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EXERCISE–1: Basic Objective Questions
Electrostatic Potential
- Electric Potential is a:
(a) Scalar quantity (b) Vector quantity
(c) Both of the above (d) None of the above
- The work done on a unit positive charge in bringing
it from infinity to any point in the field is called
(a) Electric potential at that point
(b) Electric intensity at that point
(c) Capacity
(d) Electric potential energy at that point
- Which of the following is proportional to the inverse
square of distance r.
(a) The potential at a distance r from an isolated
point charge
(b) Electric field at distance r from an isolated point
charge
(c) The force per unit length between two thin
straight charged conductors separated by distance r
(d) Electrostatic force between two large charged
sheets kept at small separation apart.
- In the figure shown, if W A represents the work done
in taking a point charge from P to A, W B to take the
point charge from P to B and W C from P to C, then
(a) A B C
W W W (b) A B C
W W W
(c) A B C
W W W (d) A B C
W W W
- The electric potential at a point in free space due to a
charge Q coulomb is Q × 10
11 V. The electric field at
that point is
(a) 4π 0
Q × 10
22 V/m
(b) 12π 0
Q × 10
22 V/m
(c) 8π 0
Q × 10
22
V/m
(d) 24π 0
Q × 10
22
V/m
6. Two electric charges 12 C and 6 Care placed 20
cm apart in air. There will be a point P on the line
joining these charges and outside the region between
them, at which the electric potential is zero. The
distance of P from 6 Ccharge is
(a) 0.10 m (b) 0.15 m
(c) 0.20 m (d) 0.25 m
- As shown in the figure, charges +q and – q are placed
at the vertices B and C of an isosceles triangle. The
potential at the vertex A is
(a)
2 2
0
q
a b
(b) Zero
(c)
2 2
0
q
a b
(d)
2 2
0
q
a b
- A point charge q is rotated along a circle in the
electric field generated by another point charge Q.
The work done by the electric field on the rotating
charge in one complete revolution is
(a) zero
(b) positive
(c) negative
(d) zero if the charge Q is at the centre and nonzero
otherwise.
- A 500 mC charge is at the Centre of a square of side
10 cm. Find the work done in moving the charge of
10 μC between two diagonally opposite points on the
square.
(a) 2 J (b) 0 J
(c) 4 J (d) 25 J
- A charge of 8 mC is located at the origin. Calculate
the work done in taking a small charge of –2 × 10
from a point P (0, 0, 3 cm) to a point Q (0, 4 cm, 0),
via a point R (0, 6 cm, 9 cm).
(a) 1.2J (b) 2J
(c) 4J (d) 1J
- Positive and negative point charges of equal
magnitude are kept at 0,0,
a
and 0, 0,
a
respectively. The work done by the electric field
when another positive point charge is moved from (–
a, 0, 0) to (0, a, 0) is
(a) positive
(b) negative
(c) zero
(d) depends on the path connecting the initial and
final positions
- Four point charges – Q, – q, 2q and 2Q are placed,
one at each corner of the square. The relation
between Q and q for which the potential at the centre
of the square is zero is
(a) Q = − q (b)
Q
q
(c) Q = q (d)
Q
q
- Four charges
8
1
q 2 10 C
8
2
q 2 10 C
8
3
q 3 10 C
and
8
4
q 6 10 C
are placed at four
corners of a square of side 2 m. What is the
potential at the centre of the square?
(a) 270 V (b) 300 V
(c)Zero (d) 100 V
Equipotential Surfaces
- Which of the following is not the property of
equipotential surfaces?
(a) They do not cross each other
(b) They are concentric spheres for uniform electric
field
(c) Rate of change of potential with distance on them
is zero
(d) They can be imaginary spheres
- What is not true for equipotential surface for uniform
electric field?
(a) Equipotential surface is flat
(b) Equipotential surface is spherical
(c) Electric field lines are perpendicular to
equipotential surface
(d) Work done is zero
- The work done in moving a positive charge on an
equipotential surface is
(a) finite and positive (b) infinite
(c) finite and negative (d) zero
- In a uniform electric field
(a) All points are at same potential
(b) no two points can have same potential
(c) pair of points separated by same distance must
have same difference of potential
(d) none of these
- The electric field lines are closer together near an
object A than they are near an object B, we can
conclude
(a) The potential near A is greater than near B
(b) The potential near A is less than near B
(c) The potential near A is equal to potential near B
(d) nothing about relative potential be predicted
- A circle of radius R is drawn in a uniform electric
field E as shown in the fig. V A
, V
B
, V
C and V D are
respectively the potentials of points A, B, C and D on
the circle then: -
(a) , A C B D
V V V V (b) , A C B D
V V V V
(c) , A C B D
V V V V (d) , A C B D
V V V V
- An electric field is spread uniformly in Y-axis.
Consider a point A as origin point. The coordinates
of point B are equal to (0, 2) m. The coordinates of
point C are (2, 0) m. At points A B, and C, electric
potentials are , , A B C
V V and V respectively. From the
following options, which is correct?
(a) A C B
V V V (b) A B C
V V V
(c) A B C
V V V (d) A C B
V V V
- The potential of the electric field produced by point
charge at any point (x,y,z) is given by
2
V 3 x 5 ,
where x, y are in metre and V is in volt. The intensity
of the electric field at
is
(a)
1
17 Vm
(b)
1
17 Vm
(c)
1
12 Vm
(d)
1
12 Vm
- In a certain region, electric field E exists along the x -
axis which is uniform. Given AB 2 3 mand BC =
4 m. Points, A, B, and C are in XY plane. Find the
potential difference V A
–V
B between the points A and
B.
(a) 3E (b) 4E
(c) E (d) 2E
Potential Energy
- In bringing an electron towards another electron, the
electrostatic potential energy of the system
(a) decreases (b) increases
(c) remains same (d) becomes zero
- If a positive charge is shifted from a low potential
region to a high potential region, then electric
potential energy
(a) decreases
(b) increases
(c) remains same
(d) may increase or decrease
- Three charges q, Q and q are placed in a straight
line as shown. If the total potential energy of the
system is zero, then the ratio q/Q is
(a) 2 (b) 5.
(c) 4 (d) 1.
- Three charges are placed at the vertex of an
equilateral triangle as shown in figure. For what
value of Q, the electrostatic potential energy of the
system is zero?
(a) – q (b) q/
(c) – 2q (d) – q/
- Two charges 1
q and 2
q are placed 30 cm apart, as
shown in the figure. A third charge 3
q is moved
along the arc of a circle of radius 40 cm from C to D.
The change in the potential energy of the system is
3
0
q
k
where k is
(a) 8q 1 (b) 6q 1
(c) 8q 2 (d) 6q 2
- As per the diagram, a point charge +q is placed at the
origin O. Work done in taking another point charge –
Q from the point A [coordinates (0, a)] to another
point B [coordinates (a; 0)] along the straight path
AB is:
(a) Zero (b) 2
0
qQ
a
a
(c)
2
0
qQ a
a
(d)
2
0
qQ
a
a
- Three point charges q, 2 q and 2 qare placed at
the vertices of an equilateral triangle of side a. The
work done by some external force to increase their
separation to 2a will be
(a)
2
0
q
a
(b)
2
0
q
a
(c) 2
0
q
a
(d) zero
- An electron of mass m and charge e is accelerated
from rest through a potential difference V in vacuum.
The final speed will be:
(a)
2 eV
m
(b)
e
v
m
(c)
3 eV
m
(d)
2 eV
m
- A proton is about 1840 times heavier than an
electron. When it is accelerated by a potential
difference of 1 kV, its kinetic energy will be:
(a) 1840 keV (b) 1/1840 keV
(c) 1 keV (d) 920 keV
- An electric dipole of moment ‘p’ is lying along a
uniform electric field ‘E’. The work done in rotating
the dipole by 90° is
(a) pE/2 (b) 2 p E
(c) p E (d) 2 p E
- An electric dipole has the magnitude of its charge as
q and its dipole moment is p. It is placed in uniform
electric field E. If its dipole moment is along the
direction of the field, the force on it and its potential
energy are respectively
(a) q. E and max. (b) 2 q. E and min.
(c) q. E and p.E (d) zero and min.
Electrostatics of Conductors
- A metallic solid sphere is placed in a uniform electric
field. The field lines follow the path(s) shown in
figure as
(a) 1 (b) 2
(c) 3 (d) 4
- Which of the following figures cannot possibly
represent electrostatics field lines
(a) i, ii, iii, iv (b) i, ii, iii only
(c) i, iii, iv only (d) ii, iii, iv only
- A point charge ‘q’ is placed at a point inside a hollow
conducting sphere. Which of the following electric
force pattern is correct?
(a) (b)
(c) (d)
- The electrostatic potential of a uniformly charged
thin spherical shell of charge Q and radius R at a
distance r from the centre is
(a)
0
Q
r
for points outside and
0
Q
R
for points
on surface of the sphere
(b)
0
Q
r
for both points inside and outside the shell
(c) zero for points outside and
0
Q
r
for points
inside the shell
(d) zero for both points inside and outside the shell
- Two charged spheres of radii R 1 and R 2 have equal
surface charge density. The ratio of their potential is
(a) R 1
/R
2 (b) R 2
/R
1
(c) (R 1
/R
2
2
(d) (R 2
/R
1
2
- An arc of radius r carries charge. The linear density
of charge is and the arc subtends an angle π/3 at
the centre. What is electric potential at the centre
(a)
0
(b)
0
(c)
0
(d)
0
- The potential of a large liquid drop when eight liquid
drops are combined is 20 V. Then, the potential of
each single drop was
(a) 10 V (b) 7.5 V
(c) 5 V (d) 2.5 V
- A solid sphere of radius R is charged uniformly
throughout the volume. At what distance from its
centre is the electric potential
of the potential at
the centre?
(a)
R
(b)
R
(c)
R
(d)
R
- A hollow charged metal sphere has radius r. If the
potential difference between its surface and a point at
a distance 3r from the centre is V, then electric field
intensity at a distance 3r is
(a)
V
r
(b)
V
r
(c)
V
r
(d)
V
r
- If the potential at the centre of a uniformly charged
hollow sphere of radius R is V then electric field at a
distance r from the centre of sphere will be (r > R) :
(a) 2
VR
r
(b) 2
Vr
R
(c)
VR
r
(d) 2 2
VR
R r
- A ball with charge – 50e is placed at the centre of a
hollow spherical shell has a net charge of – 50e.
What is the charge on the shell’s outer surface?
(a) – 50 e (b) Zero
(c) – 100 e (d) + 100 e
- n identical mercury droplets charged to the same
potential V coalesce to form a single bigger drop.
The potential of new drop will be
(a) V/n (b) nV
(c)
2
nV (d)
2/ 3
n V
- Consider a thin spherical shell of radius R with its
centre at the origin carrying uniform positive surface
charge density. The variation of the magnitude of the
electric field |E (r)| and the electric potential V (r)
with the distance r from the centre, is best
represented by which graph?
(a)
(b)
(c)
(d)
- Two concentric metallic spherical shells are given
unequal positive charges. Then,
(a) the outer sphere is always at a higher potential
(b) the inner sphere is always at a higher potential
(c) both the spheres are at the same potential
(d) no prediction can be made about their potentials
unless the actual values of charges and radii are
known
- Two concentric spheres kept in air have radii R and r.
They have similar charge and equal surface charge
density . The electrical potential at their common
centre is (where, 0
= permittivity of free space)
(a)
0
( R r)
(b)
0
( R r)
(c)
0
R r
(d)
0
R r
- A charge q is distributed uniformly on the surface of
a solid sphere of radius R. It is covered by a
concentric hollow conducting sphere of radius 2R.
Find the charge on outer surfaces of hollow sphere if
it is earthed.
(a)
q
(b) 2 q
(c) 4 q (d) Zero
- A small conducting sphere of radius a, carrying a
charge +Q, is placed inside an equal and oppositely
charged conducting shell of radius b such that their
centers coincide. Determine the potential at a point
which is at a distance c from center such that a < c <
b.
(a)
Q Q
k
c b
(b)
Q Q
k
a b
(c)
Q Q
k
a b
(d)
Q Q
k
c b
Dielectrics and Polarization
- When air medium in which two charges kept apart at
a distance r is replaced by a dielectric medium of
dielectric constant K, the force between the charges
is
(a) remain unchanged (b) 1/K times
(c) 2
times
K
(d)
2
K times
- In which type of molecule positive and negative
charges coincide with each other?
(a) Bipolar (b) Unipolar
(c) Non-polar (d) Polar
- What is the ratio of the polarization to ε o times the
electric field called?
(a) Dielectric strength
(b) Dielectric susceptibility
(c) Polarisation density
(d) Electric susceptibility
- What is the induced dipole moment developed per
unit volume of a dielectric when placed in an external
electric field called?
(a) Polarisation density
(b) Polarisation susceptibility
(c) Electric susceptibility
(d) Relative permittivity
- ‘X’ is a substance which does not allow the flow of
charges through it but permits them to exert
electrostatic forces on one another through it. Identify
X.
(a) Polar molecule (b) Dielectric
(c) Non-polar molecule (d) Equipotential
Capacitors and Capacitance
- The SI unit of capacitance is-
(a) Farad (b) Coulomb
(c) Joule/ Coulomb (d) Volt
- The capacitance (C) of a conductor or condenser is
defined as
(a) ratio of charge to its potential
(b) ratio of potential to the charge
(c) Work done per unit charge on it
(d) work done to circulate unit positive charge
through complete circuit
- The potentials of the two plates of capacitors are +
V and –10 V. The charge on one of the plates is 40 C.
The capacitance of the capacitor is
(a) 2 F (b) 4 F
(c) 0.5 F (d) 0.25 F
