DC Pandey Solutions (JEE Advance): Electrostatic- 1 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
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


For JEE Advanced 
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


For JEE Advanced 
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


For JEE Advanced 
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


For JEE Advanced 
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
?
??