Electrostatics- 3 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.16) : There are 16 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 Three charges 
,
Qq + and q + are placed at the vertices of
right-angled isosceles triangle as shown in the figure. The
net electrostatic energy of the configuration is zero if Q is
equal to
Q
+q +q
a
(a)
12
q -
+
(b)
2
22
q -
+
(c) –2q (d) q +
Q.2 Three charges of equal value ‘q’ are placed at the vertices
of an equilateral triangle. What is the net potential energy ,
if the side of equilateral Dis l ?
(a)
2
0
1
4pÎ
q
l
(b)
2
0
12
4pÎ
q
l
(c)
2
0
13
4pÎ
q
l
(d)
2
0
14
4pÎ
q
l
Q.3 If identical charges () q - are placed at each corner of a cube
of side 
b
, then electric potential energy of charge
() q + which is placed at centre of the cube will be
(a)
2
0
82
4
q
b pÎ
(b)
2
0
82q
b
-
pÎ
(c)
2
0
42q
b
-
pÎ
(d)
2
0
4
3
q
b
-
pÎ
Page 2


DIRECTIONS (Q.1-Q.16) : There are 16 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 Three charges 
,
Qq + and q + are placed at the vertices of
right-angled isosceles triangle as shown in the figure. The
net electrostatic energy of the configuration is zero if Q is
equal to
Q
+q +q
a
(a)
12
q -
+
(b)
2
22
q -
+
(c) –2q (d) q +
Q.2 Three charges of equal value ‘q’ are placed at the vertices
of an equilateral triangle. What is the net potential energy ,
if the side of equilateral Dis l ?
(a)
2
0
1
4pÎ
q
l
(b)
2
0
12
4pÎ
q
l
(c)
2
0
13
4pÎ
q
l
(d)
2
0
14
4pÎ
q
l
Q.3 If identical charges () q - are placed at each corner of a cube
of side 
b
, then electric potential energy of charge
() q + which is placed at centre of the cube will be
(a)
2
0
82
4
q
b pÎ
(b)
2
0
82q
b
-
pÎ
(c)
2
0
42q
b
-
pÎ
(d)
2
0
4
3
q
b
-
pÎ
2
DPP/ P 34
Q.4 Two charges 
1
q and 
2
q are placed 30 cm apart, 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
4
q
k
pÎ
, here 
k
is
(a)
2
8q
(b)
1
8q
(c)
2
6q
C
A B
D
30 cm
40 cm
2
q
1
q
3
q
(d)
1
6q
Q.5 Three particles, each having a charge of 10 C m are placed
at the corners of an equilateral triangle of side 10 cm. The
electrostatic potential energy of the system is (Given
9 22
0
1
9 10 Nm/C)
4
=´
pÎ
(a) Zero (b) Infinite (c) 27 J (d) 100 J
Q.6 Two equal charges q are placed at a distance of 
2a
and a
third charge 2q - is placed at the midpoint. The potential
energy of the system is
(a)
2
0
8pÎ
q
a
(b) 
2
0
6
8pÎ
q
a
(c)–
2
0
7
8pÎ
q
a
(d)
2
0
9
8pÎ
q
a
Q.7 An electric dipole has the magnitude of its charge is q and
its dipole moment is p . It is placed in a 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) 2. qE and minimum (b) . qE and . pE
(c) Zero and minimum (d) . qE and maximum
Q8 In bringing an electron towards another electron,
electrostatic potential energy of the system:
(a) decreases (b) increases
(c) remains unchanged (d) becomes zero
Q.9 Two identical charges are placed at the two corners of an
equilateral triangle. The potential energy of the system is
U. The work done in bringing an identical charge from
infinity to the third vertex is
(a)U (b) 2U (c) 3U (d) zero
Q.10 Potential energy of two equal negative point charges 2 mC
held 1 m apart in air is
(a) 2 J (b) 2eV (c) 4 J (d) 0.036 J
Q.11 Four charges + q, –q, + q and –q are put together on four
corners of a square as shown in figure. The work done by
external agent in slowly assembling this configuration is
+q
–q
+q –q
(a) zero (b) –2.59kq
2
/a
(c) +2.59kq
2
/a (d) none of these
Q.12 As shown in figure a dust particle with mass m = 5.0 × 10
–9
kg and charge q
0
 = 2.0 nC starts from rest at  point a and
moves in a straight line to point b . What is its speed v at
point b?
1.0 cm 1.0 cm 1.0 cm
3.0 nC –3.0 nC
a b
–
(a) 26 ms
–1
(b) 34 ms
–1  
(c)  46 ms
–1
(d) 14 ms
–1
Q.13 Charges –q, Q and –q are placed at equal distance on a
straight line. If the total potential energy of the system of
three charges is zero, then find the ratio Q/q.
–q –q
Q
2r
r r
(a) 1/2 (b) 1/4 (c) 2/3 (d) 3/4
Q.14When the separation between two charges is increased,
the electric potential energy of the charges
(a) increases (b) decreases
(c) remains the same (d) may increase or decrease
Page 3


DIRECTIONS (Q.1-Q.16) : There are 16 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 Three charges 
,
Qq + and q + are placed at the vertices of
right-angled isosceles triangle as shown in the figure. The
net electrostatic energy of the configuration is zero if Q is
equal to
Q
+q +q
a
(a)
12
q -
+
(b)
2
22
q -
+
(c) –2q (d) q +
Q.2 Three charges of equal value ‘q’ are placed at the vertices
of an equilateral triangle. What is the net potential energy ,
if the side of equilateral Dis l ?
(a)
2
0
1
4pÎ
q
l
(b)
2
0
12
4pÎ
q
l
(c)
2
0
13
4pÎ
q
l
(d)
2
0
14
4pÎ
q
l
Q.3 If identical charges () q - are placed at each corner of a cube
of side 
b
, then electric potential energy of charge
() q + which is placed at centre of the cube will be
(a)
2
0
82
4
q
b pÎ
(b)
2
0
82q
b
-
pÎ
(c)
2
0
42q
b
-
pÎ
(d)
2
0
4
3
q
b
-
pÎ
2
DPP/ P 34
Q.4 Two charges 
1
q and 
2
q are placed 30 cm apart, 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
4
q
k
pÎ
, here 
k
is
(a)
2
8q
(b)
1
8q
(c)
2
6q
C
A B
D
30 cm
40 cm
2
q
1
q
3
q
(d)
1
6q
Q.5 Three particles, each having a charge of 10 C m are placed
at the corners of an equilateral triangle of side 10 cm. The
electrostatic potential energy of the system is (Given
9 22
0
1
9 10 Nm/C)
4
=´
pÎ
(a) Zero (b) Infinite (c) 27 J (d) 100 J
Q.6 Two equal charges q are placed at a distance of 
2a
and a
third charge 2q - is placed at the midpoint. The potential
energy of the system is
(a)
2
0
8pÎ
q
a
(b) 
2
0
6
8pÎ
q
a
(c)–
2
0
7
8pÎ
q
a
(d)
2
0
9
8pÎ
q
a
Q.7 An electric dipole has the magnitude of its charge is q and
its dipole moment is p . It is placed in a 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) 2. qE and minimum (b) . qE and . pE
(c) Zero and minimum (d) . qE and maximum
Q8 In bringing an electron towards another electron,
electrostatic potential energy of the system:
(a) decreases (b) increases
(c) remains unchanged (d) becomes zero
Q.9 Two identical charges are placed at the two corners of an
equilateral triangle. The potential energy of the system is
U. The work done in bringing an identical charge from
infinity to the third vertex is
(a)U (b) 2U (c) 3U (d) zero
Q.10 Potential energy of two equal negative point charges 2 mC
held 1 m apart in air is
(a) 2 J (b) 2eV (c) 4 J (d) 0.036 J
Q.11 Four charges + q, –q, + q and –q are put together on four
corners of a square as shown in figure. The work done by
external agent in slowly assembling this configuration is
+q
–q
+q –q
(a) zero (b) –2.59kq
2
/a
(c) +2.59kq
2
/a (d) none of these
Q.12 As shown in figure a dust particle with mass m = 5.0 × 10
–9
kg and charge q
0
 = 2.0 nC starts from rest at  point a and
moves in a straight line to point b . What is its speed v at
point b?
1.0 cm 1.0 cm 1.0 cm
3.0 nC –3.0 nC
a b
–
(a) 26 ms
–1
(b) 34 ms
–1  
(c)  46 ms
–1
(d) 14 ms
–1
Q.13 Charges –q, Q and –q are placed at equal distance on a
straight line. If the total potential energy of the system of
three charges is zero, then find the ratio Q/q.
–q –q
Q
2r
r r
(a) 1/2 (b) 1/4 (c) 2/3 (d) 3/4
Q.14When the separation between two charges is increased,
the electric potential energy of the charges
(a) increases (b) decreases
(c) remains the same (d) may increase or decrease
DPP/ P 34
3
Q.15 A positive charge is moved from a low potential point A to
high potential point B. Then the electric potential energy
of the system
(a) increases
(b) decreases
(c) will remain the same
(d) nothing definite can be predicted
Q.16If V and u are electric potential and energy density,
respectively, at a distance r from a positive point charge,
then which of the following graph is correct ?
(a)
V
4
u
(b)
V
4
u
(c)
V
4
u
(d)
V
4
u
DIRECTIONS (Q.17-Q.18) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.17 S is a solid neutral conducting sphere. A point charge q of
1 × 10
–6
 C is placed at point A. C is the centre of sphere
and AB is a tangent. BC = 3m and AB = 4m.
A B
S
(1) The electric potential of the conductor is 1.8 kV
(2) The electric potential of the conductor is 2.25 kV
(3) The electric potential at B due to induced charges on
the sphere is – 0.45 kV
(4) The electric potential at B due to induced charges on
the sphere is  0.45 kV
Q.18A proton moves a distance d in a uniform electric field
E
®
as shown in the figure. Then which of the following
statements are correct ?
+
d
p
E
®
(1) Electric field do a negative work on the proton
(2) Electric potential energy of the proton increases
(3) Electric field do a positive work on the proton
(4) Electric potential energy of the proton decreases
DIRECTIONS (Q.19-Q.21) : Read the passage given below
and answer the questions that follows :
Three concentric spherical conductors A, B and C of radii R, 2R
and 4R respectively. A and C is shorted and B is uniformly
charged.
2R
4R
R
A
B
C
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
Q.19 Charge on conductor A is
(a) Q/3 (b)  – Q/3
(c)2Q/3 (d)  None of these
Q.20 Potential at A is
(a) 
0
4 pe
Q
R
(b)
0
16
Q
R pe
(c)  
0
20
Q
R pe
(d) None of these
Q.21 Potential at B is
(a)
0
4
Q
R pe
(b)
0
16
Q
R pe
(c)
0
5
48
Q
R pe
(d) None of these
Page 4


DIRECTIONS (Q.1-Q.16) : There are 16 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 Three charges 
,
Qq + and q + are placed at the vertices of
right-angled isosceles triangle as shown in the figure. The
net electrostatic energy of the configuration is zero if Q is
equal to
Q
+q +q
a
(a)
12
q -
+
(b)
2
22
q -
+
(c) –2q (d) q +
Q.2 Three charges of equal value ‘q’ are placed at the vertices
of an equilateral triangle. What is the net potential energy ,
if the side of equilateral Dis l ?
(a)
2
0
1
4pÎ
q
l
(b)
2
0
12
4pÎ
q
l
(c)
2
0
13
4pÎ
q
l
(d)
2
0
14
4pÎ
q
l
Q.3 If identical charges () q - are placed at each corner of a cube
of side 
b
, then electric potential energy of charge
() q + which is placed at centre of the cube will be
(a)
2
0
82
4
q
b pÎ
(b)
2
0
82q
b
-
pÎ
(c)
2
0
42q
b
-
pÎ
(d)
2
0
4
3
q
b
-
pÎ
2
DPP/ P 34
Q.4 Two charges 
1
q and 
2
q are placed 30 cm apart, 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
4
q
k
pÎ
, here 
k
is
(a)
2
8q
(b)
1
8q
(c)
2
6q
C
A B
D
30 cm
40 cm
2
q
1
q
3
q
(d)
1
6q
Q.5 Three particles, each having a charge of 10 C m are placed
at the corners of an equilateral triangle of side 10 cm. The
electrostatic potential energy of the system is (Given
9 22
0
1
9 10 Nm/C)
4
=´
pÎ
(a) Zero (b) Infinite (c) 27 J (d) 100 J
Q.6 Two equal charges q are placed at a distance of 
2a
and a
third charge 2q - is placed at the midpoint. The potential
energy of the system is
(a)
2
0
8pÎ
q
a
(b) 
2
0
6
8pÎ
q
a
(c)–
2
0
7
8pÎ
q
a
(d)
2
0
9
8pÎ
q
a
Q.7 An electric dipole has the magnitude of its charge is q and
its dipole moment is p . It is placed in a 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) 2. qE and minimum (b) . qE and . pE
(c) Zero and minimum (d) . qE and maximum
Q8 In bringing an electron towards another electron,
electrostatic potential energy of the system:
(a) decreases (b) increases
(c) remains unchanged (d) becomes zero
Q.9 Two identical charges are placed at the two corners of an
equilateral triangle. The potential energy of the system is
U. The work done in bringing an identical charge from
infinity to the third vertex is
(a)U (b) 2U (c) 3U (d) zero
Q.10 Potential energy of two equal negative point charges 2 mC
held 1 m apart in air is
(a) 2 J (b) 2eV (c) 4 J (d) 0.036 J
Q.11 Four charges + q, –q, + q and –q are put together on four
corners of a square as shown in figure. The work done by
external agent in slowly assembling this configuration is
+q
–q
+q –q
(a) zero (b) –2.59kq
2
/a
(c) +2.59kq
2
/a (d) none of these
Q.12 As shown in figure a dust particle with mass m = 5.0 × 10
–9
kg and charge q
0
 = 2.0 nC starts from rest at  point a and
moves in a straight line to point b . What is its speed v at
point b?
1.0 cm 1.0 cm 1.0 cm
3.0 nC –3.0 nC
a b
–
(a) 26 ms
–1
(b) 34 ms
–1  
(c)  46 ms
–1
(d) 14 ms
–1
Q.13 Charges –q, Q and –q are placed at equal distance on a
straight line. If the total potential energy of the system of
three charges is zero, then find the ratio Q/q.
–q –q
Q
2r
r r
(a) 1/2 (b) 1/4 (c) 2/3 (d) 3/4
Q.14When the separation between two charges is increased,
the electric potential energy of the charges
(a) increases (b) decreases
(c) remains the same (d) may increase or decrease
DPP/ P 34
3
Q.15 A positive charge is moved from a low potential point A to
high potential point B. Then the electric potential energy
of the system
(a) increases
(b) decreases
(c) will remain the same
(d) nothing definite can be predicted
Q.16If V and u are electric potential and energy density,
respectively, at a distance r from a positive point charge,
then which of the following graph is correct ?
(a)
V
4
u
(b)
V
4
u
(c)
V
4
u
(d)
V
4
u
DIRECTIONS (Q.17-Q.18) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.17 S is a solid neutral conducting sphere. A point charge q of
1 × 10
–6
 C is placed at point A. C is the centre of sphere
and AB is a tangent. BC = 3m and AB = 4m.
A B
S
(1) The electric potential of the conductor is 1.8 kV
(2) The electric potential of the conductor is 2.25 kV
(3) The electric potential at B due to induced charges on
the sphere is – 0.45 kV
(4) The electric potential at B due to induced charges on
the sphere is  0.45 kV
Q.18A proton moves a distance d in a uniform electric field
E
®
as shown in the figure. Then which of the following
statements are correct ?
+
d
p
E
®
(1) Electric field do a negative work on the proton
(2) Electric potential energy of the proton increases
(3) Electric field do a positive work on the proton
(4) Electric potential energy of the proton decreases
DIRECTIONS (Q.19-Q.21) : Read the passage given below
and answer the questions that follows :
Three concentric spherical conductors A, B and C of radii R, 2R
and 4R respectively. A and C is shorted and B is uniformly
charged.
2R
4R
R
A
B
C
+
+
+
+
+
+
+
+
+ +
+
+
+
+
+
+
+
+
+
Q.19 Charge on conductor A is
(a) Q/3 (b)  – Q/3
(c)2Q/3 (d)  None of these
Q.20 Potential at A is
(a) 
0
4 pe
Q
R
(b)
0
16
Q
R pe
(c)  
0
20
Q
R pe
(d) None of these
Q.21 Potential at B is
(a)
0
4
Q
R pe
(b)
0
16
Q
R pe
(c)
0
5
48
Q
R pe
(d) None of these
4
DPP/ P 34
DIRECTIONS (Q. 22-Q.24) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select the
correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.22 Statement-1 : No work is done in taking a small positive
charge from one point to other inside a positively charged
metallic sphere while outside the sphere work is done in
taking the charge towards the sphere. Neglect induction
due to small charge.
Statement-2 : Inside the sphere electric potential is same
at each point, but outside it is different for different points.
Q.23 Statement-1 : Electric potential of earth is taken to be
zero as a reference.
Statement-2 : The electric field produced by earth in
surrounding space is zero.
Q.24 Statement - 1 : The electric potential and the electric field
intensity at the centre of a square having four fixed point
charges at their vertices as shown in figure are zero.
+q
+q
–q
–q
Statement - 2 : If electric potential at a point is zero then
the magnitude of electric field at that point must be zero.