four point charges and the cross section of a Gaussian surface:
Which of the following statements is true concerning the situation depicted?
(A) The net electric flux through the Gaussian surface depends on all four charges shown, but
the electric field at point P depends only on charges Q
2
 and Q
3
.
(B) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, but
the electric field at point P depends on all four charges.
(C) The net electric flux through the Gaussian surface depends only on charges Q
2
 and Q
3
, and
the electric field at point P depends only on charges Q
2
, Q
3
, and Q
4
.
(D) The net electric flux through the Gaussian surface depends only on charges Q
1
 and Q
4
, and
the electric field at point P depends only on charges Q
2
 and Q
3
.
(E) Both the net electric flux through the Gaussian surface and the electric field at point P
depend on all four charges.
9. A nonconducting sphere of radius R contains a total charge of - Q distributed uniformly
throughout its volume (that is, the volume charge density, ? is constant).
The magnitude of the electric field at Point P, at a distance r < R from the sphere’s center, is
equal to
(A)
(B)
(C)
(D)
(E)
10. Calculate the electric flux through a Gaussian surface of area A enclosing an electric dipole
where each charge has magnitude q.
(A) 0
(B) Aq/(4pe
0
)
(C) Aq
2
/4pe
0
)
(D) Aq/(4pe
0
r)
(E) Aq/(4pe
0
r
2
)
Section I: Multiple Choice
1. A
The magnitude of electric force will be
F
e
 = 
Multiplying each charge by 3 will result in the force being multiplied by 9. In contrast,
doubling the distance between the charges will reduce the force by a factor of 4.
Therefore, the force will be multiplied by .
2. C
The strength of the electric force is given by kq
2
/r
2
, and the strength of the gravitational
force is Gm
2
/r
2
. Since both of these quantities have r
2
 in the denominator, we simply
need to compare the numerical values of kq
2
 and Gm
2
. There’s no contest: Since
kq
2
 = (9 × 10
9
 N·m
2
/C
2
)(1 C)
2
 = 9 × 10
9
 N·m
2
and
Gm
2
 = (6.7 × 10
-11
 N·m
2
/kg
2
)(1 kg)
2
 = 6.7 × 10
-11
 N·m
2
we see that kq
2
 >> Gm
2
, so F
E
 is much stronger than F
G
.
3. C
First, take note of the particle’s negative charge. This means it will move in the opposite
direction of the electric field, thus escaping the field after traveling only 30 cm. Next, you
can treat this as a kinematics problem since the constant electric field will result in a
constant acceleration. If we define right as the positive direction, we get
4. D
First, use the fact that electric field lines point away from positive particles and toward
negative particles. The original field, E, would point to the right (because the particle
at A is positive). To amplify that field, the particle at B would have to be negative. This
eliminates (A) and (B).
Next, use superposition to determine the strength of E that the new particle must create.
E
net
 = E
1
 + E
2
 +…
E
P
 = E
A
 + E
B
  
E
B
 = E
P
 + E
A