# Electrostatic: JEE Advance(Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

## JEE: Electrostatic: JEE Advance(Part - 1) - Physics, Solution by DC Pandey Notes | Study DC Pandey Solutions for JEE Physics - JEE

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``` Page 1

Objective Questions
Single Correct Option
Q 1.  In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from
a distance R from the fixed charge. Minimum separation between the two charges if the velocity
becomes
1
3

times of the projected velocity, at this moment is (Assume gravity to be absent)

(a)
3
R
2
(b)
1
R
3
(c)
1
R
2
(d) None of these
Q 2.  A uniform electric field of strength E
?
exists in a region. An electron enters a point A with velocity
v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is
2v at 30° with x-axis. Then

(a) electric field
2
3mv
ˆ
Ei
2ea
??
?

(b) rate of doing work done by electric field at B is
3
3mv
2ea

(c) Both (a) and (b) are correct
(d) Both (a) and (b) are wrong
Q 3.  Two point charges a and b whose magnitudes are same positioned at a certain distance along the
positive x-axis from each other, a is at origin. Graph is drawn between electrical field strength and
distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it
can be decided that

(a) a is positive, b is negative    (b) a and b both are positive
(c) a and b both are negative    (d) a is negative, b is positive
Note Graph is drawn only between a and b.
Q 4.  Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric
field on the line passing through point O and perpendicular to the plane of the figure as a function
of distance x from point

O is (x >>a)
Page 2

Objective Questions
Single Correct Option
Q 1.  In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from
a distance R from the fixed charge. Minimum separation between the two charges if the velocity
becomes
1
3

times of the projected velocity, at this moment is (Assume gravity to be absent)

(a)
3
R
2
(b)
1
R
3
(c)
1
R
2
(d) None of these
Q 2.  A uniform electric field of strength E
?
exists in a region. An electron enters a point A with velocity
v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is
2v at 30° with x-axis. Then

(a) electric field
2
3mv
ˆ
Ei
2ea
??
?

(b) rate of doing work done by electric field at B is
3
3mv
2ea

(c) Both (a) and (b) are correct
(d) Both (a) and (b) are wrong
Q 3.  Two point charges a and b whose magnitudes are same positioned at a certain distance along the
positive x-axis from each other, a is at origin. Graph is drawn between electrical field strength and
distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it
can be decided that

(a) a is positive, b is negative    (b) a and b both are positive
(c) a and b both are negative    (d) a is negative, b is positive
Note Graph is drawn only between a and b.
Q 4.  Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric
field on the line passing through point O and perpendicular to the plane of the figure as a function
of distance x from point

O is (x >>a)

(a) 0   (b)
3
0
Qa
x ??
(c)
3
0
2Qa
x ??
(d)
3
0
3Qa
x ??

Q 5.  If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the
potential at the centre will be

(a) 10 V  (b) 5 V   (c) 15 V  (d) zero
Q 6.  A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting
spherical shell of inner radius 2a and outer radius 3a as shown

in figure. Find the amount of heat
produced when switch is closed
0
1
k
4
?
??

(a)
2
kq
2a
(b)
2
kq
3a
(c)
2
kq
4a
(d)
2
kq
6a

Q 7.  There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D
are given charges + q and - q respectively. Shell C is now earthed. The potential difference V
A
-
V
C
is
0
1
k
4
?
??

(a)
kq
2a
(b)
kq
3a
(c)
kq
4a
(d)
kq
6a

Q 8.  Potential difference between centre and surface of the sphere of radius R and uniform volume
charge density within it will be
(a)
2
0
R
6
?
?
(b)
2
0
R
4
?
?
(c)
2
0
R
3
?
?
(d)
2
0
R
2
?
?

Page 3

Objective Questions
Single Correct Option
Q 1.  In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from
a distance R from the fixed charge. Minimum separation between the two charges if the velocity
becomes
1
3

times of the projected velocity, at this moment is (Assume gravity to be absent)

(a)
3
R
2
(b)
1
R
3
(c)
1
R
2
(d) None of these
Q 2.  A uniform electric field of strength E
?
exists in a region. An electron enters a point A with velocity
v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is
2v at 30° with x-axis. Then

(a) electric field
2
3mv
ˆ
Ei
2ea
??
?

(b) rate of doing work done by electric field at B is
3
3mv
2ea

(c) Both (a) and (b) are correct
(d) Both (a) and (b) are wrong
Q 3.  Two point charges a and b whose magnitudes are same positioned at a certain distance along the
positive x-axis from each other, a is at origin. Graph is drawn between electrical field strength and
distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it
can be decided that

(a) a is positive, b is negative    (b) a and b both are positive
(c) a and b both are negative    (d) a is negative, b is positive
Note Graph is drawn only between a and b.
Q 4.  Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric
field on the line passing through point O and perpendicular to the plane of the figure as a function
of distance x from point

O is (x >>a)

(a) 0   (b)
3
0
Qa
x ??
(c)
3
0
2Qa
x ??
(d)
3
0
3Qa
x ??

Q 5.  If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the
potential at the centre will be

(a) 10 V  (b) 5 V   (c) 15 V  (d) zero
Q 6.  A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting
spherical shell of inner radius 2a and outer radius 3a as shown

in figure. Find the amount of heat
produced when switch is closed
0
1
k
4
?
??

(a)
2
kq
2a
(b)
2
kq
3a
(c)
2
kq
4a
(d)
2
kq
6a

Q 7.  There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D
are given charges + q and - q respectively. Shell C is now earthed. The potential difference V
A
-
V
C
is
0
1
k
4
?
??

(a)
kq
2a
(b)
kq
3a
(c)
kq
4a
(d)
kq
6a

Q 8.  Potential difference between centre and surface of the sphere of radius R and uniform volume
charge density within it will be
(a)
2
0
R
6
?
?
(b)
2
0
R
4
?
?
(c)
2
0
R
3
?
?
(d)
2
0
R
2
?
?

Q 9.  A positively charged disc is placed on a horizontal plane. A charged particle is released from a
certain height on its axis. The particle just reaches the centre of the disc. Select the correct
alternative.
(a) Particle has negative charge on it
(b) Total potential energy (gravitational + electrostatic) of the particle first increases then
decreases
(c) Total potential energy of the particle first decreases then increases
(d) Total potential energy of the particle continuously decreases
Q 10.  The curve represents the distribution of potential along the straight line joining the two charges Q
1

and Q
2
(separated by a distance r) then which of the following statements are correct ?
1. |Q
1
| > |Q
2
|
2. Q
1
is positive in nature
3. A and B are equilibrium points
4. C is a point of unstable equilibrium
(a) 1 and 2   (b) 1,2 and 3   (c) 1,2 and 4
(d) 1,2, 3 and 4
Q 11.  A point charge q
1
= q is placed at point P. Another point charge q
2
=-q is placed at point Q. At
some point R(R ? P, R ? Q), electric potential due to q
1
is V
1
and electric potential due to q
2
is V
2
.
Which of the following is correct?
(a) Only for some points V
1
> V
2
(b) Only for some points V
2
> V
1

(c) For all points V
1
> V
2
(d) For all points V
2
>V
1

Q 12.  The variation of electric field between the two charges q
1
and q
2
along the line joining the charges
is plotted against distance from q
1
(taking rightward direction of electric field as positive) as
shown in the figure. Then the correct statement is

(a) q
1
and q
2
are positive and q
1
< q
2
(b) q
1
and q
2
are positive and q
1
> q
2

(c) q
1
is positive and q
2
is negative q
1
< | q
2
| (d) q
1
and q
2
are negative and |q
1
| < | q
2
|
Q 13.  A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the
conductor. If q is displaced from O towards S (still remaining within the cavity)

(a) electric field at S will increase  (b) electric field at S will decrease
(c) electric field at S will first increase and then decrease
(d) electric field at S will not change
Page 4

Objective Questions
Single Correct Option
Q 1.  In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from
a distance R from the fixed charge. Minimum separation between the two charges if the velocity
becomes
1
3

times of the projected velocity, at this moment is (Assume gravity to be absent)

(a)
3
R
2
(b)
1
R
3
(c)
1
R
2
(d) None of these
Q 2.  A uniform electric field of strength E
?
exists in a region. An electron enters a point A with velocity
v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is
2v at 30° with x-axis. Then

(a) electric field
2
3mv
ˆ
Ei
2ea
??
?

(b) rate of doing work done by electric field at B is
3
3mv
2ea

(c) Both (a) and (b) are correct
(d) Both (a) and (b) are wrong
Q 3.  Two point charges a and b whose magnitudes are same positioned at a certain distance along the
positive x-axis from each other, a is at origin. Graph is drawn between electrical field strength and
distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it
can be decided that

(a) a is positive, b is negative    (b) a and b both are positive
(c) a and b both are negative    (d) a is negative, b is positive
Note Graph is drawn only between a and b.
Q 4.  Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric
field on the line passing through point O and perpendicular to the plane of the figure as a function
of distance x from point

O is (x >>a)

(a) 0   (b)
3
0
Qa
x ??
(c)
3
0
2Qa
x ??
(d)
3
0
3Qa
x ??

Q 5.  If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the
potential at the centre will be

(a) 10 V  (b) 5 V   (c) 15 V  (d) zero
Q 6.  A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting
spherical shell of inner radius 2a and outer radius 3a as shown

in figure. Find the amount of heat
produced when switch is closed
0
1
k
4
?
??

(a)
2
kq
2a
(b)
2
kq
3a
(c)
2
kq
4a
(d)
2
kq
6a

Q 7.  There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D
are given charges + q and - q respectively. Shell C is now earthed. The potential difference V
A
-
V
C
is
0
1
k
4
?
??

(a)
kq
2a
(b)
kq
3a
(c)
kq
4a
(d)
kq
6a

Q 8.  Potential difference between centre and surface of the sphere of radius R and uniform volume
charge density within it will be
(a)
2
0
R
6
?
?
(b)
2
0
R
4
?
?
(c)
2
0
R
3
?
?
(d)
2
0
R
2
?
?

Q 9.  A positively charged disc is placed on a horizontal plane. A charged particle is released from a
certain height on its axis. The particle just reaches the centre of the disc. Select the correct
alternative.
(a) Particle has negative charge on it
(b) Total potential energy (gravitational + electrostatic) of the particle first increases then
decreases
(c) Total potential energy of the particle first decreases then increases
(d) Total potential energy of the particle continuously decreases
Q 10.  The curve represents the distribution of potential along the straight line joining the two charges Q
1

and Q
2
(separated by a distance r) then which of the following statements are correct ?
1. |Q
1
| > |Q
2
|
2. Q
1
is positive in nature
3. A and B are equilibrium points
4. C is a point of unstable equilibrium
(a) 1 and 2   (b) 1,2 and 3   (c) 1,2 and 4
(d) 1,2, 3 and 4
Q 11.  A point charge q
1
= q is placed at point P. Another point charge q
2
=-q is placed at point Q. At
some point R(R ? P, R ? Q), electric potential due to q
1
is V
1
and electric potential due to q
2
is V
2
.
Which of the following is correct?
(a) Only for some points V
1
> V
2
(b) Only for some points V
2
> V
1

(c) For all points V
1
> V
2
(d) For all points V
2
>V
1

Q 12.  The variation of electric field between the two charges q
1
and q
2
along the line joining the charges
is plotted against distance from q
1
(taking rightward direction of electric field as positive) as
shown in the figure. Then the correct statement is

(a) q
1
and q
2
are positive and q
1
< q
2
(b) q
1
and q
2
are positive and q
1
> q
2

(c) q
1
is positive and q
2
is negative q
1
< | q
2
| (d) q
1
and q
2
are negative and |q
1
| < | q
2
|
Q 13.  A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the
conductor. If q is displaced from O towards S (still remaining within the cavity)

(a) electric field at S will increase  (b) electric field at S will decrease
(c) electric field at S will first increase and then decrease
(d) electric field at S will not change
Q 14.  A uniform electric field of 400 V/m is directed at 45° above the x-axis as shown in the figure. The
potential difference V
A
- V
B
is given by

(a) 0   (b) 4 V   (c) 6.4 V  (d) 2.8 V
Q 15.  Initially the spheres A and B are at potential V
A
and V
B
respectively. Now sphere B is earthed by
closing the switch. The potential of A will now become

(a) 0   (b) V
A
(c)V
A
- V
B
(d) V
B
Q 16.  A particle of mass m and charge q is fastened to one end of a string of length l. The other end of
the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially,
the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then

(a) the speed of the particle when it reaches B is
2qEl
m

(b) the speed of the particle when it reaches B is
qEl
m

(c) the tension in the string when the particle reaches at B is qE
(d) the tension in the string when the particle reaches at B is zero
Q 17.  A charged particle of mass m and charge q is released from rest from the position (x
0
,, 0) in a
uniform electric field
0
ˆ
Ej . The angular momentum of the particle about origin
(a) is zero   (b) is constant   (c) increases with time  (d) decreases with time
Q 18.  A charge + Q is uniformly distributed in a spherical volume of radius R. A particle of charge + q
and mass m projected with velocity v
0
from the surface of the spherical volume to its centre inside
a smooth tunnel dug across the sphere. The minimum value of v
0
such that it just reaches the
centre (assume that there

is no resistance on the particle except electrostatic force) of the spherical
volume is
(a)
0
Qq
2 mR ??
(b)
0
Qq
mR ??
(c)
0
2Qq
mR ??
(d)
0
Qq
4 mR ??

Page 5

Objective Questions
Single Correct Option
Q 1.  In the diagram shown, the charge +Q is fixed. Another charge + 2q and mass M is projected from
a distance R from the fixed charge. Minimum separation between the two charges if the velocity
becomes
1
3

times of the projected velocity, at this moment is (Assume gravity to be absent)

(a)
3
R
2
(b)
1
R
3
(c)
1
R
2
(d) None of these
Q 2.  A uniform electric field of strength E
?
exists in a region. An electron enters a point A with velocity
v as shown. It moves through the electric field and reaches at point B. Velocity of particle at B is
2v at 30° with x-axis. Then

(a) electric field
2
3mv
ˆ
Ei
2ea
??
?

(b) rate of doing work done by electric field at B is
3
3mv
2ea

(c) Both (a) and (b) are correct
(d) Both (a) and (b) are wrong
Q 3.  Two point charges a and b whose magnitudes are same positioned at a certain distance along the
positive x-axis from each other, a is at origin. Graph is drawn between electrical field strength and
distance x from a. E is taken positive if it is along the line joining from a to b. From the graph it
can be decided that

(a) a is positive, b is negative    (b) a and b both are positive
(c) a and b both are negative    (d) a is negative, b is positive
Note Graph is drawn only between a and b.
Q 4.  Six charges are placed at the vertices of a rectangular hexagon as shown in the figure. The electric
field on the line passing through point O and perpendicular to the plane of the figure as a function
of distance x from point

O is (x >>a)

(a) 0   (b)
3
0
Qa
x ??
(c)
3
0
2Qa
x ??
(d)
3
0
3Qa
x ??

Q 5.  If the electric potential of the inner shell is 10 V and that of the outer shell is 5 V, then the
potential at the centre will be

(a) 10 V  (b) 5 V   (c) 15 V  (d) zero
Q 6.  A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting
spherical shell of inner radius 2a and outer radius 3a as shown

in figure. Find the amount of heat
produced when switch is closed
0
1
k
4
?
??

(a)
2
kq
2a
(b)
2
kq
3a
(c)
2
kq
4a
(d)
2
kq
6a

Q 7.  There are four concentric shells A,B,C and D of radii a, 2a, 3a and 4a respectively. Shells B and D
are given charges + q and - q respectively. Shell C is now earthed. The potential difference V
A
-
V
C
is
0
1
k
4
?
??

(a)
kq
2a
(b)
kq
3a
(c)
kq
4a
(d)
kq
6a

Q 8.  Potential difference between centre and surface of the sphere of radius R and uniform volume
charge density within it will be
(a)
2
0
R
6
?
?
(b)
2
0
R
4
?
?
(c)
2
0
R
3
?
?
(d)
2
0
R
2
?
?

Q 9.  A positively charged disc is placed on a horizontal plane. A charged particle is released from a
certain height on its axis. The particle just reaches the centre of the disc. Select the correct
alternative.
(a) Particle has negative charge on it
(b) Total potential energy (gravitational + electrostatic) of the particle first increases then
decreases
(c) Total potential energy of the particle first decreases then increases
(d) Total potential energy of the particle continuously decreases
Q 10.  The curve represents the distribution of potential along the straight line joining the two charges Q
1

and Q
2
(separated by a distance r) then which of the following statements are correct ?
1. |Q
1
| > |Q
2
|
2. Q
1
is positive in nature
3. A and B are equilibrium points
4. C is a point of unstable equilibrium
(a) 1 and 2   (b) 1,2 and 3   (c) 1,2 and 4
(d) 1,2, 3 and 4
Q 11.  A point charge q
1
= q is placed at point P. Another point charge q
2
=-q is placed at point Q. At
some point R(R ? P, R ? Q), electric potential due to q
1
is V
1
and electric potential due to q
2
is V
2
.
Which of the following is correct?
(a) Only for some points V
1
> V
2
(b) Only for some points V
2
> V
1

(c) For all points V
1
> V
2
(d) For all points V
2
>V
1

Q 12.  The variation of electric field between the two charges q
1
and q
2
along the line joining the charges
is plotted against distance from q
1
(taking rightward direction of electric field as positive) as
shown in the figure. Then the correct statement is

(a) q
1
and q
2
are positive and q
1
< q
2
(b) q
1
and q
2
are positive and q
1
> q
2

(c) q
1
is positive and q
2
is negative q
1
< | q
2
| (d) q
1
and q
2
are negative and |q
1
| < | q
2
|
Q 13.  A charge q is placed at O in the cavity in a spherical uncharged conductor. Point S is outside the
conductor. If q is displaced from O towards S (still remaining within the cavity)

(a) electric field at S will increase  (b) electric field at S will decrease
(c) electric field at S will first increase and then decrease
(d) electric field at S will not change
Q 14.  A uniform electric field of 400 V/m is directed at 45° above the x-axis as shown in the figure. The
potential difference V
A
- V
B
is given by

(a) 0   (b) 4 V   (c) 6.4 V  (d) 2.8 V
Q 15.  Initially the spheres A and B are at potential V
A
and V
B
respectively. Now sphere B is earthed by
closing the switch. The potential of A will now become

(a) 0   (b) V
A
(c)V
A
- V
B
(d) V
B
Q 16.  A particle of mass m and charge q is fastened to one end of a string of length l. The other end of
the string is fixed to the point O. The whole system lies on a frictionless horizontal plane. Initially,
the mass is at rest at A. A uniform electric field in the direction shown is then switched on. Then

(a) the speed of the particle when it reaches B is
2qEl
m

(b) the speed of the particle when it reaches B is
qEl
m

(c) the tension in the string when the particle reaches at B is qE
(d) the tension in the string when the particle reaches at B is zero
Q 17.  A charged particle of mass m and charge q is released from rest from the position (x
0
,, 0) in a
uniform electric field
0
ˆ
Ej . The angular momentum of the particle about origin
(a) is zero   (b) is constant   (c) increases with time  (d) decreases with time
Q 18.  A charge + Q is uniformly distributed in a spherical volume of radius R. A particle of charge + q
and mass m projected with velocity v
0
from the surface of the spherical volume to its centre inside
a smooth tunnel dug across the sphere. The minimum value of v
0
such that it just reaches the
centre (assume that there

is no resistance on the particle except electrostatic force) of the spherical
volume is
(a)
0
Qq
2 mR ??
(b)
0
Qq
mR ??
(c)
0
2Qq
mR ??
(d)
0
Qq
4 mR ??

Q 19.  Two identical coaxial rings each of radius R are separated by a distance of 3R .

They are
uniformly charged with charges +Q and - Q respectively. The minimum kinetic energy with which
a charged particle (charge + q) should be projected from the centre of the negatively charged ring
along the axis of the rings such that it reaches the centre of the positively charged ring is
(a)
0
Qq
4R ??
(b)
0
Qq
2R ??
(c)
0
Qq
8R ??
(d)
0
3Qq
4R ??

Q 20.  A uniform electric field exists in x-y plane. The potential of points A (2m, 2m), B(-2m, 2m) and
C(2m, 4m) are 4 V, 16 V and 12 V respectively. The electric field is
(a)
ˆˆ
(4i 5j)V/ m ?  (b)
ˆˆ
(3i 4j)V/ m ?  (c)
ˆˆ
(3i 4j)V/ m ??  (d)
ˆˆ
(3i 4j)V/ m ?
Q 21.  Two fixed charges - 2Q and + Q are located at points (- 3a, 0) and (+ 3a, 0) respectively. Then
which of the following statement is correct?
(a) Points where the electric potential due to the two charges is zero in x-y plane, lie on a circle of
radius 4a and centre (5a, 0)
(b) Potential is zero at x = a and x = 9a
(c) Both (a) and (b) are wrong
(d) Both (a) and (b) are correct
Q 22.  A particle of mass m and charge - q is projected from the origin with a horizontal speed v into an
electric field of intensity E directed downward. Choose the wrong statement. Neglect gravity

(a) The kinetic energy after a displacement y is qEy
(b) The horizontal and vertical components of acceleration are a
x
= 0, a
y
=
qE
m

(c) The equation of trajectory is
2
2
1 qEx
y
2 mv
??
?
??
??

(d) The horizontal and vertical displacements x and y after a time t are x = vt and
2
y
1
y a t
2
?
Q 23.  A particle of charge - q and mass m moves in a circle of radius r around an infinitely long

line
charge of linear charge density + ?.

Then time period will be where,
0
1
k
4
?
??

(a)
m
T 2 r
2k q
??
?
(b)
2
23
4m
Tr
2k q
?
?
?
(c)
1 2k q
T
2 r m
?
?
?
(d)
1m
T
2 r 2k q
?
??

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## DC Pandey Solutions for JEE Physics

210 docs

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