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HKAL Extra Exercise : Part 4 Electricity and Electromagnetism
Chapter 13 Electrostatics
13.1 Electric Charges : Charging Object
1.
Two uncharged metal spheres, A and B,
supported by insulating stands are placed
side by side but not touching each other. A
student places a positively-charged rod
near sphere A and he touches sphere B
with his finger. After the rod is removed,
he moves his finger away from the sphere.
What are the signs of the charges induced
on the spheres ?
Sphere A
Sphere B
A. positive
neutral
B. negative
neutral
C. neutral
positive
D. neutral
neutral
(1) The ball always carries negative
charges.
(2) If the separation of the metal plates
decreases,
the
frequency
of
oscillation of the ball decreases.
(3) The galvanometer shows a current,
sometimes positive, and sometimes
negative.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
3.
2.
insulating thread
A conducting ball is suspended between
two metal plates connected through a
sensitive centre-zero galvanometer to a
source of high p.d. The ball shuttles back
A light conducting sphere is hanged from
a long insulating thread between
oppositely charged metal plates connected
to a high voltage supply. If the sphere is
given a positive charge, it will
A. oscillate, touching each plate in
turn, beginning with the negative plate.
B. oscillate, touching each plate in
turn, beginning with the positive plate.
C. move to the positive plate and
and forth between the plates, making
alternate contacts with each plate. Which
of the following statements is/are
stick to it.
D. move to the negative plate and
stick to it.
source of
high voltage
G
+
INCORRECT?
HKAL Extra Exercise Chapter 13 Electrostatics
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13.2 Electric Fields
Electric Field Strength
4.
Two parallel metal plates are placed horizontally with a separation of 0.20 m. A p.d. V is
connected across the plates. An oil drop with a charge of –1.6 × 10-19 C and mass 8.0 × 10-17
kg is observed to remain at rest between the plates. (Assume g = 10 m/s2.) The p.d. V is
A. 10 V.
B. 100 V.
C. 1 kV.
D. 5 kV.
5.
A stationary charged particle is accelerated across the gap between two parallel metal plates
maintained at a certain potential difference in a vacuum. Assuming there is no gravitational
force, the speed acquired by the charged particle in crossing the gap depends on
(1) the mass of the charged particle.
(2) the potential difference between the plates.
(3) the charge of the charged particle.
A. (1) only
B. (1) and (2) only
C.
(2) and (3) only
D.
(1), (2) and (3)
Motion of a charge in a uniform E-field
6.
7.
4 3
IV
v
X
III
II
1
2
The diagram shows an electron in a
uniform, vertical electric field E. At the
instant shown, the electron is traveling in
the direction of the arrow v. Which of the
arrows 1 to 4 gives the direction of the
acceleration of the electron at this instant?
A. 1
B. 2
C. 3
D. 4
HKAL Extra Exercise Chapter 13 Electrostatics
I
E
Y
E
A particle carrying a positive charge is
free to move in a uniform electric field E.
If the particle starts with a certain velocity
from point X, which of the paths shown
could represent the route which the
particle would follow from X to Y?
A.
B.
C.
D.
II only
I and II only
III and IV only
I, II, III and IV
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8.
The straight lines in the diagram represent
electric field lines. Which of the following
9.
Y
statements about this electric field is/are
INCORRECT ?
P
X
Q
R
(1) A stationary positive charge placed at
Q tends to move to P.
(2) Work has to be done in moving a
positive charge from P to R.
(3) The electric field strength at P is
stronger than that at Q.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
13.3 Coulomb’s Law
E due to a Point Charge
10.
+Q
q
W
In the above figure the solid lines represent part
of an electric field due to a fixed point charge
Q ( not shown in the figure). A charged particle
q, subjected only to electric force in the field,
travels along the dotted curve shown. Which of
the following conclusions can be drawn ?
A.
B.
C.
q is travelling from Y to X.
q has a greater speed at Y than at X.
The electric potential at X due to Q is
higher than that at Y.
The charge of q has different sign as
that of Q.
D.
E due to a Circle of Charge
11.
P2
4b
X
Z
+Q
Y
-Q
Three charges +Q, -Q and +Q are fixed at
the corners W, Y and Z respectively of a
square as shown. A fourth charge, q, is
fixed at X, after which the charge at X
experiences a NET electrostatic force
indicated by the arrow. q is equal to
A. -Q.
B. -2Q.
C.
D.
- 2 Q.
-2 2 Q.
P1
b
b
b
A uniformly charged wire has the form of
a circular loop of radius b. P1 and P2 are
two points on the axis of the loop. P1 is at
a distance b from the loop centre and P2 is
at a distance 5b from the loop centre. At
P1, P2, the potentials are V1, V2
respectively. V1 / V2 is equal to
A.
C.
HKAL Extra Exercise Chapter 13 Electrostatics
13 .
3.
B.
D.
17 / 2 .
5.
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12. Six identical point charges, each of charge Q, are fixed evenly on a circle of radius r. How
much work has to be done to bring another point charge Q from infinity to the centre of the
circle ? (ε0 = permittivity of free space)
A.
zero
B.
3Q
20 r
C.
3Q 2
20 r
D.
3Q 2
20 r 2
E on the surface of a Uniform Conductor
13. An uncharged metal sphere is placed in a uniform electric field. Which of the following best
represents the electric field pattern around the metal sphere ?
A.
B.
C.
D.
13.4 Electric Potential
Potential
14. Which of the following pairs of physical quantities is/are both vectors ?
(1) electric force and electric field intensity
(2) pressure and force
(3) mass and gravitational potential
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only
15. Two insulated uncharged metal spheres X and Y are in contact with each other. A positively
charged rod is brought near X without any contact while sphere X is earthed as shown.
X
Y
At steady state, which of the following descriptions is/are correct ?
(1)
(2)
(3)
(4)
Sphere X gains electrons.
Sphere Y loses electrons.
Sphere X acquires a positive electric potential.
Sphere Y acquires a positive electric potential.
A. (1) only
B. (1) and (2) only
C. (1) and (3) only
D. (1), (2), (3) and (4).
HKAL Extra Exercise Chapter 13 Electrostatics
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Potential Difference
16. The specific charge (charge per unit mass)
of a Zn+2 ion is 5.1 × 106 C/kg. A dry cell
with a zine anode has an e.m.f. of 2.17 V.
When the cell drives a current round a
circuit, zinc is removed from the anode.
Assuming that the system is a perfectly
efficient converter of energy, what is the
electrical energy produced per kg of zinc ?
A. 0.43 J
B. 1.1 MJ
C. 2.43 MJ
D. 11 MJ
A.
(1) only
B.
C.
D.
(3) only
(1) and (2) only
(2) and (3) only
18.
H
Y
vertical
X
A potential difference V is maintained
17. Which of the following statements about
the coulomb is/are correct?
(1) When one coulomb of charge flows
across a potential difference of one
volt, 103 joule of energy is released.
(2) 1 coulomb is the charge on 1 mole of
electrons.
(3) The force exerted on a charge of 1
coulomb in an electrostatic field of 1
volt/metre is 1 newton.
between plates X and Y, separated by a
distance h. A particle of mass m and
negative charge -q enters the region
between X and Y through the hole H with
negligible velocity. If it makes no
collisions on the way, it will strike X with
kinetic energy.
A. mgh.
B. qV + mgh.
C. qV - mgh.
D. mgh – qV.
Potential due to a Point Charge
19. Which of these statements concerning
electric potential is correct?
A. Potential is a scalar quantity.
B. The potential at a point is
proportional to the gradient of
the strength of the electric field
at that point.
C.
D.
The potential due to a point
charge varies as 1/r2, where r is
the distance from the point
charge.
The potential is zero whether the
electric field is zero.
20. How do the two physical quantities below
change along the direction indicated by an
electric field line from a point positive
charge ?
(1) electric field intensity E
(2) potential V
A. Only E will increase
B.
C.
D.
21.
A
HKAL Extra Exercise Chapter 13 Electrostatics
Both E and V will increase
Both E and V will decrease
Both E and V will remain
constant
B
C
D
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A, B, C and D are four points on a straight
line as shown. A point charge –Q is fixed
following statements is/are correct ?
(1) The two charges +q are at the same
at A. When another point charge +Q is
moved from B to C, which of the
following quantities will increase ?
(1) The magnitude of the electric field
strength at the point D.
(2) The electric potential energy of the
system of charges.
(3) The electric potential at the point D.
A. (1) only
B. (3) only
C. (2) and (3) only
potential.
(2) The work done in bringing the two
charges +q from infinity to their
respective positions is the same.
(3) The potential energy of the system
would increase if d decreases.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
D.
(1), (2) and (3)
24.
a
-q
+2 q
22.
a
-particle
electron
The above diagram shows a α-particle
and an electron moving directly away
from each other with the same speed.
Which of the following statements is/are
correct ?
(1) The two particles repel one another.
(2) The total momentum of the two
particles remains constant in the
subsequent motion.
(3) The electric potential energy of the
two particles is decreasing at the
instant shown.
A. (1) only
B. (2) only
C. (1) and (3) only
D. (1), (2) and (3)
23.
+q
+q
d
a
+Q
d
In the above arrangement, two small test
charges +q are brought from infinity to the
positions shown. The two charges are
collinear with another charge +Q and their
mutual separation is d. Which of the
HKAL Extra Exercise Chapter 13 Electrostatics
+2 q
a
-q
Four particles carrying charges +2q, +2q,
-q and -q are placed at the vertices of a
square of side a. The electric potential at
the center of the square is
A.
 2q
2 0 a
B.
 2q
 0 a
C.
 2q
2 0 a
D.
 2q
 0 a
25. The electric potential energy of a system
of charges at infinitely large distances
from one another is taken to be zero. What
is the electric potential energy stored in a
system of three charges, each of +1 C,
placed at the vertices of a equilateral
triangle with length of side 1 m ? (  o =
permittivity of vacuum)
A.
C.
3

1
2 
B.
D.
1 
1 
2 

 o 
2
3
4
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Potential due to a Metal Sphere
26. Permittivity of free space = 8.85 × 10-12
29.
F/m. A conducting sphere of radius 0.15 m
carries a positive charge of 10-6 C. A
particle P of mass 4 × 10-5 kg carrying a
a
negative charge of 10-8 C is released from
rest at a distance of 0.5 m from the center
of the sphere. If the force due to gravity is
neglected, the velocity of P when it strikes
the surface of the sphere will be
A. 3.3 m/s.
B. 4.6 m/s.
C.
D.
A.
C.
28. Which of the graphs below best represents
the variation of electrical field intensity E
with distance r from the centre of a
charged hollow metal sphere of external
radius a ?
A.
B.
0
E
a
r
C.
0
a
r
D.
E
0
A negatively-charged metal sphere A of
radius a is joined by a conducting wire to
an uncharged metal sphere B of radius b
placed far away from the first sphere. The
ratio of the total surface charge on sphere
A to that on sphere B is
8.1 × 10-9 C m-2
9.8 × 10-9 C m-2
E
E
a
r
B
A
13.5 m/s.
21.0 m/s.
27. A metal sphere is charged to a potential of
300 V. If the radius of the sphere is 0.27 m,
find the charge density on its surface.
(Given : permittivity of free space = 8.85
× 10-12 F m-1)
A. 1.1 × 10-9 C m-2
B. 4.9 × 10-9 C m-2
C.
D.
b
0
a
HKAL Extra Exercise Chapter 13 Electrostatics
r
b/a .
b/a.
B.
D.
a/b.
a2/b2.
30.
small hole
+Q
The arrangement above shows two
concentric hollow metal spheres of inner
radius b and outer radius a. A charge +Q is
given to the outer sphere and the inner
sphere is earthed.
What is the work done in bringing a small
positive charge q from infinity to the
surface of the inner sphere?
A. qQ(1/a – 1/b)/(4πε0)
B.
C.
D.
qQ(1/b – 1/a)/(4πε0)
qQ/(4πε0a)
qQ/(4πε0b)
31. An isolated spherical conductor of radius r
is charged to a total charge of Q. The total
electrical energy stored is
A. Q2 / (8πε0r).
B. Q2 / (4πε0r).
C. Q2 × 2πε0r. D.Q2 × 4πε0r.
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32. Which of the following graphs shows correctly the relationship between the energy E stored in
an isolated conducting sphere and the potential V at the surface of it ?
A.
B.
E
0
C.
E
V
0
E
V
0
Electric Field and Potential
33.
X
Y
D.
Z
The diagram shows a pattern of electric
field lines in which X, Y and Z are points
marked on one of the field lines. It would
be correct to say that
(1) a positive charge placed at Z would
accelerate to the right along the
tangent to the field line at Z.
(2) X is at a higher potential than Z.
(3) the force exerted on a charge at Z
would be greater than if the charge
were placed at X.
A. (1) only B. (1) and (2) only
C. (2) and (3) only
D. (1), (2) and (3)
34.
E
V
V
0
lines in which X, Y and Z are points
marked on one of the field lines with XY =
YZ. If the potential at X is -400 V, which of
the following can give the possible
potentials at Y and at Z ?
Potential at Y Potential at Z
A.
- 150 V
0V
B.
- 250 V
0V
C.
- 550 V
- 750 V
D.
- 600 V
- 750 V
35. X, Y are two different points in an electric
field. A small charged object is released
from rest at X. Which of the following
conditions would ensure that the charged
object will NOT pass through Y ?
A. The electric potential at X is
stronger than that at Y.
B. The electric field at Y is stronger
than that at X.
C. The electric potentials at X and
Y are equal.
D. The electric potential at Y is
zero.
X Y Z
The figure shows a pattern of electric field
HKAL Extra Exercise Chapter 13 Electrostatics
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36. Two insulated parallel metal plates are
connected to the terminals of an EHT.
37. Two parallel plates are connected to an
E.H.T. of 2.0 kV. Electric breakdown
When a charged aluminium foil strip is
placed between the plates, deflection of
the foil is observed as shown.
occurs when the separation of the plates is
reduced to 1.2 mm. Estimate the
maximum acceleration of an electron
between the plates.(Given : charge of an
electron = 1.6 × 10-19 C; mass of an
electron = 9.1 × 10-31 kg)
A. 2.0 × 109 m s-2
B. 4.2 × 1011 m s-2
C. 3.7 × 1015 m s-2
D. 2.9 × 1017 m s-2
polystyrene
rod metal
plate
metal
plate
aluminium
foil strip
+
EHT -
Which of the following statements is/are
true ?
(1) Deflection of the foil increases if the
separation between the plates increases.
(2) The charge on the foil is negative.
(3) When moving the foil towards the
negative plate, the deflection of the foil
remains unchanged.
A. (1) only
B. (3) only
C. (1) and (2) only
D.
(2) and (3) only
Equipotential Surface
38.
- 100 V
X
Y
Z
- 200 V
- 300 V
- 400 V
The diagram shows points of equal potential joined as equipotential lines. Which of the
following statements is/are correct ?
(1) The electric field at Z is in a direction tangential to the line passing through Z.
(2) The electric field at point Y is greater than that at X.
(3) Work has to be done in moving an electron from point X to point Z.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
HKAL Extra Exercise Chapter 13 Electrostatics
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39. Which of the following statements about equipotential lines is incorrect ?
A. They are closest where the field is strongest.
B.
C.
D.
They are always perpendicular to electric field lines.
The electric field strength is the same at the same equipotential line.
Work has to be done in moving a proton from a low potential line to a high potential
line.
Ice-pail Experiment (Gold-leaf Electroscope)
40. A gold-leaf electroscope is negatively charged. Which of the following objects when placed
near the cap, will cause the leaf of the electroscope to raise ?
(1) a negatively charged rod
(2) a lighted match
(3) an earthed metal plate
A. (1) only
B. (3) only
C. (2) and (3) only
D. (1), (2) and (3)
KEY :
1 – 10 : DDACD, BCDDD, 11 – 20 : ACDCC, DBBAC,
21 – 30 : DBBCD, BDDBA, 31 – 40 : ADBDC, BDBCA.
HKAL Extra Exercise Chapter 13 Electrostatics
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