Page 1
DIRECTIONS (Q.1Q.18) : There are 18 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A total charge Q is broken in two parts
1
Q and
2
Q and they
are placed at a distance R from each other. The maximum
force of repulsion between them will occur, when
(a)
21
Q,
QQ
QQ
RR
= = (b)21
2
Q,
43
QQ
QQ = =
(c)
21
3
Q,
44
QQ
Q == (d)
12
Q,
22
==
QQ
Q
Q.2 Two small balls each having the charge + Q are suspended
by insulating threads of length L from a hook. This
arrangement is taken in space where there is no
gravitational effect, then the angle between the two
suspensions and the tension in each thread will be
(c)
2
2
0
1
180,
4
2
pÎ
Q
L
o
(d)
2
2
0
1
180,
4pÎ
Q
L
o
Q.3 Electric charges of 1 ,1 CC m m and 2 C m are placed in air at
the corners A,B and C respectively of an equilateral triangle
ABC having length of each side 10 cm. The resultant force
on the charge at C is
(a) 0.9 N (b) 1.8N (c) 2.7 N (d) 3.6 N
Q.4 An electron is moving round the nucleus of a hydrogen
atom in a circular orbit of radius . r The coulomb force
F
ur
between the two is (here
0
1
)
4
=
pÎ
K
(a)
2
3
e
Kr
r

$
(b)
2
3
e
Kr
r
r
(c)
2
3
e
Kr
r

r
(d)
2
2
e
Kr
r
$
Q.5 Equal charges q are placed at the four corners , ,, A B CD of a
square of length a . The magnitude of the force on the charge (a)
2
2
0
1
180 ,
4
(2)
pÎ
Q
L
o
(b)
2
2
0
1
90,
4pÎ
Q
L
o
Page 2
DIRECTIONS (Q.1Q.18) : There are 18 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A total charge Q is broken in two parts
1
Q and
2
Q and they
are placed at a distance R from each other. The maximum
force of repulsion between them will occur, when
(a)
21
Q,
QQ
QQ
RR
= = (b)21
2
Q,
43
QQ
QQ = =
(c)
21
3
Q,
44
QQ
Q == (d)
12
Q,
22
==
QQ
Q
Q.2 Two small balls each having the charge + Q are suspended
by insulating threads of length L from a hook. This
arrangement is taken in space where there is no
gravitational effect, then the angle between the two
suspensions and the tension in each thread will be
(c)
2
2
0
1
180,
4
2
pÎ
Q
L
o
(d)
2
2
0
1
180,
4pÎ
Q
L
o
Q.3 Electric charges of 1 ,1 CC m m and 2 C m are placed in air at
the corners A,B and C respectively of an equilateral triangle
ABC having length of each side 10 cm. The resultant force
on the charge at C is
(a) 0.9 N (b) 1.8N (c) 2.7 N (d) 3.6 N
Q.4 An electron is moving round the nucleus of a hydrogen
atom in a circular orbit of radius . r The coulomb force
F
ur
between the two is (here
0
1
)
4
=
pÎ
K
(a)
2
3
e
Kr
r

$
(b)
2
3
e
Kr
r
r
(c)
2
3
e
Kr
r

r
(d)
2
2
e
Kr
r
$
Q.5 Equal charges q are placed at the four corners , ,, A B CD of a
square of length a . The magnitude of the force on the charge (a)
2
2
0
1
180 ,
4
(2)
pÎ
Q
L
o
(b)
2
2
0
1
90,
4pÎ
Q
L
o
2
DPP/ P 32
at B will be
(a)
2
2
0
3
4pÎ
q
a
(b)
2
2
0
q
a pÎ
(c)
2
2
0
1 22
2
4
æö
+
ç÷
èø pÎ
q
a
(d)
2
2
0
1
2
2 4
æö
+
ç÷
èø
pÎ
q
a
Q.6 The charges on two spheres are +7mC and –5mC
respectively. They experience a force F. If each of them is
given an additional charge of –2mC, the new force of
attraction will be
(a)F (b) F/2 (c) /3 F (d) 2F
Q.7 Electric lines of force about negative point charge are
(a) Circular, anticlockwise (b) Circular, clockwise
(c) Radial, inward (d) Radial, outward
Q.8 Figure shows the electric lines of force emerging from a
charged body. If the electric field at A and B are
A
E and
B
E respectively and if the distance between A and B is r then
(a)
AB
EE >
(b)
AB
EE <
(c)
B
A
E
E
r
=
r
A B
(d)
2
B
A
E
E
r
=
Q.9 The magnitude of electric field intensity
E
is such that,
an electron placed in it would experience an electrical
force equal to its weight is given by
(a) mge (b)
mg
e
(c)
e
mg
(d)
2
2
e
g
m
Q.10A charge particle is free to move in an electric field. It
will travel
(a) Always along a line of force
(b) Along a line of force, if its initial velocity is zero
(c) Along a line of force, if it has some initial velocity in
the direction of an acute angle with the line of force
(d) None of the above
Q.11 Two point charges Q and –3Q are placed at some distance apart.
If the electric field at the location of Q is E then at the locality
of –3Q, it is
(a) –E (b) E/3 (c) –3E (d) –E/3
Q.12 Charges , 2 ,3 q qq and 4q are placed at the corners A, B, C
and D of a square as shown in the following figure. The
direction of electric field at the centre of the square is
parallel to side.
(a) AB
(b) CB
(c) BD
A B
D C
O
4q 3q
2q
q
(d) AC
Q.13Three infinitely long nonconducting charge sheets are
placed as shown in figure. The electric field at point P is
(a)
$
0
2
k
s
e
(b) –
$
0
2
k
s
e
(c)
$
0
4
k
s
e
P
Z
x
Za = –
Za =
Za = 3
2 s
(d) –
$
0
4
k
s
e
Q.14 Gauss's law is true only if force due to a charge varies as
(a) r
–1
(b) r
–2
(c) r
–3
(d) r
–4
Q.15 The electric intensity due to an infinite cylinder of radius
R and having charge q per unit length at a distance r(r > R)
from its axis is
(a) Directly proprotional to r
2
(b) Directly proprotional to r
3
(c) Inversely proprotional to r
(d) Inversely proprotional to r
2
Q.16 A sphere of radius R has a uniform distribution of electric
charge in its volume. At a distance x from its centre, for
x < R, the eletric field is directly proportional to
(a)
2
1
x
(b)
1
x
(c) x (d) x
2
Q.17 A charged ball B hangs from a silk thread S, which makes an
angle q with a large charged conducting sheet P, as shown
Page 3
DIRECTIONS (Q.1Q.18) : There are 18 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A total charge Q is broken in two parts
1
Q and
2
Q and they
are placed at a distance R from each other. The maximum
force of repulsion between them will occur, when
(a)
21
Q,
QQ
QQ
RR
= = (b)21
2
Q,
43
QQ
QQ = =
(c)
21
3
Q,
44
QQ
Q == (d)
12
Q,
22
==
QQ
Q
Q.2 Two small balls each having the charge + Q are suspended
by insulating threads of length L from a hook. This
arrangement is taken in space where there is no
gravitational effect, then the angle between the two
suspensions and the tension in each thread will be
(c)
2
2
0
1
180,
4
2
pÎ
Q
L
o
(d)
2
2
0
1
180,
4pÎ
Q
L
o
Q.3 Electric charges of 1 ,1 CC m m and 2 C m are placed in air at
the corners A,B and C respectively of an equilateral triangle
ABC having length of each side 10 cm. The resultant force
on the charge at C is
(a) 0.9 N (b) 1.8N (c) 2.7 N (d) 3.6 N
Q.4 An electron is moving round the nucleus of a hydrogen
atom in a circular orbit of radius . r The coulomb force
F
ur
between the two is (here
0
1
)
4
=
pÎ
K
(a)
2
3
e
Kr
r

$
(b)
2
3
e
Kr
r
r
(c)
2
3
e
Kr
r

r
(d)
2
2
e
Kr
r
$
Q.5 Equal charges q are placed at the four corners , ,, A B CD of a
square of length a . The magnitude of the force on the charge (a)
2
2
0
1
180 ,
4
(2)
pÎ
Q
L
o
(b)
2
2
0
1
90,
4pÎ
Q
L
o
2
DPP/ P 32
at B will be
(a)
2
2
0
3
4pÎ
q
a
(b)
2
2
0
q
a pÎ
(c)
2
2
0
1 22
2
4
æö
+
ç÷
èø pÎ
q
a
(d)
2
2
0
1
2
2 4
æö
+
ç÷
èø
pÎ
q
a
Q.6 The charges on two spheres are +7mC and –5mC
respectively. They experience a force F. If each of them is
given an additional charge of –2mC, the new force of
attraction will be
(a)F (b) F/2 (c) /3 F (d) 2F
Q.7 Electric lines of force about negative point charge are
(a) Circular, anticlockwise (b) Circular, clockwise
(c) Radial, inward (d) Radial, outward
Q.8 Figure shows the electric lines of force emerging from a
charged body. If the electric field at A and B are
A
E and
B
E respectively and if the distance between A and B is r then
(a)
AB
EE >
(b)
AB
EE <
(c)
B
A
E
E
r
=
r
A B
(d)
2
B
A
E
E
r
=
Q.9 The magnitude of electric field intensity
E
is such that,
an electron placed in it would experience an electrical
force equal to its weight is given by
(a) mge (b)
mg
e
(c)
e
mg
(d)
2
2
e
g
m
Q.10A charge particle is free to move in an electric field. It
will travel
(a) Always along a line of force
(b) Along a line of force, if its initial velocity is zero
(c) Along a line of force, if it has some initial velocity in
the direction of an acute angle with the line of force
(d) None of the above
Q.11 Two point charges Q and –3Q are placed at some distance apart.
If the electric field at the location of Q is E then at the locality
of –3Q, it is
(a) –E (b) E/3 (c) –3E (d) –E/3
Q.12 Charges , 2 ,3 q qq and 4q are placed at the corners A, B, C
and D of a square as shown in the following figure. The
direction of electric field at the centre of the square is
parallel to side.
(a) AB
(b) CB
(c) BD
A B
D C
O
4q 3q
2q
q
(d) AC
Q.13Three infinitely long nonconducting charge sheets are
placed as shown in figure. The electric field at point P is
(a)
$
0
2
k
s
e
(b) –
$
0
2
k
s
e
(c)
$
0
4
k
s
e
P
Z
x
Za = –
Za =
Za = 3
2 s
(d) –
$
0
4
k
s
e
Q.14 Gauss's law is true only if force due to a charge varies as
(a) r
–1
(b) r
–2
(c) r
–3
(d) r
–4
Q.15 The electric intensity due to an infinite cylinder of radius
R and having charge q per unit length at a distance r(r > R)
from its axis is
(a) Directly proprotional to r
2
(b) Directly proprotional to r
3
(c) Inversely proprotional to r
(d) Inversely proprotional to r
2
Q.16 A sphere of radius R has a uniform distribution of electric
charge in its volume. At a distance x from its centre, for
x < R, the eletric field is directly proportional to
(a)
2
1
x
(b)
1
x
(c) x (d) x
2
Q.17 A charged ball B hangs from a silk thread S, which makes an
angle q with a large charged conducting sheet P, as shown
DPP/ P 32
3
in the figure. The surface charge density s of the sheet is
proportional to
(a) sin q
+
+
+
+
+
+
+
q
S
B
P
(b) tan q
(c) cos q
(d) cot q
Q.18 A charge q is placed at the centre of a cube. Then the flux
passing through one face of cube will be
(a)
0
Î
q
(b)
0
2 Î
q
(c)
0
4 Î
q
(d)
0
6 Î
q
DIRECTIONS (Q.19Q.20) : 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.19 A solid sphere S
1
is connected to a charge reservoir through
a heater H as shown in figure.
Solid
sphere
Solid
sphere
H
Heater
S
1
S
2
Flux through a closed spherical surface around S
1
is given
by f = a t
2
where a is a constant and t is time in seconds.
If resistance of heater is R then select correct statements
(1) Power consumed by heater will be 4a
2
e
0
2
Rt
2
.
(2) Electric flux through a closed spherical surface around
S
2
will be – a t
2
.
(3) Rate of change of electric flux through a closed
spherical surface around S
2
will be –2a t
(4) All of the above are correct
Q.20A simple pendulum has a time period T. The bob is now
given some positive charge –
(1) If some positive charge is placed at the point of
suspension, T will increases
(2) If some positive charge is placed at the point of
suspension, T will not change
(3) If a uniform downward electric field is switched on, T will
increase
(4) If a uniform downward electric field is switched on,
T will decrease
DIRECTIONS (Q.21Q.23) : Read the passage given below
and answer the questions that follows :
A sphere of radius R contains charge density ( ) ( ), r ARr r =
for
0. rR <<
The total electric charge inside the sphere is Q.
Q.21 The value of A in terms of Q and R is
(a)
2
4
2Q
R p
(b)
4
3Q
R p
(c)
2
3
3Q
R p
(d)
3Q
R p
Q.22The electric field inside the sphere is
(a)
2
2
0
3 11
34
Q rr
RR
R
éù
æö æö
ê ú
ç÷ ç÷
èø èø êú Î
ëû
(b)
2 2
3
12 11
34
Q rr
RR
R
éù
æ ö æö
ê ú
ç ÷ ç÷
è ø èø êú
ëû
(c)
2
2
0
120 11
43
5
éù
æö æö
ê ú
ç÷ ç÷
èø èø êú Î
ëû
Q rr
RR
R
(d)
2
2
1211
34
rr
RR
RQ
éù
æö æö
 êú
ç÷ ç÷
èø èø
êú
ëû
Q.23 The electric field outside the sphere is
0
1
4
k
æö
=
ç÷
pÎ
èø
(a)
kQ
r
(b)
2
kQ
r
(c)
3
kQ
r
(d)
2
2
kQ
r
DIRECTIONS (Q. 24Q.26) : Each of these questions
contains two statements: Statement1 (Assertion) and
Statement2 (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) Statement1 is True, Statement2 is True; Statement2 is a
correct explanation for Statement1.
(b) Statement1 is True, Statement2 is True; Statement2 is
NOT a correct explanation for Statement1.
(c) Statement 1 is False, Statement2 is True.
(d) Statement 1 is True, Statement2 is False.
Q.24 Statement1 : Electric lines of force cross each other.
Statement2 : Electric field at a point superimpose to give
Page 4
DIRECTIONS (Q.1Q.18) : There are 18 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A total charge Q is broken in two parts
1
Q and
2
Q and they
are placed at a distance R from each other. The maximum
force of repulsion between them will occur, when
(a)
21
Q,
QQ
QQ
RR
= = (b)21
2
Q,
43
QQ
QQ = =
(c)
21
3
Q,
44
QQ
Q == (d)
12
Q,
22
==
QQ
Q
Q.2 Two small balls each having the charge + Q are suspended
by insulating threads of length L from a hook. This
arrangement is taken in space where there is no
gravitational effect, then the angle between the two
suspensions and the tension in each thread will be
(c)
2
2
0
1
180,
4
2
pÎ
Q
L
o
(d)
2
2
0
1
180,
4pÎ
Q
L
o
Q.3 Electric charges of 1 ,1 CC m m and 2 C m are placed in air at
the corners A,B and C respectively of an equilateral triangle
ABC having length of each side 10 cm. The resultant force
on the charge at C is
(a) 0.9 N (b) 1.8N (c) 2.7 N (d) 3.6 N
Q.4 An electron is moving round the nucleus of a hydrogen
atom in a circular orbit of radius . r The coulomb force
F
ur
between the two is (here
0
1
)
4
=
pÎ
K
(a)
2
3
e
Kr
r

$
(b)
2
3
e
Kr
r
r
(c)
2
3
e
Kr
r

r
(d)
2
2
e
Kr
r
$
Q.5 Equal charges q are placed at the four corners , ,, A B CD of a
square of length a . The magnitude of the force on the charge (a)
2
2
0
1
180 ,
4
(2)
pÎ
Q
L
o
(b)
2
2
0
1
90,
4pÎ
Q
L
o
2
DPP/ P 32
at B will be
(a)
2
2
0
3
4pÎ
q
a
(b)
2
2
0
q
a pÎ
(c)
2
2
0
1 22
2
4
æö
+
ç÷
èø pÎ
q
a
(d)
2
2
0
1
2
2 4
æö
+
ç÷
èø
pÎ
q
a
Q.6 The charges on two spheres are +7mC and –5mC
respectively. They experience a force F. If each of them is
given an additional charge of –2mC, the new force of
attraction will be
(a)F (b) F/2 (c) /3 F (d) 2F
Q.7 Electric lines of force about negative point charge are
(a) Circular, anticlockwise (b) Circular, clockwise
(c) Radial, inward (d) Radial, outward
Q.8 Figure shows the electric lines of force emerging from a
charged body. If the electric field at A and B are
A
E and
B
E respectively and if the distance between A and B is r then
(a)
AB
EE >
(b)
AB
EE <
(c)
B
A
E
E
r
=
r
A B
(d)
2
B
A
E
E
r
=
Q.9 The magnitude of electric field intensity
E
is such that,
an electron placed in it would experience an electrical
force equal to its weight is given by
(a) mge (b)
mg
e
(c)
e
mg
(d)
2
2
e
g
m
Q.10A charge particle is free to move in an electric field. It
will travel
(a) Always along a line of force
(b) Along a line of force, if its initial velocity is zero
(c) Along a line of force, if it has some initial velocity in
the direction of an acute angle with the line of force
(d) None of the above
Q.11 Two point charges Q and –3Q are placed at some distance apart.
If the electric field at the location of Q is E then at the locality
of –3Q, it is
(a) –E (b) E/3 (c) –3E (d) –E/3
Q.12 Charges , 2 ,3 q qq and 4q are placed at the corners A, B, C
and D of a square as shown in the following figure. The
direction of electric field at the centre of the square is
parallel to side.
(a) AB
(b) CB
(c) BD
A B
D C
O
4q 3q
2q
q
(d) AC
Q.13Three infinitely long nonconducting charge sheets are
placed as shown in figure. The electric field at point P is
(a)
$
0
2
k
s
e
(b) –
$
0
2
k
s
e
(c)
$
0
4
k
s
e
P
Z
x
Za = –
Za =
Za = 3
2 s
(d) –
$
0
4
k
s
e
Q.14 Gauss's law is true only if force due to a charge varies as
(a) r
–1
(b) r
–2
(c) r
–3
(d) r
–4
Q.15 The electric intensity due to an infinite cylinder of radius
R and having charge q per unit length at a distance r(r > R)
from its axis is
(a) Directly proprotional to r
2
(b) Directly proprotional to r
3
(c) Inversely proprotional to r
(d) Inversely proprotional to r
2
Q.16 A sphere of radius R has a uniform distribution of electric
charge in its volume. At a distance x from its centre, for
x < R, the eletric field is directly proportional to
(a)
2
1
x
(b)
1
x
(c) x (d) x
2
Q.17 A charged ball B hangs from a silk thread S, which makes an
angle q with a large charged conducting sheet P, as shown
DPP/ P 32
3
in the figure. The surface charge density s of the sheet is
proportional to
(a) sin q
+
+
+
+
+
+
+
q
S
B
P
(b) tan q
(c) cos q
(d) cot q
Q.18 A charge q is placed at the centre of a cube. Then the flux
passing through one face of cube will be
(a)
0
Î
q
(b)
0
2 Î
q
(c)
0
4 Î
q
(d)
0
6 Î
q
DIRECTIONS (Q.19Q.20) : 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.19 A solid sphere S
1
is connected to a charge reservoir through
a heater H as shown in figure.
Solid
sphere
Solid
sphere
H
Heater
S
1
S
2
Flux through a closed spherical surface around S
1
is given
by f = a t
2
where a is a constant and t is time in seconds.
If resistance of heater is R then select correct statements
(1) Power consumed by heater will be 4a
2
e
0
2
Rt
2
.
(2) Electric flux through a closed spherical surface around
S
2
will be – a t
2
.
(3) Rate of change of electric flux through a closed
spherical surface around S
2
will be –2a t
(4) All of the above are correct
Q.20A simple pendulum has a time period T. The bob is now
given some positive charge –
(1) If some positive charge is placed at the point of
suspension, T will increases
(2) If some positive charge is placed at the point of
suspension, T will not change
(3) If a uniform downward electric field is switched on, T will
increase
(4) If a uniform downward electric field is switched on,
T will decrease
DIRECTIONS (Q.21Q.23) : Read the passage given below
and answer the questions that follows :
A sphere of radius R contains charge density ( ) ( ), r ARr r =
for
0. rR <<
The total electric charge inside the sphere is Q.
Q.21 The value of A in terms of Q and R is
(a)
2
4
2Q
R p
(b)
4
3Q
R p
(c)
2
3
3Q
R p
(d)
3Q
R p
Q.22The electric field inside the sphere is
(a)
2
2
0
3 11
34
Q rr
RR
R
éù
æö æö
ê ú
ç÷ ç÷
èø èø êú Î
ëû
(b)
2 2
3
12 11
34
Q rr
RR
R
éù
æ ö æö
ê ú
ç ÷ ç÷
è ø èø êú
ëû
(c)
2
2
0
120 11
43
5
éù
æö æö
ê ú
ç÷ ç÷
èø èø êú Î
ëû
Q rr
RR
R
(d)
2
2
1211
34
rr
RR
RQ
éù
æö æö
 êú
ç÷ ç÷
èø èø
êú
ëû
Q.23 The electric field outside the sphere is
0
1
4
k
æö
=
ç÷
pÎ
èø
(a)
kQ
r
(b)
2
kQ
r
(c)
3
kQ
r
(d)
2
2
kQ
r
DIRECTIONS (Q. 24Q.26) : Each of these questions
contains two statements: Statement1 (Assertion) and
Statement2 (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) Statement1 is True, Statement2 is True; Statement2 is a
correct explanation for Statement1.
(b) Statement1 is True, Statement2 is True; Statement2 is
NOT a correct explanation for Statement1.
(c) Statement 1 is False, Statement2 is True.
(d) Statement 1 is True, Statement2 is False.
Q.24 Statement1 : Electric lines of force cross each other.
Statement2 : Electric field at a point superimpose to give
4
DPP/ P 32
one resultant electric field.
Q.25 Statement1 : A point charge is brought in an electric field. The
field at a nearby point will increase, whatever be the nature of
the charge.
Statement2 : The electric field is dependent on the nature of
charge.
Q.26 Statement1 : Direction of electric field at a point signifies
direction of force experienced by a point charge placed at
that point.
Statement2 : Electric field is a vector quantity.
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