Electrostatics- 2 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.19) : There are 19 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d),
out of which ONLY ONE choice is correct.
Q1. In the electric field of a point charge q , a certain charge is
carried from point A to B, C, D and E. Then the work done
by electric force is
(a) least along the path AB
(b) least along the path AD
(c) zero along all the paths AB,
+q
A
B
C D
E
AC, AD and AE
(d) least along AE
Q2. Four equal charges Q are placed at the four corners of a
square of each side 
'' a
. Work done in removing a charge
– Q from its centre to infinity is
(a)0 (b)
2
0
2
4
Q
a pÎ
(c)
2
0
2Q
a pÎ
(d)
2
0
2
Q
a pÎ
Q3. A particle A has charge +q and a particle B has charge +4q
with each of them having the same mass m. When allowed
to fall from rest through the same electric potential
difference, the ratio of their speed 
A
B
v
v
will become
(a) 2 : 1 (b) 1 : 2
(c) 1 : 4 (d) 4 : 1
Page 2


DIRECTIONS (Q.1-Q.19) : There are 19 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d),
out of which ONLY ONE choice is correct.
Q1. In the electric field of a point charge q , a certain charge is
carried from point A to B, C, D and E. Then the work done
by electric force is
(a) least along the path AB
(b) least along the path AD
(c) zero along all the paths AB,
+q
A
B
C D
E
AC, AD and AE
(d) least along AE
Q2. Four equal charges Q are placed at the four corners of a
square of each side 
'' a
. Work done in removing a charge
– Q from its centre to infinity is
(a)0 (b)
2
0
2
4
Q
a pÎ
(c)
2
0
2Q
a pÎ
(d)
2
0
2
Q
a pÎ
Q3. A particle A has charge +q and a particle B has charge +4q
with each of them having the same mass m. When allowed
to fall from rest through the same electric potential
difference, the ratio of their speed 
A
B
v
v
will become
(a) 2 : 1 (b) 1 : 2
(c) 1 : 4 (d) 4 : 1
2
DPP/ P 33
Q4. In the figure the charge Q is at the centre of the circle.
Work done (by electrostatic force on q) is maximum when
another charge q is taken from point P to (consider both
the charges to be positive)
P
L
M
N
Q
K
(a) K (b) L (c) M (d) N
Q5. How much kinetic energy will be gained by an a- particle
in going from a point at 70V to another point at 50V ?
(a) 40 eV (b) 40 keV (c) 40 MeV (d) 0 eV
Q6. Ten electrons are equally spaced and fixed around a circle
of radius R. Relative to 
0 V =
at infinity, the electrostatic
potential V and the electric field E at the centre C are
(a)
0 ¹ V
and 0 ¹
ur
E (b)
0 V ¹
and 
0 E =
ur
(c)
0 V =
and 0 E =
ur
(d)
0 V =
and 0 E ¹
ur
Q7. The displacement of a charge Q in the electric field
$ $
1 23
E eie jek = ++
ur
$
 is 
$
r ai bj
r
$
=+ . The work done is
(a)Q( )
12
ae be + (b)Q
( ) ()
22
12
ae be +
(c)Q
( )
22
12
e e ab ++ (d)Q
22
12
ee
æö
+
ç÷
èø
( ) ab +
Q8. 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)
22
0
12
.
4
q
ab
pe
+
(b) Zero
(c)
22
0
1
.
4
q
ab
pe
+
a
b b
A
C B
– q + q
(d)
( )
22
0
1
.
4
q
ab
-
pe
+
Q9. Two electric charges  12µC and – 6µC are placed 20 cm
apart in air. If 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, then the distance of P from – 6µC
charge is
(a) 0.10 m (b) 0.15 m (c) 0.20 m (d) 0.25 m
Q10. In the rectangle shown below , the two corners have charges
q
1
 = –5 mC and q
2
 = +2.0 mC. The work done by external
agent in moving a charge q = +3.0 C m slowly from B to A is
(Take 
10 22
0
1/ 4 10 Nm /C pe= )
(a) 2.8 J
(b) 3.5 J
(c) 4.5 J
B
A
1
q
2
q
15 cm
5 cm
(d) 5.5 J
Q11. Electric charges q, q, –2q are placed at the corners of an
equilateral triangle ABC of side l. The magnitude of electric
dipole moment of the system is
(a) ql (b) 2ql (c) 3ql (d) 4ql
Q12. A charge (–q) and another charge (+Q) are kept at two
points A and B respectively . Keeping the charge (+Q) fixed
at B, the charge (–q) at A is moved to another point C such
that ABC forms an equilateral triangle of side l . The net
work done by electrostatic field in moving the charge (–q)
is
(a)
0
1
4
Qq
l pÎ
(b) 
2
0
1
4
Qq
l
pÎ
(c)
0
1
4
Qql
pÎ
(d) zero
Q13.In an hydrogen atom, the electron revolves around the
nucleus in an orbit of radius 0.53 × 10
–10
m. Then the
electrical potential produced by the nucleus at the position
of the electron is
(a) –13.6V (b)   –27.2V (c) 27.2V (d) 13.6V
Q14. Point charge q 2C
1
=m and q 1C
2
=-m are kept at points x =
0 and x = 6 respectively. Electrical potential will be zero at
points
(a)
2 x =
and 
9 x =
(b)
1 x =
and 
5 x =
(c)
4 x =
and 
12 x =
(d)
2 x =-
and 
2 x =
Page 3


DIRECTIONS (Q.1-Q.19) : There are 19 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d),
out of which ONLY ONE choice is correct.
Q1. In the electric field of a point charge q , a certain charge is
carried from point A to B, C, D and E. Then the work done
by electric force is
(a) least along the path AB
(b) least along the path AD
(c) zero along all the paths AB,
+q
A
B
C D
E
AC, AD and AE
(d) least along AE
Q2. Four equal charges Q are placed at the four corners of a
square of each side 
'' a
. Work done in removing a charge
– Q from its centre to infinity is
(a)0 (b)
2
0
2
4
Q
a pÎ
(c)
2
0
2Q
a pÎ
(d)
2
0
2
Q
a pÎ
Q3. A particle A has charge +q and a particle B has charge +4q
with each of them having the same mass m. When allowed
to fall from rest through the same electric potential
difference, the ratio of their speed 
A
B
v
v
will become
(a) 2 : 1 (b) 1 : 2
(c) 1 : 4 (d) 4 : 1
2
DPP/ P 33
Q4. In the figure the charge Q is at the centre of the circle.
Work done (by electrostatic force on q) is maximum when
another charge q is taken from point P to (consider both
the charges to be positive)
P
L
M
N
Q
K
(a) K (b) L (c) M (d) N
Q5. How much kinetic energy will be gained by an a- particle
in going from a point at 70V to another point at 50V ?
(a) 40 eV (b) 40 keV (c) 40 MeV (d) 0 eV
Q6. Ten electrons are equally spaced and fixed around a circle
of radius R. Relative to 
0 V =
at infinity, the electrostatic
potential V and the electric field E at the centre C are
(a)
0 ¹ V
and 0 ¹
ur
E (b)
0 V ¹
and 
0 E =
ur
(c)
0 V =
and 0 E =
ur
(d)
0 V =
and 0 E ¹
ur
Q7. The displacement of a charge Q in the electric field
$ $
1 23
E eie jek = ++
ur
$
 is 
$
r ai bj
r
$
=+ . The work done is
(a)Q( )
12
ae be + (b)Q
( ) ()
22
12
ae be +
(c)Q
( )
22
12
e e ab ++ (d)Q
22
12
ee
æö
+
ç÷
èø
( ) ab +
Q8. 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)
22
0
12
.
4
q
ab
pe
+
(b) Zero
(c)
22
0
1
.
4
q
ab
pe
+
a
b b
A
C B
– q + q
(d)
( )
22
0
1
.
4
q
ab
-
pe
+
Q9. Two electric charges  12µC and – 6µC are placed 20 cm
apart in air. If 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, then the distance of P from – 6µC
charge is
(a) 0.10 m (b) 0.15 m (c) 0.20 m (d) 0.25 m
Q10. In the rectangle shown below , the two corners have charges
q
1
 = –5 mC and q
2
 = +2.0 mC. The work done by external
agent in moving a charge q = +3.0 C m slowly from B to A is
(Take 
10 22
0
1/ 4 10 Nm /C pe= )
(a) 2.8 J
(b) 3.5 J
(c) 4.5 J
B
A
1
q
2
q
15 cm
5 cm
(d) 5.5 J
Q11. Electric charges q, q, –2q are placed at the corners of an
equilateral triangle ABC of side l. The magnitude of electric
dipole moment of the system is
(a) ql (b) 2ql (c) 3ql (d) 4ql
Q12. A charge (–q) and another charge (+Q) are kept at two
points A and B respectively . Keeping the charge (+Q) fixed
at B, the charge (–q) at A is moved to another point C such
that ABC forms an equilateral triangle of side l . The net
work done by electrostatic field in moving the charge (–q)
is
(a)
0
1
4
Qq
l pÎ
(b) 
2
0
1
4
Qq
l
pÎ
(c)
0
1
4
Qql
pÎ
(d) zero
Q13.In an hydrogen atom, the electron revolves around the
nucleus in an orbit of radius 0.53 × 10
–10
m. Then the
electrical potential produced by the nucleus at the position
of the electron is
(a) –13.6V (b)   –27.2V (c) 27.2V (d) 13.6V
Q14. Point charge q 2C
1
=m and q 1C
2
=-m are kept at points x =
0 and x = 6 respectively. Electrical potential will be zero at
points
(a)
2 x =
and 
9 x =
(b)
1 x =
and 
5 x =
(c)
4 x =
and 
12 x =
(d)
2 x =-
and 
2 x =
DPP/ P 33
3
Q15. The distance between H
+
 and Cl
–
 ions in HCl molecule is 1.28
Å. What will be the potential due to this dipole at a distance of
12 Å on the axis of dipole
(a) 0.13 V (b) 1.3 V (c) 13 V (d) 130 V
Q16.Two identical thin rings each of radius R metres are
coaxially placed at a distance R metres apart. If Q
1 
coulomb
and Q
2 
coulomb are respectively the charges uniformly
spread on the two rings, the work done by external agent in
moving a charge q slowly from the centre of ring with
charge Q
1
 to that of other is
(a) zero (b)
21
0
( )( 2 1)
2.4
qQQ
R
--
pÎ
(c)
12
0
2()
4
q QQ
R
+
pÎ
(d)
12
0
( )( 2 1)
4
qQQ
R
++
pÎ
Q17. Identical point charges, each having q + charge, are fixed
at each of the points 
00
, 3, == x xxx 
0
5= xx .........
infinite, on the x-axis and a identical point charges, each
having q - charge, are fixed at each of the points
000
2, 4,6 xxx xxx === ....... infinite. Here 
0
x is a
positive constant. Potential at the origin due to the above
system of charges is
(a)0 (b)
00
8 ln2
q
x pÎ
(c)
¥
(d)
00
ln2
4
q
x pÎ
Q18. A uniform electric field pointing in positive x - direction
exists in a region. Let A be the origin, B be the point on the
x - axis at 1 x =+ cm and C be the point on the y - axis at
1 y =+ cm. Then the potentials at the points A, B and C
satisfy
(a)
AB
VV < (b)
AB
VV > (c)
AC
VV < (d)
AC
VV >
Q19. A point Q lies on the perpendicular bisector of an electrical
dipole of dipole moment p . If the distance of Q from the
dipole is r (much larger than the size of the dipole), then
electric field at Q is proportional to
(a)P
–1
and r
–2
(b) p and r
–2
(c)P
2 
and r
–3
(d)p and r
–3
DIRECTIONS (Q.20-Q.21) : 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
Q20. Consider a system of three charges 
q q 2q
, and
333
- placed at
point A, B and C respectively, as shown in the figure. Take
O to be the centre of the circle of radius R and angle
CAB = 60°. Choose the incorrect options
(1) The electric field at point O is 
2
0
q
8R pe
directed along the negative x-axis
(2) The potential energy of the
C
A
B
y
x
60°
O
system is zero
(3) The potential at point O is 
0
q
12R pe
(4) The magnitude of the force between the  charges at C
and B is 
2
2
0
q
54R pe
Q21.For spherical symmetrical charge distribution, variation
of electric potential with distance from centre is given in
d iag ra m . G iven that : 
00
q
V
4R
=
pe
 for r £ R
0
 and 
0
q
V
4r
=
pe
for r ³ R
0
Then which option (s) are correct :
(1) Total charge within 2R
0
 is q
V
r = R
0
r
(2) Total electrostatic energy
  for r £ R
0
 is non-zero
(3) At r = R
0
 electric field is discontinuous
(4) There will be no charge anywhere except at r < R
0
.
DIRECTIONS (Q.22-Q.23) : Read the passage given below
and answer the questions that follows :
An electric dipole (AB) consisting of two particles of equal and
opposite charge and same mass is released in an electric field.
In the figure field lines are without considering effect of field
of dipole.
Page 4


DIRECTIONS (Q.1-Q.19) : There are 19 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d),
out of which ONLY ONE choice is correct.
Q1. In the electric field of a point charge q , a certain charge is
carried from point A to B, C, D and E. Then the work done
by electric force is
(a) least along the path AB
(b) least along the path AD
(c) zero along all the paths AB,
+q
A
B
C D
E
AC, AD and AE
(d) least along AE
Q2. Four equal charges Q are placed at the four corners of a
square of each side 
'' a
. Work done in removing a charge
– Q from its centre to infinity is
(a)0 (b)
2
0
2
4
Q
a pÎ
(c)
2
0
2Q
a pÎ
(d)
2
0
2
Q
a pÎ
Q3. A particle A has charge +q and a particle B has charge +4q
with each of them having the same mass m. When allowed
to fall from rest through the same electric potential
difference, the ratio of their speed 
A
B
v
v
will become
(a) 2 : 1 (b) 1 : 2
(c) 1 : 4 (d) 4 : 1
2
DPP/ P 33
Q4. In the figure the charge Q is at the centre of the circle.
Work done (by electrostatic force on q) is maximum when
another charge q is taken from point P to (consider both
the charges to be positive)
P
L
M
N
Q
K
(a) K (b) L (c) M (d) N
Q5. How much kinetic energy will be gained by an a- particle
in going from a point at 70V to another point at 50V ?
(a) 40 eV (b) 40 keV (c) 40 MeV (d) 0 eV
Q6. Ten electrons are equally spaced and fixed around a circle
of radius R. Relative to 
0 V =
at infinity, the electrostatic
potential V and the electric field E at the centre C are
(a)
0 ¹ V
and 0 ¹
ur
E (b)
0 V ¹
and 
0 E =
ur
(c)
0 V =
and 0 E =
ur
(d)
0 V =
and 0 E ¹
ur
Q7. The displacement of a charge Q in the electric field
$ $
1 23
E eie jek = ++
ur
$
 is 
$
r ai bj
r
$
=+ . The work done is
(a)Q( )
12
ae be + (b)Q
( ) ()
22
12
ae be +
(c)Q
( )
22
12
e e ab ++ (d)Q
22
12
ee
æö
+
ç÷
èø
( ) ab +
Q8. 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)
22
0
12
.
4
q
ab
pe
+
(b) Zero
(c)
22
0
1
.
4
q
ab
pe
+
a
b b
A
C B
– q + q
(d)
( )
22
0
1
.
4
q
ab
-
pe
+
Q9. Two electric charges  12µC and – 6µC are placed 20 cm
apart in air. If 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, then the distance of P from – 6µC
charge is
(a) 0.10 m (b) 0.15 m (c) 0.20 m (d) 0.25 m
Q10. In the rectangle shown below , the two corners have charges
q
1
 = –5 mC and q
2
 = +2.0 mC. The work done by external
agent in moving a charge q = +3.0 C m slowly from B to A is
(Take 
10 22
0
1/ 4 10 Nm /C pe= )
(a) 2.8 J
(b) 3.5 J
(c) 4.5 J
B
A
1
q
2
q
15 cm
5 cm
(d) 5.5 J
Q11. Electric charges q, q, –2q are placed at the corners of an
equilateral triangle ABC of side l. The magnitude of electric
dipole moment of the system is
(a) ql (b) 2ql (c) 3ql (d) 4ql
Q12. A charge (–q) and another charge (+Q) are kept at two
points A and B respectively . Keeping the charge (+Q) fixed
at B, the charge (–q) at A is moved to another point C such
that ABC forms an equilateral triangle of side l . The net
work done by electrostatic field in moving the charge (–q)
is
(a)
0
1
4
Qq
l pÎ
(b) 
2
0
1
4
Qq
l
pÎ
(c)
0
1
4
Qql
pÎ
(d) zero
Q13.In an hydrogen atom, the electron revolves around the
nucleus in an orbit of radius 0.53 × 10
–10
m. Then the
electrical potential produced by the nucleus at the position
of the electron is
(a) –13.6V (b)   –27.2V (c) 27.2V (d) 13.6V
Q14. Point charge q 2C
1
=m and q 1C
2
=-m are kept at points x =
0 and x = 6 respectively. Electrical potential will be zero at
points
(a)
2 x =
and 
9 x =
(b)
1 x =
and 
5 x =
(c)
4 x =
and 
12 x =
(d)
2 x =-
and 
2 x =
DPP/ P 33
3
Q15. The distance between H
+
 and Cl
–
 ions in HCl molecule is 1.28
Å. What will be the potential due to this dipole at a distance of
12 Å on the axis of dipole
(a) 0.13 V (b) 1.3 V (c) 13 V (d) 130 V
Q16.Two identical thin rings each of radius R metres are
coaxially placed at a distance R metres apart. If Q
1 
coulomb
and Q
2 
coulomb are respectively the charges uniformly
spread on the two rings, the work done by external agent in
moving a charge q slowly from the centre of ring with
charge Q
1
 to that of other is
(a) zero (b)
21
0
( )( 2 1)
2.4
qQQ
R
--
pÎ
(c)
12
0
2()
4
q QQ
R
+
pÎ
(d)
12
0
( )( 2 1)
4
qQQ
R
++
pÎ
Q17. Identical point charges, each having q + charge, are fixed
at each of the points 
00
, 3, == x xxx 
0
5= xx .........
infinite, on the x-axis and a identical point charges, each
having q - charge, are fixed at each of the points
000
2, 4,6 xxx xxx === ....... infinite. Here 
0
x is a
positive constant. Potential at the origin due to the above
system of charges is
(a)0 (b)
00
8 ln2
q
x pÎ
(c)
¥
(d)
00
ln2
4
q
x pÎ
Q18. A uniform electric field pointing in positive x - direction
exists in a region. Let A be the origin, B be the point on the
x - axis at 1 x =+ cm and C be the point on the y - axis at
1 y =+ cm. Then the potentials at the points A, B and C
satisfy
(a)
AB
VV < (b)
AB
VV > (c)
AC
VV < (d)
AC
VV >
Q19. A point Q lies on the perpendicular bisector of an electrical
dipole of dipole moment p . If the distance of Q from the
dipole is r (much larger than the size of the dipole), then
electric field at Q is proportional to
(a)P
–1
and r
–2
(b) p and r
–2
(c)P
2 
and r
–3
(d)p and r
–3
DIRECTIONS (Q.20-Q.21) : 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
Q20. Consider a system of three charges 
q q 2q
, and
333
- placed at
point A, B and C respectively, as shown in the figure. Take
O to be the centre of the circle of radius R and angle
CAB = 60°. Choose the incorrect options
(1) The electric field at point O is 
2
0
q
8R pe
directed along the negative x-axis
(2) The potential energy of the
C
A
B
y
x
60°
O
system is zero
(3) The potential at point O is 
0
q
12R pe
(4) The magnitude of the force between the  charges at C
and B is 
2
2
0
q
54R pe
Q21.For spherical symmetrical charge distribution, variation
of electric potential with distance from centre is given in
d iag ra m . G iven that : 
00
q
V
4R
=
pe
 for r £ R
0
 and 
0
q
V
4r
=
pe
for r ³ R
0
Then which option (s) are correct :
(1) Total charge within 2R
0
 is q
V
r = R
0
r
(2) Total electrostatic energy
  for r £ R
0
 is non-zero
(3) At r = R
0
 electric field is discontinuous
(4) There will be no charge anywhere except at r < R
0
.
DIRECTIONS (Q.22-Q.23) : Read the passage given below
and answer the questions that follows :
An electric dipole (AB) consisting of two particles of equal and
opposite charge and same mass is released in an electric field.
In the figure field lines are without considering effect of field
of dipole.
4
DPP/ P 33
y
x
B
A
+q
–q
Q22. The centre of mass of the dipole
(a) Has no acceleration
(b) Has acceleration with positive x and y components
(c) Has acceleration with positive x component and nega-
tive y component
(d) Has acceleration with negative x component and posi-
tive y component
Q23. Angular acceleration of the dipole, immediately after it is
released
(a) is zero
(b) is clockwise
(c) is anticlockwise
(d) cannot be determined from the given information.
DIRECTIONS (Q. 24-Q.26) : 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.
Q24. Statement -1 : A bird perches on a high power line and
nothing happens to the bird.
Statement -2 : The level of bird is very high from the
ground.
Q25. Statement -1  : Electrons move away from a low potential
to high potential region.
Statement- 2 : Because electrons have negative charge
Q26.Statement -1 : Surface of a symmetrical conductor can
be treated as equipotential surface.
Statement  -2 : Charges can easily flow in a conductor.