# Electrostatic Potential And Capacitance MCQ | Class 12 | Physics | Chapter-2

## Electrostatic Potential And Capacitance MCQ Chapter 2

Electrostatic potential is the amount of work done to move a charge from a reference point to a specific point.

Below are some of the very important NCERT Electrostatic Potential and Capacitance MCQ Class 12 Physics Chapter 2 with answers. These Electrostatic Potential and Capacitance MCQ have been prepared by expert teachers and subject experts based on the latest syllabus and pattern of CBSE Term 1 examination.

We have given these Electrostatic Potential and Capacitance MCQ Class 12 Physics Questions with Answers to help students understand the concept.

MCQ Questions for Class 12 Physics are very important for the latest CBSE Term 1 and Term 2 pattern. These MCQs are very important for students who want to score high in CBSE Board, NEET and JEE exam.

We have put together these NCERT MCQ Questions of Electrostatic Potential and Capacitance for Class 12 Physics Chapter 2 with Answers for the practice on a regular basis to score high in exams. Refer to these MCQs Questions with Answers here along with a detailed explanation.

## MCQ

1 . The electric potential inside a conducting sphere

1. Increases from centre to surface decreases
2. from centre to surface
3. Remains constant from centre to surface
4. Is zero at every point inside

2. One volt is equivalent to

1. newton/second
2. newton/coulomb
3. joule/coulomb
4. joule/second

3. The potential at a point due to a charge of 4 x 10-7 C located 10 cm away is?

1. 3.6 x 105 V
2. 3.6 x 104 V
3. 4.5 x 104
4. 4.5 x 105 V

4. The electric potential at a point in free space due to a 1 charge Q coulomb is Q x 1011 V. The electric field at that point is

1. 12π?oQ x 1022 Vm-1
2. 4π?oQ x 1020 Vm-1
3. 12π?oQ x 1020 Vm-1
4. 4π?oQ x 1022 Vm-1

5. An electric dipole is placed at the centre of a hollow conducting sphere. Which of the following is correct?

1. Electric field is zero at every point of the sphere
2. Electric field is not zero anywhere on the sphere
3. The flux of electric field is not zero through the sphere
4. None of these

6. Figure shows the field lines of a positive point charge. The work done by the field in moving a small positive charge from Q to P is

1. zero
2. positive
3. negative
4. data insufficient

7. The value of electric potential at any point due to any electric dipole is

1. (a)
2. (b)
3. (c)
4. (d)

8. As shown in the figure, charges +q and -q are placed at the vertices B and C of an isosceles triangle. The potential at the vertex A is:

1. (a)
2. (b)
3. (c)
4. (d)

9. Four charges each equal to q are placed at the corners of a square of side l. The electric potential at the centre of the square is

1. (a)
2. (b)
3. (c)
4. (d)

10. Can two equipotential surfaces intersect each other?

1. Yes
2. No
3. Sometimes
4. Only when surfaces intersect at 900

11. If a unit positive charge is taken from one point to  another over an equipotential surface, then

1. Work is done on the charge
2. Work is done by the charge
3. Work done is constant
4. No work is done

12. A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. Let VA, VB, VC be the potentials at points A, B and C respectively. Then

1. VB
2. VB > VC
3. VA > VB
4. VA = VB

13. A test charge is moved from lower potential point a higher potential point. The potential energy of the charge will

1. remains the same
2. increase
3. decrease
4. becomes zero

14. The potential energy of a system of two charges is negative when

1. both the charges are positive
2. both the charges are negative
3. one charge is positive and other is negative
4. both the charges are separated by infinite distance

15. An electric dipole of moment P is placed normal to the lines of force of electric field intensity E, then the work done in deflecting it through an angle of 180° is

1. pE
2. 2pE
3. -2pE
4. zero

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16. When one electron is taken towards the other electron, then the electric potential energy of system

1. decreases
2. increases
3. remains unchanged
4. becomes zero

17. Q amount of electric charge is present on the surface 2 of a sphere having radius R. Then electrical potential energy of this system is

1. kQ/R
2. kQ2/R
3. kQ2/2R
4. kQ2/2R2

18. The electrostatic potential energy of a charge of 5C at a point in the electrostatic field is 50 J. The potential at that point is

1. 0.1 V
2. 5 V
3. 10 v
4. 250V

19. Two charges of equal magnitude ‘q’ are placed in air at a distance ‘2a’ apart and third charge ‘-2q’ is placed at midpoint. The potential energy of the system is: (?o = permittivity of free space)

1. -q2/8π?oa
2. -3q2/8π?oa
3. -5q2/8π?oa
4. -7q2/8π?oa

20. A conductor which can be given almost d charge is

1. copper
2. air
3. gold
4. earth

21. If a conductor has a potential zero and there are o charges anywhere else outside, then

1. there must be charges on the surface or inside itself
2. cannot be any charge in the body of conductor
3. there must be charges only on the surface
4. both 1 and 2 are correct

22. There are two metallic spheres of same radii but one is solid and the other is hollow, then

1. solid sphere can be given more charge
2. hollow sphere can be given more charge
3. they can be charged equally (maximum)
4. none of the above

23. A conductor with a positive charge:

1. is always at positive potential
2. is always at zero potential
3. is always at negative potential
4. may be at positive, zero or negative potential

24. When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance

1. increases K times
2. remains unchanged
3. decreases K times
4. increases K-l times

25. Dielectric constant of a medium is also known as

1. relative permeability
2. permeability
3. permittivity
4. relative permittivity

26. On decreasing the distance between the plates Of a parallel plate capacitor, its capacitance

1. remains unaffected
2. decreases
3. first increases then decreases
4. increases

27. Energy is stored in a capacitor in the form of

1. magnetic energy
2. light energy
3. heat energy
4. electrostatic energy

28. If in a parallel plate capacitor, which is connected to a battery, we fill dielectrics in whole space of its plates, then which of the following increases?

1. Q and V
2. V and E
3. E and C
4. Q and C

29.  In a parallel plate capacitor, the capacity increases if

1. area of the plate is decreased
2. distance between the plates increases
3. area of the plate is increased
4. dielectric constant decreases

30. The energy stored in a condenser of capacity C which has been raised to a potential V is given by

1. -CV
2. -CV2
3. CV
4. CV2

31. The work done in placing a charge of 8 x 10-18 C on a condenser of capacity 100µF is

1. 3.2 x 10-26
2. 3.2 x 10-31
3. 3.2 x 10-32J
4. 4 x 10-26J

32. A parallel plate capacitor has two square plates with equal and opposite charges. The surface charge  densities on the plates are +σ and -σ respectively. In the region between the plates the magnitude of the electric field is

1. σ/2?o
2. σ/?o
3. 0
4. None of these

33. In a charged capacitor, the energy resides

1. in the positive charges
2. in both the positive and negative charges
3. in the field between the plates
4. around the edges of the capacitor plates

34. A parallel plate air capacitor hag capacitance 100 µF. The plates are at a distance d apart. If a slab of thickness t (t < d) and dielectric constant 5 introduced between the parallel plates, then the capacitance will be

1. 30 µC
2. 100 µC
3. 200 µC
4. 500 µC

35. A parallel plate capacitor is connected across a 2 V battery and charged. The battery is then disconnected and a glass slab is introduced between plates. Which of the following pairs of quantities decreases?

1. Charge and potential difference.
2. Potential difference and energy stored.
3. Energy stored and capacitance.
4. Capacitance and charge.

36. An example of an equipotential surface in earth is

1. A line passing through the centre of the earth connecting two points along the diameter
2. A plane that passes through the circular section of the hemisphere of the earth
3. A spherical surface at a distance of 1 km from the surface of the earth with its centre at the centre of earth
4. a plane on the surface of the earth, which is a tangent to the earth

37. Work done in moving a substance through an equipotential surface is

1. positive
2. negative
3. zero
4. depends on the direction of the field

38. Two fixed charges separated by a distance d experience a force F. A dielectric medium of thickness d/4 and dielectric constant 4 is introduces in the space between them. Find the new force acting between the charges.

1. F / 4
2. F / 3
3. F
4. 16F / 25

39. Water is not used as a dielectric between the plates of capacitor because

1. dielectric constant is very low
2. dielectric strength is very low
3. dielectric constant is very high
4. dielectric strength is very high

40. 64 small drops of mercury coalesce to form a big drop. The ratio of the surface charge density of each small drop with that of big drop is

1. 4 : 1
2. 1 : 4
3. 1 : 64
4. 64 : 1

41. Electric charge given to the hollow conductor resides

1. on the outer surface
2. at the centre
3. on the inner surface
4. uniformly on the outer as well as on the inner surface

42. A man stands inside a large metal charged sphere. Will his hair stand on end?

1. yes
2. no
3. data insufficient
4. no guess

43. Stainless steel pans are usually provided with copper bottoms. The reason behind this is

1. Copper bottoms makes the pan more durable
2. Such pans looks colourful
3. Copper is easier to clean
4. Copper is a better conductor of heat than steel

44. The radii of two metallic spheres are 5 cm and 10 cm and both carry and equal charge of 75µC. If the two spheres are shorted then the charge will be transferred

1. 25µC from smaller to bigger
2. 25µC from bigger to smaller
3. 50µC from smaller to bigger
4. 50µC from bigger to smaller

45. A system has been given which has 3 point charges q, 2q and xq which are separated by equal finite distance so that electric potential energy of the system is zero, then the value of x is

1. -2/3
2. -1/3
3. 2/3
4. 3/2

### Electrostatic Potential and Capacitance MCQAnswers

1 . (3)

Electric potential inside a conductor is constant and it is equal to that in the surface of the conductor.

2. (3)

V = W/Q

3. (2)

V = q/(4π?or) = (9 x 109 x 4 x 10-7) / 0.1 = 3.6 x 104 V

4. (4)

V = Q/(4π?or) = Q x 1011

4π?or = 10-11

E = (Q x 4π ?o) / (4π ?o r)2 = (Q x 4π ?o) / (10-11)2 = 4π ?oQ x 1022 Vm-1

5. (2)

When electric field is held in the sphere, electric field is not zero anywhere on the sphere. However, net electric flux through the sphere is zero.

6. (3)

In moving a small positive charge from Q to P, work has to be done by an external agency against the electric field. Therefore, work done by the electric field is negative.

7. (4)

V = (pcosΘ) / (4π?or2)

8. (4)

Potential at A = Potential due to +q charge + Potential due to -q charge

q / 4π?o√(a2) – q / 4π?o√(a2) = 0

9. (3)

Electric potential due to each charge at the centre of the square is √2q / 4π?ol

Total potential will be = 4 x (√2q / 4π?ol) = √2q / π?ol

10. (2)

Intersection of two equipotential surfaces at a point will give two directions of electric field intensity at that point, which is not possible.

11. (4)

On the equipotential surface the electric field is normal to the charged surface. So, no work will be done.

12. (4)

Conducting surface behaves as an equipotential surface.

13. (2)

By using U = QV

Q = +1, U = V

At higher potential, potential energy will be high and at lower potential, lower energy will be present

14. (3)

The potential energy is negative whenever there is attraction. Since a positive and negative charge attract each other, their energy is negative. When both the charges are separated by infinite distance, they do not attract each other and their energy is zero .

15. (4)

W = pE (cos 90o-cos 270o)

16. (2)

Potential energy of the system U = ((-e) x (-e)) / 4π?or

17. (3)

18. (3)

Potential = Potential energy / test charge

19. (4)

20. (4)

Earth is conductor which can be given almost unlimited charge.

21. (3)

If a conductor has a non zero potential and there are no charges anywhere else outside, then there must be charges on the surface of the conductor or inside the conductor. There can not be any charge in the body of the conductor.

22. (3)

In case of metallic sphere either solid or hollow, the charge will reside on the surface of the sphere. Since both spheres have same surface area, they can hold amount of maximum charge .

23. (4)

The conductor may be a positive, zero or negative potential. It is according to the way one defines the zero potential .

24. (3)

Fm = Fo/k

25. (4)

k = εr = ε/εo = Relative permitivity

26. (4)

C = εoKA / d, capacitance is inversely proportional to the distance.

27. (4)

Energy stored in the capacitor is called electrostatic energy.

28. (4)

C = εoKA/d and q = CV

29. (3)

Capacitance is directly proportional to the area.

30. (2)

31. (2)

W = q2 / 2C = ( 8 x 10-18 )2 / 2 x 100 x 10-6 = 3.2 x 10-31 J

32. (2)

σ/?o

33. (3)

Energy resides in the field between the plates in a charged capacitor.

34. (3)

Capacitance will increase but not 5 times as the dielectric is not completely filled.

35. (2)

When battery is disconnected, charge remains constant. On introducing glass slab, capacitance increases. Potential difference and energy stored decreases.

36. (3)

A line passing through the centre of the earth connecting two points along the diameter

37. (3)

Work done in moving a charge over an equipotential surface is always zero.

38. (1)

39. (2)

Water is not used as dielectric between the plates of the capacitor as it has a large dielectric constant but a quite low amount of dielectric strength, which is why it is not used inside a capacitor.

40. (2)

1 : 4

41. (1)

In all conductors, charges reside on the surface.

42. (2)

A metallic sphere means a conductors and as the electric field is zero inside a conductor, the hairs won’t stand up of the man.

43. (4)

Cooper is a better conductor of heat than stainless steel.

44. (1)

45. (1)

## Assertion and Reasoning MCQ

Codes

(a) Both A and R are true and R is the correct explanation of A

(b) Both A and R are true and but R is not a correct explanation of A

(c) A is true but R is false

(d) A is false, but R is true

1 . Assertion (A) Work done in moving a charge between any two points in an electric field is dependent of the path followed by the charge, between these points.

Reason (R) Electrostatic force is a non-conservative force

2. Assertion (A) The electric potential at any point on the equitorial plane of a dipole is non-zero.

Reason (R) The work done in bringing a unit positive charge from infinity to a point in equitorial plane is not equal for the two charges of the dipole.

3. Assertion (A) For a non-uniformly charged thin circular ring with net charge is zero, the electric field at any point on axis of the ring is zero.

Reason (R) For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is zero.

4. Assertion (A) For a point charge concentric spheres centred at a location of the charge are equipotential surface.

Reason (R) An equipotential surface is a surface over which potential has constant value.

5. Assertion (A) Electric potential and electric potential energy are different quantities

Reason (R) For a system of positive test charge and point charge electric potential energy = electric potential

6. Assertion (A) Surface of a symmetrical conductor can be treated as equipotential surface

Reason (R) Charge can easily flow in a conductor.

7. Assertion (A) Two adjacent conductors of unequal dimensions, carrying the same positive charge have a potential difference between them.

Reason (R) The potential of a conductor depends upon the charge given to it.

8. Assertion (A) When a dielectric slab is gradually inserted between the plates of an isolated parallel plate capacitor, the energy of the system decreases.

Reason (R) The force between the plates decreases.

9. Assertion (A) Polar molecules have temporary dipole moment.

Reason (R) In polar molecule, the centres of positive and negative charges conincide even there is no external field.

10. Assertion (A) In the Van de Graaff generator, the process of spraying the charge is called electron discharge.

Reason (R) Van de Graaff generator produces high voltage and high current.

1 . (d)

Electrostatic force is a conservative force.

2. (d)

The electric potential at any point on equatorial plane of a dipole is zero.

3. (d)

For a non uniformly charged thin circular ring with net zero charge, electric potential at each point on its axis is zero. Hence electric field at each point on its axis must be perpendicular to the axis.

4. (b)

An equipotential surface is a surface over which potential is same.

5. (c)

Potential and potential energy at different quantities and cannot be equated.

6. (a)

Potential is constant on surface of a sphere so it behaves as an equipotential surface.

7. (b)

Let us considered to spherical shells of radii ‘a’ and ‘b’ which are having the same positive charge Q. Hence, the potential on the surface of each conductor will be,

V1 = kQ/a V2 = kQ/b

As a ≠ b, V1 ≠ V2 and there will be a potential difference too.

8. (c)

C’ = KC and U’ = q2/2C’ = q2/2KC

9. (d)

The molecules of a substance may be polar or non-polar. In a polar molecule, the centres of positive and negative charges coincide. This molecule has no permanent dipole moment. A polar molecule has its centres of posiitve and negative charges separated, even when there is no electric field. Such molecules have permanent dipole moment.

10. (d)

In Van de Graaff generator, the process of spraying the charge is called corona discharge. Van de Graaff generator produces high voltage and low current.

## Case-Study Based MCQ

The electric field at a point is the force experienced by unit positive charge at that point. It is a vector quantity. The electric field due to a point charge q at a distance r from it is given by:

Its direction is towards the charge when it is negative and away from the charge when the charge is positive. If there are a system of charges, then field due to each charge will get added vectorially. Electric potential at a point is the work done in bringing unit positive charge from infinity to that point. The potential due to a point charge at a distance r from it is given by

If there are a number of charge in the vicinity of the point, then the potential due to each charge gets add up algebraically (one need to specify the sign of the charge in calculation).

Now consider the following situation.

Four charges +q, +q, -q and -q are placed at the four corners A, B, C and D respectively of a square of side a arranged in the same order. Midpoint of BC is E and that of CD is F. O is the centre of the square.

(i) The direction of the net electric field at O is towards

(a) AB
(b) BC
(c) CD

(ii) The magnitude of the electric field at O is

(iii) The electric potential at O is

(iv) The work done in carrying a change from O to E is

(v) The work done in carrying a charge from O to F is

Several capacitors can be connected together to be used in a variety of applications. Multiple connections of capacitors act as a single equivalent capacitor. The total capacitance of this single equivalent capacitor depends both on individual capacitor and how they are connected. Capacitors can be arranged in two simple and common types of connection, known as series and parallel.

(i) 3 capacitors of capacitance 1microF, 2microF and 3microF are connected in series and a potential difference of 11V is applied across the combination. Then potential difference across the plate of 1microF would be\

(a) 2V
(b) 4V
(c) 1V
(d) 6V

(ii) The equivalent capacitance is

(a) 15microF
(b) 20microF
(c) 25microF
(d) 30microF

(iii) The capacitors shown in the following diagram has a capacitance of 4microF each. If C2 capacitor has a capacitance of 10microF, then effective capacitance between A and B is

(a) 2microF
(b) 4microF
(c) 6microF
(d) 8microF

1. (i)(c) (ii)(d) (iii)(d) (iv)(d)

2. (i)(d) (ii)(b) (iii)(b)

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Final Words

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