Electrostatic Potential & Capacitance Practice Questions - DPP for JEE

 Page 1


1. (c) Charges reside only on the outer surface of a conductor with
cavity.
2. (a) and  
and 
or 
or .
3. (c) Since, potential difference across C
2
 is greater than C
1
.
4. (b) In shell, q charge is uniformly distributed over its surface, it
behaves as a conductor.
V= potential at surface and inside 
Because of this it behaves as an equipotential surface.
5. (c)
Potential at C = V
C
 = 0
Page 2


1. (c) Charges reside only on the outer surface of a conductor with
cavity.
2. (a) and  
and 
or 
or .
3. (c) Since, potential difference across C
2
 is greater than C
1
.
4. (b) In shell, q charge is uniformly distributed over its surface, it
behaves as a conductor.
V= potential at surface and inside 
Because of this it behaves as an equipotential surface.
5. (c)
Potential at C = V
C
 = 0
Potential at D = V
D
Potential difference
V
D
 – V
C
 = 
? Work done = Q (V
D
 – V
C
)
6. (a) Potential at B, V
B
 is maximum
V
B
 > V
C
 > V
A
As in the direction of electric field potential decreases.
7. (b) At. equipotential surface, the potential is same at  any point i.e., V
A
= V
B
 as shown in figure. Hence no work is required to move unit
change from one point to another i.e.,
8. (b)
(i) Electrostatic field is zero inside a charged conductor or neutral
conductor.
(ii) Electrostatic field at the surface of a charged conductor must be normal
to the surface at every point.
(iii) There is no net charge at any point inside the conductor and any excess
charge must reside at the surface.
(iv) Electrostatic potential is constant throughout  the volume of the
conductor and has the same value (as insde) on its surface.
Page 3


1. (c) Charges reside only on the outer surface of a conductor with
cavity.
2. (a) and  
and 
or 
or .
3. (c) Since, potential difference across C
2
 is greater than C
1
.
4. (b) In shell, q charge is uniformly distributed over its surface, it
behaves as a conductor.
V= potential at surface and inside 
Because of this it behaves as an equipotential surface.
5. (c)
Potential at C = V
C
 = 0
Potential at D = V
D
Potential difference
V
D
 – V
C
 = 
? Work done = Q (V
D
 – V
C
)
6. (a) Potential at B, V
B
 is maximum
V
B
 > V
C
 > V
A
As in the direction of electric field potential decreases.
7. (b) At. equipotential surface, the potential is same at  any point i.e., V
A
= V
B
 as shown in figure. Hence no work is required to move unit
change from one point to another i.e.,
8. (b)
(i) Electrostatic field is zero inside a charged conductor or neutral
conductor.
(ii) Electrostatic field at the surface of a charged conductor must be normal
to the surface at every point.
(iii) There is no net charge at any point inside the conductor and any excess
charge must reside at the surface.
(iv) Electrostatic potential is constant throughout  the volume of the
conductor and has the same value (as insde) on its surface.
(v) Electric field at the surface of a charged conductor is
9. (c) since effective capacitance between plates A and E is
zero.
?   
10. (c)
11. (c) The value of dielectric constant is given as,
And, 
= 
Page 4


1. (c) Charges reside only on the outer surface of a conductor with
cavity.
2. (a) and  
and 
or 
or .
3. (c) Since, potential difference across C
2
 is greater than C
1
.
4. (b) In shell, q charge is uniformly distributed over its surface, it
behaves as a conductor.
V= potential at surface and inside 
Because of this it behaves as an equipotential surface.
5. (c)
Potential at C = V
C
 = 0
Potential at D = V
D
Potential difference
V
D
 – V
C
 = 
? Work done = Q (V
D
 – V
C
)
6. (a) Potential at B, V
B
 is maximum
V
B
 > V
C
 > V
A
As in the direction of electric field potential decreases.
7. (b) At. equipotential surface, the potential is same at  any point i.e., V
A
= V
B
 as shown in figure. Hence no work is required to move unit
change from one point to another i.e.,
8. (b)
(i) Electrostatic field is zero inside a charged conductor or neutral
conductor.
(ii) Electrostatic field at the surface of a charged conductor must be normal
to the surface at every point.
(iii) There is no net charge at any point inside the conductor and any excess
charge must reside at the surface.
(iv) Electrostatic potential is constant throughout  the volume of the
conductor and has the same value (as insde) on its surface.
(v) Electric field at the surface of a charged conductor is
9. (c) since effective capacitance between plates A and E is
zero.
?   
10. (c)
11. (c) The value of dielectric constant is given as,
And, 
= 
= 
= 
Now it is given that capacitance of vacuum = C
0
.
Thus, 
= (Let surface area of  plates = s)
= 
=  ( in vacuum e
0
 =1)
   
12. (d) Initial charge on capacitors C
1
 and C
2
 is given by,
q
1
 = C
1
V
1
 = 60 pC
q
2
 = C
2
V
2
 = 60pC
When S
1
 and S
3
 are closed, capacitors C
1
 and C
2 
get connected in series.
As a result charge on them should be same and so the charge do
not redistribute on them. So potential on them remains same.
Page 5


1. (c) Charges reside only on the outer surface of a conductor with
cavity.
2. (a) and  
and 
or 
or .
3. (c) Since, potential difference across C
2
 is greater than C
1
.
4. (b) In shell, q charge is uniformly distributed over its surface, it
behaves as a conductor.
V= potential at surface and inside 
Because of this it behaves as an equipotential surface.
5. (c)
Potential at C = V
C
 = 0
Potential at D = V
D
Potential difference
V
D
 – V
C
 = 
? Work done = Q (V
D
 – V
C
)
6. (a) Potential at B, V
B
 is maximum
V
B
 > V
C
 > V
A
As in the direction of electric field potential decreases.
7. (b) At. equipotential surface, the potential is same at  any point i.e., V
A
= V
B
 as shown in figure. Hence no work is required to move unit
change from one point to another i.e.,
8. (b)
(i) Electrostatic field is zero inside a charged conductor or neutral
conductor.
(ii) Electrostatic field at the surface of a charged conductor must be normal
to the surface at every point.
(iii) There is no net charge at any point inside the conductor and any excess
charge must reside at the surface.
(iv) Electrostatic potential is constant throughout  the volume of the
conductor and has the same value (as insde) on its surface.
(v) Electric field at the surface of a charged conductor is
9. (c) since effective capacitance between plates A and E is
zero.
?   
10. (c)
11. (c) The value of dielectric constant is given as,
And, 
= 
= 
= 
Now it is given that capacitance of vacuum = C
0
.
Thus, 
= (Let surface area of  plates = s)
= 
=  ( in vacuum e
0
 =1)
   
12. (d) Initial charge on capacitors C
1
 and C
2
 is given by,
q
1
 = C
1
V
1
 = 60 pC
q
2
 = C
2
V
2
 = 60pC
When S
1
 and S
3
 are closed, capacitors C
1
 and C
2 
get connected in series.
As a result charge on them should be same and so the charge do
not redistribute on them. So potential on them remains same.
13. (a)
At (1) using, potential 
  = 
At  (2) using potential 
  = 
= 
= 
14. (c) All the charge given to inner sphere will pass on to the outer one.
So capacitance that of outer one is .
15. (c) Equipotential surfaces are normal to the electric field lines. The
following figure shows the equipotential surfaces along with
electric field lines for a system of two positive charges.