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# 1 PRACTICE SET: ELECTROSTATICS LEVEL: Conceptual & Advanced Level- SET-1 Class 12 Notes | EduRev

## Class 12 : 1 PRACTICE SET: ELECTROSTATICS LEVEL: Conceptual & Advanced Level- SET-1 Class 12 Notes | EduRev

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1
PRACTICE SET: ELECTROSTATICS
LEVEL: Conceptual & Advanced Level- SET-1
1. A small point mass m has a
charge q, which is constrained to
move inside a narrow frictionless
cylinder. At the base of the
cylinder is a point mass of charge
Q having the same sign as q. If the
mass m is displaced by a small amount from
its equilibrium position and released, it will
exhibit simple harmonic motion. Find the
angular frequency of the mass.
2. A small bead of mass
m having charge –q is
constrained to move
along a frictionless
wire. A positive charge
Q lies at a distance L from the wire. Initially
bead is just above charge +Q. Show that if the
bead is displaced a distance x, where x < < L,
and released, it will exhibit simple harmonic
motion. Obtain an expression for the time
period of simple harmonic motion.
3. A charged particle q of mass (m) is in
equilibrium at a height h from a horizontal
infinite line charge with uniform linear charge
density ?. The charge lies in the vertical plane
containing the line charge. If the particle is
displaced slightly (vertically). Prove that the
motion of the charged particle will be simple
harmonic and find its time period. (write time
period of oscillation.
4. An infinitely long straight conductor carrying
a charge density ? = 100 ?C/m and a point
charge Q = ?1600 ?C are placed at a distance
1m on x ?y plane as shown in the figure.

(a) Plot schematically (without a definite
scale) the variation of electric field on
X-axis in the region I, II and III.
(b) Find the coordinate of the points on the
X-axis where electric field is zero and
locate them on the graph.
5. A small cork ball A of
mass m is suspended by a
thread of length l. Another
ball B is fixed at a distance
l from point of suspension
and distance l/2 from
thread when it is vertical, as shown in figure.
Ball A and B, each has positive charge q. Ball
A is held by an external force such that the
thread remains vertical. When ball A is
released from rest, thread deflects through a
maximum angle of ? = 30
0
, calculate m in
terms of the other parameters.
?
Y
1m
Q
X
I II III
m
q
y
0
Q
A
B
l
l/2
?
O
?
?
L
+Q
m
-q
X
x
Page 2

1
PRACTICE SET: ELECTROSTATICS
LEVEL: Conceptual & Advanced Level- SET-1
1. A small point mass m has a
charge q, which is constrained to
move inside a narrow frictionless
cylinder. At the base of the
cylinder is a point mass of charge
Q having the same sign as q. If the
mass m is displaced by a small amount from
its equilibrium position and released, it will
exhibit simple harmonic motion. Find the
angular frequency of the mass.
2. A small bead of mass
m having charge –q is
constrained to move
along a frictionless
wire. A positive charge
Q lies at a distance L from the wire. Initially
bead is just above charge +Q. Show that if the
bead is displaced a distance x, where x < < L,
and released, it will exhibit simple harmonic
motion. Obtain an expression for the time
period of simple harmonic motion.
3. A charged particle q of mass (m) is in
equilibrium at a height h from a horizontal
infinite line charge with uniform linear charge
density ?. The charge lies in the vertical plane
containing the line charge. If the particle is
displaced slightly (vertically). Prove that the
motion of the charged particle will be simple
harmonic and find its time period. (write time
period of oscillation.
4. An infinitely long straight conductor carrying
a charge density ? = 100 ?C/m and a point
charge Q = ?1600 ?C are placed at a distance
1m on x ?y plane as shown in the figure.

(a) Plot schematically (without a definite
scale) the variation of electric field on
X-axis in the region I, II and III.
(b) Find the coordinate of the points on the
X-axis where electric field is zero and
locate them on the graph.
5. A small cork ball A of
mass m is suspended by a
thread of length l. Another
ball B is fixed at a distance
l from point of suspension
and distance l/2 from
thread when it is vertical, as shown in figure.
Ball A and B, each has positive charge q. Ball
A is held by an external force such that the
thread remains vertical. When ball A is
released from rest, thread deflects through a
maximum angle of ? = 30
0
, calculate m in
terms of the other parameters.
?
Y
1m
Q
X
I II III
m
q
y
0
Q
A
B
l
l/2
?
O
?
?
L
+Q
m
-q
X
x

2
PRACTICE SET: ELECTROSTATICS
LEVEL: Conceptual & Advanced Level- SET-1
6. A non-conducting ring of mass m and radius r
is lying at rest in the vertical XY plane on a
smooth non conducting horizontal XZ plane.
Charge +q and –q are distributed uniformly on
the ring. On the two sides of the vertical
diameter of the ring. A constant and uniform
electric field E
?
is set up along the x-direction.
The ring is given a small rotation about the
vertical diameter of the ring and released. Find
the period of oscillation of the ring.
7. A positive charge
+Q is fixed at a
point A. Another
positively
charged particle of mass m and charge +q is
projected from a point B with velocity u as
shown in the fig. the point B is at large
distance from A and at distance ‘d’ from the
line AC. The initial velocity is parallel to the
line AC. The point C is at very large distance
from A. Find the minimum distance (in meter)
of +q from +Q during the motion.  Take Qq =
4 ? ?
0
mu
2
d and  d =
? ?
21 ? meter.
8. Two small identical balls lying on a horizontal
plane are connected by a weightless spring.
One ball (ball 2) is fixed at O and the other
(ball 1) is fee. The balls are charged identically
as a result of which the spring length increases
? = 2 times. Determine the change in
frequency.
+ +
2 1
O

9. Two small balls having the same mass and
charge and located on the same vertical at
heights h
1
and h
2
are thrown in the same
direction along the horizontal at the same
velocity v. The first ball touches the ground at
a horizontal distance R from the initial vertical
position. At what height h
2
will the second ball
be at this instant? Neglect any frictional
resistance of air and the effect of any induced
charges on the ground.
1.
0
2g
y

2.
3
0
4
2
mL
Qq
??
?
3. 2 ?
2
2
mh
kq ?

4. (b) ? 4 24 m
5.
9
2
9 10 ( ) 2
(2 3)
qx
xg
??
?

6. 2
4
mr
qE
?
7. d(1 + 2 )
8. frequency increases 2 times.
9.
2
12
R
h h g
v
??
??
??
??

B
u
d
A C
+Q
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