# Physics MCQs for Class 12 with Answers Chapter 2 Electrostatic Potential and Capacitance

Home » CBSE Class 12 Physics » MCQ Questions for Class 12 Physics » Physics MCQs for Class 12 with Answers Chapter 2 Electrostatic Potential and Capacitance

1. A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge [NCERT Exemplar]
(a) remains a constant because the electric field is uniform.
(b) increases because the charge moves along the electric field.
(c) decreases because the charge moves along the electric field.
(d) decreases because the charge moves opposite to the electric field.

Explanation: (c) The positively charged particle experiences electrostatic force along the direction of electric field, hence moves in the direction of electric field. Electric potential decreases in the direction of electric field. Thus, positive work is done by the electric field on the charge. We = -ΔU = -qΔV = q(Vin – Vf) Hence electrostatic potential energy of the positive charge decreases.

2. Figures show some equipotential lines distributed in space. A charged object is moved from point A to point B. [NCERT Exemplar] (a) The work done in Fig. (i) is the greatest.
(b) The work done in Fig. (ii) is least.
(c) The work done is the same in Fig. (i), Fig.(ii) and Fig. (iii).
(d) The work done in Fig. (iii) is greater than Fig. (ii) but equal to that in Fig. (i).

Explanation: (c) The work done by the electric field on the charge will be negative. Welectrical = -ΔU = – qΔV— q( Vinitial – Vfinal) Here initial and final potentials are same in all three cases and the same charge is moved, so work done is same in all three cases.

3. Equipotentials at a great distance from a collection of charges whose total sum is not zero are approximately [NCERT Exemplar]
(a) spheres
(b) planes
(c) paraboloids
(d) ellipsoids

Explanation: (a) The collection of charges at great distance is considered as a single point charge. The equipotential surfaces due to a point charge are spherical.

4. Two small spheres each carrying a charge q are placed r metre apart. If one of the spheres is taken around the other one in a circular path of radius r, the work done will be equal to
(a) force between them × r
(b) force between them × 2πr
(c) force between them/2πr
(d) zero

Explanation: (d) The force is perpendicular to the displacement.

5. The electric potential V at any point O (x, y, z all in metres) in space is given by V = 4x² volt. The electric field at the point (1 m, 0, 2 m) in volt/metre is
(a) 8 along negative x-axis
(b) 8 along positive x-axis
(c) 16 along negative x-axis
(d) 16 along positive z-axis

Explanation: (a) The electric field E = \frac{-dV}{dx} = -8x V/m

6. If a unit positive charge is taken from one point to another over an equipotential surface, then
(a) work is done on the charge.
(b) work is done by the charge.
(c) work done is constant.
(d) no work is done.

Explanation: (d) On the equipotential surface, electric field is normal to the charged surface (where potential exists) so that no work will be done.

7. A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is
(a) 0 V
(b) 10 V
(c) Same as at point 5 cm away from the surface
(d) Same as at point 25 cm away from the surface

Explanation: (b) Since potential inside the hollow sphere is same as that on the surface.

8. The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is
(a) proportional to the square root of the distance between the plates.
(b) linearly proportional to the distance between the plates.
(c) independent of the distance between the plates.
(d) inversely proportional to the distance between the plates.

Answer Answer: c Explanation: (c) For isolated capacitor Q = Constant, force between plate = Q2/2Aε0

9. A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system
(a) increases by a factor of 4.
(b) decreases by a factor of 2.
(c) remains the same.
(d) increases by a factor of 2.

Explanation: (b) Using, Vc = \frac{V}{2}, U = \frac{1}{2}CV².

10. A conductor with a positive charge
(a) is always at +ve potential.
(b) is always at zero potential.
(c) is always at negative potential.
(d) may be at +ve, zero or -ve potential.

Explanation: (d) May be at positive, zero or negative potential, it is according to the way one defines the zero potential.

11 v Figure shows the electric lines of force emerging from a charged body. If the electric field at A and B are EA and EB respectively and if the displacement between A and B is r then (a) EA > EB
(b) EA < EB
(c) EA = EB/r
(d) EA = EB /r²

Explanation: (a) In non-uniform electric field, intensity is more, where the lines are more denser.

12. Which of the following options are correct? If a conductor has a potential V 4- 0 and there are no charges anywhere else outside, then [NCERT Exemplar]
(a) there must not be charges on the surface or inside itself.
(b) there cannot be any charge in the body of the conductor.
(c) there must be charges only on the surface.
(d) there must be charges inside the surface.

Explanation: (b) The charge resides on the outer surface of a closed charged conductor. Hence there cannot be any charge in the body of the conductor. Hence option (b) is correct.

13. Which of the following options is correct? In a region of constant potential [NCERT Exemplar]
(a) the electric field is uniform.
(b) the electric field is zero.
(c) there can be charge inside the regiofi.
(d) the electric field shall necessarily change if a charge is placed outside the region.

Answer Answer: b Explanation: (b) as E = -dV/dr Since, V = constant, -dV/dr = 0 this implies that electric field intensity E=0. If some charge is present inside the region then electric field cannot be zero at that region, for this V=constant is not valid.

14. 64 drops each having the capacity C and potential V are combined to form a big drop. If the charge on the small drop is q, then the charge on the big drop will be
(a) 2q
(b) 4q
(c) 16q
(d) 64q

Explanation: (d) By using Q = nq or Q = 6Aq

15. The radii of two metallic spheres A and B are r1 and r2 respectively (r1 > r2). They are connected by a thin wire and the system is given a certain charge. The charge will be greater
(a) on the surface of the sphere B.
(b) on the surface of the sphere A.
(c) equal on both.
(d) zero on both.

Explanation: (b) After connection of wire, potential becomes equal, i.e, Q1/r1 = Q2/r2 or Q1/Q2 = r1/r2 when r1 > r2, then Q1 > Q2.

16. A parallel plate condenser is connected with the terminals of a battery. The distance between the plates is 6mm. If a glass plate (dielectric constant K = 9) of 4.5 mm is introduced between them, then the capacity will become
(a) 2 times.
(b) the same.
(c) 3 times.
(d) 4 times.

Explanation: 17. Three charges Q, +q and +q are placed at the vertices of an equilateral triangle of side l as shown in the figure. If the net electrostatic energy of the system is zero, then Q is equal to (a) -q
(b) +q
(c) zero
(d) – $\frac{q}{2}$

Explanation: 18. Two metal plates form a parallel plate capacitor. The distance between the plates is d. A metal sheet of thickness $\frac{d}{2}$ and of the same area is introduced between the plates.
What is the ratio of the capacitance in the two cases?
(a) 2 : 1
(b) 3 : 1
(c) 2 : 1
(d) 5 : 1

Explanation: 19. Acapacitor of 4 pF is connected as shown in the circuit. The internal resistance of the battery is 0.5 Q. The amount of charge on the capacitor plates will be [NCERT Exemplar] (a) 0
(b) 4
(c) 16 μC
(d) 8 μC

Explanation: 20. A capacitor is charged by using a battery which is then disconnected. A dielectric slab
then slipped between the plates, which results in
(a) reduction of charge on the plates and increase of potential difference across the plates.
(b) increase in the potential difference across the plate, reduction in stored energy, but no change in the charge on the plates.
(c) decrease in the potential difference across the plates, reduction in the stored energy, but no change in the charge on the plates.
(d) none of these

21. Which of the following statement is true?
(a) Electrostatic force is a conservative force.
(b) Potential at a point is the work done per unit charge in bringing a charge from any point to infinity.
(c) Electrostatic force is non-conservative
(d) Potential is the product of charge and work.

22. 1 volt is equivalent to 23. The work done in bringing a unit positive charge from infinite distance to a point at distance x from a positive charge Q is W. Then the potential at that point is 24. Consider a uniform electric field in the z-direction. The potential is a constant
(a) for any x for a given z
(b) for any y for a given z
(c) on the x-y plane for a given z
(d) all of these

25. Equipotential surfaces
(a) are closer in regions of large electric fields compared to regions of lower electric fields.
(b) will be more crowded near sharp edges of a conductor.
(c) will always be equally spaced.
(d) both (a) and (b) are correct.

26. In a region of constant potential
(a) the electric field is uniform.
(b) the electric field is zero.
(c) there can be no charge inside the region.
(d) both (b) and (c) are correct.

27. A test charge is moved from lower potential point to a higher potential point. The potential energy of test charge will
(a) remain the same
(b) increase
(c) decrease
(d) become zero

28. An electric dipole of moment $\vec{p}$ is placed in a uniform electric field $\vec{E}$ . Then
(i) the torque on the dipole is $\vec{p} \times \overrightarrow{\mathrm{E}}$
(ii) the potential energy of the system is $\vec{p} . \overrightarrow{\mathrm{E}}$
(iii) the resultant force on the dipole is zero. Choose the correct option.
(a) (i), (ii) and (iii) are correct
(b) (i) and (iii) are correct and (ii) is wrong
(c) only (i) is correct
(d) (i) and (ii) are correct and (iii) is wrong

29. If a conductor has a potential V ≠ 0 and there are no charges anywhere else outside, then
(a) there must be charges on the surface or in¬side itself.
(b) there cannot be any charge in the body of the conductor.
(c) there must be charges only on the surface.
(d) both (a) and (b) are correct.

30. Which of the following statements is false for a perfect conductor?
(a) The surface of the conductor is an equipoten-tial surface.
(b) The electric field just outside the surface of a conductor is perpendicular to the surface.
(c) The charge carried by a conductor is always uniformly distributed over the surface of the conductor.
(d) None of these.

31. Dielectric constant for a metal is
(a) zero
(b) infinite
(c) 1
(d) 10

32. When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance
(a) increases K times
(b) remains unchanged
(c) decreases K times
(d) increases K-1 times

33. In a parallel plate capacitor, the capacity increases if
(a) area of the plate is decreased.
(b) distance between the plates increases.
(c) area of the plate is increased.
(d) dielectric constantly decreases.

34. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulating handle. As a result the potential difference between the plates
(a) increases
(b) decreases
(c) does not change
(d) becomes zero

35. Two identical capacitors are joined in parallel, charged to a potential V, separated and then connected in series, the positive plate of one is connected to the negative of the other. Which of the following is true?
(a) The charges on the free plated connected to-gether are destroyed.
(b) The energy stored in ths system increases.
(c) The potential difference between the free plates is 2V.
(d) The potential difference remains constant.

36. A capacitor has some dielectric between its plates, and the capacitor is connected to a dc source. The battery is now disconnected and then the dielectric is removed, then
(a) capacitance will increase.
(b) energy stored will decrease.
(c) electric field will increase.
(d) voltage will decrease.

37. Two spherical conductors each of capacity C are charged to potential V and -V. These are then connected by means of a fine wire. The loss of energy is
(a) zero
(b) $\frac{1}{2}$CV2
(c) CV2
(d) 2 CV2

## Quiz on Capacitance

General Instructions:

(1) Total number of question is 5.

(2) Each question has 4 choices, out of which ONLY ONE CHOICE is correct.

1.
The equivalent capacitance of the combination shown in figure is :- 2.
During charging and discharging of a capacitor :-

3.
Find capacitance across AB :- 4.
If the distance between parallel plates of a capacitor is halved and dielectric constant is doubled then the capacitance will become :-

5.
A parallel plate capacitor is connected across a source of constant potential difference. When a dielectric plate is introduced between the two plates then:

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