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

Created by: Bhuvan Midha

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

 Page 1


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

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