DC Pandey Solutions (JEE Advance): Electrostatic- 2 | DC Pandey Solutions for JEE Physics PDF Download

 Page 1


For JEE Advanced 
Objective Questions 
More than One Correct Options 
Q 1.  Two concentric shells have radii R and 2R charges q
A
 and q
B
 and potentials 2Vand (3/2) V 
respectively. Now shell B is earthed and let charges on them become q
A
' and q
B
'. Then 
 
  (a) q
A
/q
B
= 1/2   (b) q
A
'/q
B
'=1  
  (c) potential of A after earthing becomes (3/2) V  
  (d) potential difference between A and B after earthing becomes V/2 
Q 2.  A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity 10 ms
-1
. There is a 
uniform horizontal electric field of 10
4
 N/C 
(a) The horizontal range of the particle is 10 m (b) The time of flight of the particle is 2 s 
  (c) The maximum height reached is 5 m  (d) The horizontal range of the particle is 5 m 
Q 3.  At the distance of 5 cm and 10 cm from surface of a uniformly charged solid sphere, the potentials 
are 100 V and 75 V respectively. Then 
  (a) Potential at its surface is 150 V   (b) The charge on the sphere is 
10
50
10 C
3
?
? 
  (c) The electric field on the surface is 1500 V/m (d) The electric potential at its centre is 25 V 
Q 4.  Three charged particles are in equilibrium under their electrostatic forces only. Then 
(a) The particles must be collinear  (b) All the charges cannot have the same magnitude 
  (c) All the charges cannot have the same sign (d) The equilibrium is unstable 
Q 5.  Charges Q
1
 and Q
2
 lie inside and outside respectively of a closed surface S. Let E be the field at 
any point on S and ?
 
be the flux of E over S 
  (a) If Q
1
 changes, both E and ?
 
will change (b) If Q
2
 changes, E will change but ?
 
will not change 
  (c) if Q
1
 =0 and Q
2 
? 0 then E ? 0 but ? = 0 (d) If Q
1 
? 0and Q
2
 = 0 then E = 0 but ? ? 0 
Q 6.  An electric dipole is placed at the centre of a sphere. Mark the correct options. 
  (a) The flux of the electric field through the sphere is zero 
  (b) The electric field is zero at every point of the sphere 
  (c) The electric field is not zero at any where on the sphere 
  (d) The electric field is zero on a circle on the sphere 
Q 7.  Mark the correct options. 
  (a) Gauss's law is valid only for uniform charge distributions 
  (b) Gauss's law is valid only for charges placed in vacuum 
  (c) The electric field calculated by Gauss's law is the field due to all the charges 
(d) The flux of the electric field through a closed surface due to all the charges is equal to the flux 
due to the charges enclosed by the surface 
Page 2


For JEE Advanced 
Objective Questions 
More than One Correct Options 
Q 1.  Two concentric shells have radii R and 2R charges q
A
 and q
B
 and potentials 2Vand (3/2) V 
respectively. Now shell B is earthed and let charges on them become q
A
' and q
B
'. Then 
 
  (a) q
A
/q
B
= 1/2   (b) q
A
'/q
B
'=1  
  (c) potential of A after earthing becomes (3/2) V  
  (d) potential difference between A and B after earthing becomes V/2 
Q 2.  A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity 10 ms
-1
. There is a 
uniform horizontal electric field of 10
4
 N/C 
(a) The horizontal range of the particle is 10 m (b) The time of flight of the particle is 2 s 
  (c) The maximum height reached is 5 m  (d) The horizontal range of the particle is 5 m 
Q 3.  At the distance of 5 cm and 10 cm from surface of a uniformly charged solid sphere, the potentials 
are 100 V and 75 V respectively. Then 
  (a) Potential at its surface is 150 V   (b) The charge on the sphere is 
10
50
10 C
3
?
? 
  (c) The electric field on the surface is 1500 V/m (d) The electric potential at its centre is 25 V 
Q 4.  Three charged particles are in equilibrium under their electrostatic forces only. Then 
(a) The particles must be collinear  (b) All the charges cannot have the same magnitude 
  (c) All the charges cannot have the same sign (d) The equilibrium is unstable 
Q 5.  Charges Q
1
 and Q
2
 lie inside and outside respectively of a closed surface S. Let E be the field at 
any point on S and ?
 
be the flux of E over S 
  (a) If Q
1
 changes, both E and ?
 
will change (b) If Q
2
 changes, E will change but ?
 
will not change 
  (c) if Q
1
 =0 and Q
2 
? 0 then E ? 0 but ? = 0 (d) If Q
1 
? 0and Q
2
 = 0 then E = 0 but ? ? 0 
Q 6.  An electric dipole is placed at the centre of a sphere. Mark the correct options. 
  (a) The flux of the electric field through the sphere is zero 
  (b) The electric field is zero at every point of the sphere 
  (c) The electric field is not zero at any where on the sphere 
  (d) The electric field is zero on a circle on the sphere 
Q 7.  Mark the correct options. 
  (a) Gauss's law is valid only for uniform charge distributions 
  (b) Gauss's law is valid only for charges placed in vacuum 
  (c) The electric field calculated by Gauss's law is the field due to all the charges 
(d) The flux of the electric field through a closed surface due to all the charges is equal to the flux 
due to the charges enclosed by the surface 
Q 8.  Two concentric spherical shells have charges + q and - q as shown in figure. Choose the correct 
options 
 
  (a) At A electric field is zero, but electric potential is non-zero 
  (b) At B electric field and electric potential both are non-zero 
  (c) At C electric field is zero but electric potential is non-zero 
  (d) At C electric field and electric potential both are zero 
Q 9.  A rod is hinged (free to rotate) at its centre O as shown in figure. Two point charges + q and + q 
are kept at its two ends. Rod is placed in uniform electric field E as shown. Space is gravity free. 
Choose the correct options. 
 
  (a) Net force from the hinge on the rod is zero 
  (b) Net force from the hinge on the rod is left wards 
  (c) Equilibrium of rod is neutral 
  (d) Equilibrium of rod is stable 
Q 10. Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third 
charge + q is moved from A to B, then from B to C. 
 
  (a) From A to B electrostatic potential energy will decrease 
  (b) From A to B electrostatic potential energy will increase 
  (c) From B to C electrostatic potential energy will increase 
  (d) From B to C electrostatic potential energy will decrease 
Answers 
   1.(a,d) 2.(a,b,c) 3.(a,b,c) 4.(all) 5.(a,b,c) 6.(a,c) 7.(c,d) 8.(a,b,d) 9.(b,c) 10.(b,c) 
Solutions 
1.  (a) V
A
 = 2V = 
   
  Solving these two equations we get 
    
Page 3


For JEE Advanced 
Objective Questions 
More than One Correct Options 
Q 1.  Two concentric shells have radii R and 2R charges q
A
 and q
B
 and potentials 2Vand (3/2) V 
respectively. Now shell B is earthed and let charges on them become q
A
' and q
B
'. Then 
 
  (a) q
A
/q
B
= 1/2   (b) q
A
'/q
B
'=1  
  (c) potential of A after earthing becomes (3/2) V  
  (d) potential difference between A and B after earthing becomes V/2 
Q 2.  A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity 10 ms
-1
. There is a 
uniform horizontal electric field of 10
4
 N/C 
(a) The horizontal range of the particle is 10 m (b) The time of flight of the particle is 2 s 
  (c) The maximum height reached is 5 m  (d) The horizontal range of the particle is 5 m 
Q 3.  At the distance of 5 cm and 10 cm from surface of a uniformly charged solid sphere, the potentials 
are 100 V and 75 V respectively. Then 
  (a) Potential at its surface is 150 V   (b) The charge on the sphere is 
10
50
10 C
3
?
? 
  (c) The electric field on the surface is 1500 V/m (d) The electric potential at its centre is 25 V 
Q 4.  Three charged particles are in equilibrium under their electrostatic forces only. Then 
(a) The particles must be collinear  (b) All the charges cannot have the same magnitude 
  (c) All the charges cannot have the same sign (d) The equilibrium is unstable 
Q 5.  Charges Q
1
 and Q
2
 lie inside and outside respectively of a closed surface S. Let E be the field at 
any point on S and ?
 
be the flux of E over S 
  (a) If Q
1
 changes, both E and ?
 
will change (b) If Q
2
 changes, E will change but ?
 
will not change 
  (c) if Q
1
 =0 and Q
2 
? 0 then E ? 0 but ? = 0 (d) If Q
1 
? 0and Q
2
 = 0 then E = 0 but ? ? 0 
Q 6.  An electric dipole is placed at the centre of a sphere. Mark the correct options. 
  (a) The flux of the electric field through the sphere is zero 
  (b) The electric field is zero at every point of the sphere 
  (c) The electric field is not zero at any where on the sphere 
  (d) The electric field is zero on a circle on the sphere 
Q 7.  Mark the correct options. 
  (a) Gauss's law is valid only for uniform charge distributions 
  (b) Gauss's law is valid only for charges placed in vacuum 
  (c) The electric field calculated by Gauss's law is the field due to all the charges 
(d) The flux of the electric field through a closed surface due to all the charges is equal to the flux 
due to the charges enclosed by the surface 
Q 8.  Two concentric spherical shells have charges + q and - q as shown in figure. Choose the correct 
options 
 
  (a) At A electric field is zero, but electric potential is non-zero 
  (b) At B electric field and electric potential both are non-zero 
  (c) At C electric field is zero but electric potential is non-zero 
  (d) At C electric field and electric potential both are zero 
Q 9.  A rod is hinged (free to rotate) at its centre O as shown in figure. Two point charges + q and + q 
are kept at its two ends. Rod is placed in uniform electric field E as shown. Space is gravity free. 
Choose the correct options. 
 
  (a) Net force from the hinge on the rod is zero 
  (b) Net force from the hinge on the rod is left wards 
  (c) Equilibrium of rod is neutral 
  (d) Equilibrium of rod is stable 
Q 10. Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third 
charge + q is moved from A to B, then from B to C. 
 
  (a) From A to B electrostatic potential energy will decrease 
  (b) From A to B electrostatic potential energy will increase 
  (c) From B to C electrostatic potential energy will increase 
  (d) From B to C electrostatic potential energy will decrease 
Answers 
   1.(a,d) 2.(a,b,c) 3.(a,b,c) 4.(all) 5.(a,b,c) 6.(a,c) 7.(c,d) 8.(a,b,d) 9.(b,c) 10.(b,c) 
Solutions 
1.  (a) V
A
 = 2V = 
   
  Solving these two equations we get 
    
  (b)    
    
(c) & (d) Potential difference between A and B will remain unchanged as by earthing B, charge on 
will not change. 
   
   
2.   
   
   
   
   = 10m 
3.  
   
  Solving these equations we get, and 
   R = 0.1 m 
  (a) 
   = 150V  
  (c) 
   = 1500 V/m 
  (d) V
centre
 = 1.5 V
surface
 
4.  See the hint of Q. No. 6 of subjective questions. 
5.  Electric field at any point depends on both charges Q
1
 and Q
2
. But electric flux passing from any 
closed surface depends on the charged enclosed by that closed surface only. 
6.  Flux from any closed surface due to a dipole. 
7.  Solution is not required. 
8.  
  E
A 
= E
C
 = 0 but E
B
 ? 0 
Page 4


For JEE Advanced 
Objective Questions 
More than One Correct Options 
Q 1.  Two concentric shells have radii R and 2R charges q
A
 and q
B
 and potentials 2Vand (3/2) V 
respectively. Now shell B is earthed and let charges on them become q
A
' and q
B
'. Then 
 
  (a) q
A
/q
B
= 1/2   (b) q
A
'/q
B
'=1  
  (c) potential of A after earthing becomes (3/2) V  
  (d) potential difference between A and B after earthing becomes V/2 
Q 2.  A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity 10 ms
-1
. There is a 
uniform horizontal electric field of 10
4
 N/C 
(a) The horizontal range of the particle is 10 m (b) The time of flight of the particle is 2 s 
  (c) The maximum height reached is 5 m  (d) The horizontal range of the particle is 5 m 
Q 3.  At the distance of 5 cm and 10 cm from surface of a uniformly charged solid sphere, the potentials 
are 100 V and 75 V respectively. Then 
  (a) Potential at its surface is 150 V   (b) The charge on the sphere is 
10
50
10 C
3
?
? 
  (c) The electric field on the surface is 1500 V/m (d) The electric potential at its centre is 25 V 
Q 4.  Three charged particles are in equilibrium under their electrostatic forces only. Then 
(a) The particles must be collinear  (b) All the charges cannot have the same magnitude 
  (c) All the charges cannot have the same sign (d) The equilibrium is unstable 
Q 5.  Charges Q
1
 and Q
2
 lie inside and outside respectively of a closed surface S. Let E be the field at 
any point on S and ?
 
be the flux of E over S 
  (a) If Q
1
 changes, both E and ?
 
will change (b) If Q
2
 changes, E will change but ?
 
will not change 
  (c) if Q
1
 =0 and Q
2 
? 0 then E ? 0 but ? = 0 (d) If Q
1 
? 0and Q
2
 = 0 then E = 0 but ? ? 0 
Q 6.  An electric dipole is placed at the centre of a sphere. Mark the correct options. 
  (a) The flux of the electric field through the sphere is zero 
  (b) The electric field is zero at every point of the sphere 
  (c) The electric field is not zero at any where on the sphere 
  (d) The electric field is zero on a circle on the sphere 
Q 7.  Mark the correct options. 
  (a) Gauss's law is valid only for uniform charge distributions 
  (b) Gauss's law is valid only for charges placed in vacuum 
  (c) The electric field calculated by Gauss's law is the field due to all the charges 
(d) The flux of the electric field through a closed surface due to all the charges is equal to the flux 
due to the charges enclosed by the surface 
Q 8.  Two concentric spherical shells have charges + q and - q as shown in figure. Choose the correct 
options 
 
  (a) At A electric field is zero, but electric potential is non-zero 
  (b) At B electric field and electric potential both are non-zero 
  (c) At C electric field is zero but electric potential is non-zero 
  (d) At C electric field and electric potential both are zero 
Q 9.  A rod is hinged (free to rotate) at its centre O as shown in figure. Two point charges + q and + q 
are kept at its two ends. Rod is placed in uniform electric field E as shown. Space is gravity free. 
Choose the correct options. 
 
  (a) Net force from the hinge on the rod is zero 
  (b) Net force from the hinge on the rod is left wards 
  (c) Equilibrium of rod is neutral 
  (d) Equilibrium of rod is stable 
Q 10. Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third 
charge + q is moved from A to B, then from B to C. 
 
  (a) From A to B electrostatic potential energy will decrease 
  (b) From A to B electrostatic potential energy will increase 
  (c) From B to C electrostatic potential energy will increase 
  (d) From B to C electrostatic potential energy will decrease 
Answers 
   1.(a,d) 2.(a,b,c) 3.(a,b,c) 4.(all) 5.(a,b,c) 6.(a,c) 7.(c,d) 8.(a,b,d) 9.(b,c) 10.(b,c) 
Solutions 
1.  (a) V
A
 = 2V = 
   
  Solving these two equations we get 
    
  (b)    
    
(c) & (d) Potential difference between A and B will remain unchanged as by earthing B, charge on 
will not change. 
   
   
2.   
   
   
   
   = 10m 
3.  
   
  Solving these equations we get, and 
   R = 0.1 m 
  (a) 
   = 150V  
  (c) 
   = 1500 V/m 
  (d) V
centre
 = 1.5 V
surface
 
4.  See the hint of Q. No. 6 of subjective questions. 
5.  Electric field at any point depends on both charges Q
1
 and Q
2
. But electric flux passing from any 
closed surface depends on the charged enclosed by that closed surface only. 
6.  Flux from any closed surface due to a dipole. 
7.  Solution is not required. 
8.  
  E
A 
= E
C
 = 0 but E
B
 ? 0 
   
9.  
  Higher force = 2qE (toward left) 
    
  If we displace the rod,  in displaced position too. Hence equilibrium is neutral. 
10.  Along the line AB, charge q is at unstable equilibrium position at B (When displaced from B 
along AB, net force on it is away from B, whereas force at B is zero). Hence potential energy at B 
is maximum. 
  Along CD equilibrium of q is stable. Hence potential energy at B is minimum along CD. 
 
Match the Columns 
Q 1.  Five identical charges are kept at five vertices of a regular hexagon. Match the following two 
columns at centre of the hexagon. If in the given situation electric field at centre is E. Then 
 
Column I Column. II 
(a) If charge at B is removed then electric field will become (P) 2E 
(b) If charge at C is removed then electric field will become (q) E 
(c) If charge at D is removed then electric field will become (r) zero 
(d) If charges at B and C both are removed then electric field will become 
(s) 3E 
  Note Only magnitudes of electric field are given. 
Q 2.  In an electric field 
ˆˆ
E (2i 4j)N/ C, ??
?
 
electric potential at origin is 0 V. Match the following two 
columns. 
Column I Column II 
Page 5


For JEE Advanced 
Objective Questions 
More than One Correct Options 
Q 1.  Two concentric shells have radii R and 2R charges q
A
 and q
B
 and potentials 2Vand (3/2) V 
respectively. Now shell B is earthed and let charges on them become q
A
' and q
B
'. Then 
 
  (a) q
A
/q
B
= 1/2   (b) q
A
'/q
B
'=1  
  (c) potential of A after earthing becomes (3/2) V  
  (d) potential difference between A and B after earthing becomes V/2 
Q 2.  A particle of mass 2 kg and charge 1 mC is projected vertically with a velocity 10 ms
-1
. There is a 
uniform horizontal electric field of 10
4
 N/C 
(a) The horizontal range of the particle is 10 m (b) The time of flight of the particle is 2 s 
  (c) The maximum height reached is 5 m  (d) The horizontal range of the particle is 5 m 
Q 3.  At the distance of 5 cm and 10 cm from surface of a uniformly charged solid sphere, the potentials 
are 100 V and 75 V respectively. Then 
  (a) Potential at its surface is 150 V   (b) The charge on the sphere is 
10
50
10 C
3
?
? 
  (c) The electric field on the surface is 1500 V/m (d) The electric potential at its centre is 25 V 
Q 4.  Three charged particles are in equilibrium under their electrostatic forces only. Then 
(a) The particles must be collinear  (b) All the charges cannot have the same magnitude 
  (c) All the charges cannot have the same sign (d) The equilibrium is unstable 
Q 5.  Charges Q
1
 and Q
2
 lie inside and outside respectively of a closed surface S. Let E be the field at 
any point on S and ?
 
be the flux of E over S 
  (a) If Q
1
 changes, both E and ?
 
will change (b) If Q
2
 changes, E will change but ?
 
will not change 
  (c) if Q
1
 =0 and Q
2 
? 0 then E ? 0 but ? = 0 (d) If Q
1 
? 0and Q
2
 = 0 then E = 0 but ? ? 0 
Q 6.  An electric dipole is placed at the centre of a sphere. Mark the correct options. 
  (a) The flux of the electric field through the sphere is zero 
  (b) The electric field is zero at every point of the sphere 
  (c) The electric field is not zero at any where on the sphere 
  (d) The electric field is zero on a circle on the sphere 
Q 7.  Mark the correct options. 
  (a) Gauss's law is valid only for uniform charge distributions 
  (b) Gauss's law is valid only for charges placed in vacuum 
  (c) The electric field calculated by Gauss's law is the field due to all the charges 
(d) The flux of the electric field through a closed surface due to all the charges is equal to the flux 
due to the charges enclosed by the surface 
Q 8.  Two concentric spherical shells have charges + q and - q as shown in figure. Choose the correct 
options 
 
  (a) At A electric field is zero, but electric potential is non-zero 
  (b) At B electric field and electric potential both are non-zero 
  (c) At C electric field is zero but electric potential is non-zero 
  (d) At C electric field and electric potential both are zero 
Q 9.  A rod is hinged (free to rotate) at its centre O as shown in figure. Two point charges + q and + q 
are kept at its two ends. Rod is placed in uniform electric field E as shown. Space is gravity free. 
Choose the correct options. 
 
  (a) Net force from the hinge on the rod is zero 
  (b) Net force from the hinge on the rod is left wards 
  (c) Equilibrium of rod is neutral 
  (d) Equilibrium of rod is stable 
Q 10. Two charges + Q each are fixed at points C and D. Line AB is the bisector line of CD. A third 
charge + q is moved from A to B, then from B to C. 
 
  (a) From A to B electrostatic potential energy will decrease 
  (b) From A to B electrostatic potential energy will increase 
  (c) From B to C electrostatic potential energy will increase 
  (d) From B to C electrostatic potential energy will decrease 
Answers 
   1.(a,d) 2.(a,b,c) 3.(a,b,c) 4.(all) 5.(a,b,c) 6.(a,c) 7.(c,d) 8.(a,b,d) 9.(b,c) 10.(b,c) 
Solutions 
1.  (a) V
A
 = 2V = 
   
  Solving these two equations we get 
    
  (b)    
    
(c) & (d) Potential difference between A and B will remain unchanged as by earthing B, charge on 
will not change. 
   
   
2.   
   
   
   
   = 10m 
3.  
   
  Solving these equations we get, and 
   R = 0.1 m 
  (a) 
   = 150V  
  (c) 
   = 1500 V/m 
  (d) V
centre
 = 1.5 V
surface
 
4.  See the hint of Q. No. 6 of subjective questions. 
5.  Electric field at any point depends on both charges Q
1
 and Q
2
. But electric flux passing from any 
closed surface depends on the charged enclosed by that closed surface only. 
6.  Flux from any closed surface due to a dipole. 
7.  Solution is not required. 
8.  
  E
A 
= E
C
 = 0 but E
B
 ? 0 
   
9.  
  Higher force = 2qE (toward left) 
    
  If we displace the rod,  in displaced position too. Hence equilibrium is neutral. 
10.  Along the line AB, charge q is at unstable equilibrium position at B (When displaced from B 
along AB, net force on it is away from B, whereas force at B is zero). Hence potential energy at B 
is maximum. 
  Along CD equilibrium of q is stable. Hence potential energy at B is minimum along CD. 
 
Match the Columns 
Q 1.  Five identical charges are kept at five vertices of a regular hexagon. Match the following two 
columns at centre of the hexagon. If in the given situation electric field at centre is E. Then 
 
Column I Column. II 
(a) If charge at B is removed then electric field will become (P) 2E 
(b) If charge at C is removed then electric field will become (q) E 
(c) If charge at D is removed then electric field will become (r) zero 
(d) If charges at B and C both are removed then electric field will become 
(s) 3E 
  Note Only magnitudes of electric field are given. 
Q 2.  In an electric field 
ˆˆ
E (2i 4j)N/ C, ??
?
 
electric potential at origin is 0 V. Match the following two 
columns. 
Column I Column II 
(a) Potential at (4m. 0) (p.) 8 V 
(b) Potential at (-4m, 0) (q) -8V 
(c) Potential at (0, 4m) (r) 16 V 
(d) Potential at (0, -4 m) (s) -16 V 
Q 3.  Electric potential on the surface of a solid sphere of charge is V. Radius of the sphere is 1 m. 
Match the following two columns. 
Column I Column II 
(a) Electric potential at 
R
r
2
? (p) 
V
4
 
(b) Electric potential at r = 2R 
(q) 
V
2
 
(c) Electric field at 
R
r
2
? (r) 
3V
4
 
(d) Electric field at r = 2R (s) None of these 
Q 4.  Match the following two columns. 
Column I Column II 
(a) Electric potential (p) [MLT
-3
A
-1
] 
(b) Electrical field (q) [ML
3
T
-3
A
-1
] 
(c) Electric flux (r) [ML
2
T
-3
A
-1
] 
(d) Permittivity of free space (s) None of these 
Q 5.  Match the following two columns. 
Column I Column II 
(a) Electric field due to charged spherical shell (P) 
(b) Electric potential due to charged spherical shell (q) 
(c) Electric field due to charged solid sphere (r) 
(d) Electric potential due to charged solid sphere (s) None of these 
Answers 
  1. (a) ? s (b) ? q (c) ? r (d) ? p  2. (a) ? q (b) ? p (c) ? s (d) ? r 
  3. (a) ? s (b) ? q (c) ? q (d) ? p  4. (a) ? r (b) ? p (c) ? q (d) ? s 
  5. (a) ? p (b) ? q (c) ? r (d) ? s 
Solutions 
1,  (a) are cancelled. at 60° 
  (b) are cancelled. at 120°.