JEE Physics Electrostatic Potential And Capacitance MCQs Set 29

Multiple Choice Questions (MCQs) for JEE Physics: Electrostatic Potential and Capacitance

Access targeted multiple-choice questions for Electrostatic Potential and Capacitance designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

Practice Electrostatic Potential and Capacitance MCQs for JEE Physics

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Multiple Choice Questions

Question 1: The resultant capacitance of n condensers of capacitances C₁, C₂, …, Cₙ connected in series is given by
(a) \( C_s=\frac1{C_1}+\frac1{C_2}+\cdots+\frac1{C_n} \)
(b) \( \frac1{C_s}=\frac1{C_1}+\cdots+\frac1{C_n} \)
(c) \( C_s=C_1+C_2+\cdots+C_n \)
(d) \( C_s=C_1-C_2+\cdots-C_n \)
Show Answer & Explanation

Answer: (b) \( \frac1{C_s}=\frac1{C_1}+\cdots+\frac1{C_n} \)

Explanation:
1. In series the reciprocals add: 1/C_s = 1/C₁ + 1/C₂ + … + 1/Cₙ.

Teacher's Note:
1. Series: reciprocals add.

Question 2: Energy is stored in a capacitor in the form of
(a) electrostatic energy
(b) magnetic energy
(c) light energy
(d) heat energy
Show Answer & Explanation

Answer: (a) electrostatic energy

Explanation:
1. A capacitor stores energy in the electric field between its plates, as electrostatic energy.

Teacher's Note:
1. Energy in the electric field.

Question 3: The potential gradient at which the dielectric of a condenser just gets punctured is called
(a) dielectric constant
(b) dielectric strength
(c) dielectric resistance
(d) dielectric number
Show Answer & Explanation

Answer: (b) dielectric strength

Explanation:
1. The maximum field a dielectric can bear before breakdown is its dielectric strength.

Teacher's Note:
1. Breakdown field.

Question 4: The electric potential inside a conducting sphere
(a) increases from the centre to the surface
(b) decreases from the centre to the surface
(c) remains constant from the centre to the surface
(d) is zero at every point inside
Show Answer & Explanation

Answer: (c) remains constant from the centre to the surface

Explanation:
1. The field inside a conductor is zero, so there is no potential difference between points inside.
2. The potential is constant and equals its surface value.

Teacher's Note:
1. Conductor is an equipotential.

Question 5: A charge is brought from a point on the equatorial plane of a dipole to its mid-point. Which of the following quantities remains constant?
(a) electric field
(b) force on the charge brought
(c) torque exerted by the charge on the dipole
(d) electric potential
Show Answer & Explanation

Answer: (d) electric potential

Explanation:
1. The equatorial plane of a dipole is an equipotential (V = 0).
2. The field and force vary with distance, but the potential is constant.

Teacher's Note:
1. Equatorial plane is an equipotential.

Question 6: A parallel plate capacitor is charged by connecting it to a battery. Now the distance between the plates of the capacitor is increased (battery remaining connected). Which of the following remains constant?
(a) capacitance
(b) charge on each plate of the capacitor
(c) potential difference across the capacitor
(d) energy stored in the capacitor
Show Answer & Explanation

Answer: (c) potential difference across the capacitor

Explanation:
1. The battery keeps the potential difference fixed.
2. C, Q and U all change.

Teacher's Note:
1. V is fixed by the battery.

Question 7:
Assertion (A): The electric field is discontinuous across the surface of a spherical charged shell.
Reason (R): The electric potential is continuous across the surface of a spherical charged shell.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. E jumps from zero inside to kq/R² outside, so it is discontinuous, and V is continuous.
2. Both are true but the continuity of V does not explain the jump of E.

Teacher's Note:
1. Field jumps, potential does not.

Question 8:
Assertion (A): In the absence of an external electric field, the dipole moment per unit volume of a polar dielectric is zero.
Reason (R): The dipoles of a polar dielectric are randomly oriented.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The random orientation of the permanent dipoles makes their vector sum zero.
2. So the net polarisation is zero without a field.

Teacher's Note:
1. Random orientation cancels.

Question 9:
Assertion (A): A dielectric is inserted between the plates of a battery-connected capacitor. The energy of the capacitor increases.
Reason (R): The energy of a capacitor is U = ½CV².
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. V is fixed and C increases, so U = ½CV² increases.
2. The reason is the relation used.

Teacher's Note:
1. U ∝ C at fixed V.

Question 10: An electric dipole of moment p is placed in a uniform electric field E. Which of the following is/are correct? I. The torque on the dipole is p × E. II. The potential energy of the system is p·E. III. The resultant force on the dipole is zero.
(a) I, II and III
(b) I and III
(c) II and III
(d) I and II
Show Answer & Explanation

Answer: (b) I and III

Explanation:
1. The torque is p × E and the net force is zero in a uniform field.
2. The potential energy is −p·E, so II is false.

Teacher's Note:
1. U = −p·E.

Question 11: There are two metallic spheres of the same radii, but one is solid and the other is hollow. Then
(a) the solid sphere can be given more charge
(b) the hollow sphere can be given more charge
(c) they can be charged equally (maximum)
(d) none of the above
Show Answer & Explanation

Answer: (c) they can be charged equally (maximum)

Explanation:
1. Charge resides only on the outer surface of a conductor.
2. Both spheres have the same surface area, so they can hold the same maximum charge.

Teacher's Note:
1. Charge sits on the surface.

Question 12: A parallel plate capacitor with air between the plates is charged to a potential difference of 500 V and then insulated. A plastic plate is inserted between the plates, filling the whole gap. The potential difference between the plates now becomes 75 V. The dielectric constant of the plastic is
(a) \( 10/3 \)
(b) 5
(c) \( 20/3 \)
(d) 10
Show Answer & Explanation

Answer: (c) \( 20/3 \)

Explanation:
1. With the charge fixed, V = V₀/K.
2. K = 500/75 = 20/3.

Teacher's Note:
1. V = V₀/K.

Question 13: A given charge is situated at a certain distance from an electric dipole in the end-on position and experiences a force F. If the distance of the charge is doubled, the force acting on the charge will be
(a) 2F
(b) F/2
(c) F/4
(d) F/8
Show Answer & Explanation

Answer: (d) F/8

Explanation:
1. The axial field of a dipole varies as 1/r³.
2. Doubling r reduces the force to F/8.

Teacher's Note:
1. E ∝ 1/r³.

Question 14: Two concentric spherical conductors A and B of radii a and b (b > a) are connected by a copper wire. The equivalent capacitance of the system is
(a) \( 4\pi\varepsilon_0\frac{ab}{b-a} \)
(b) \( 4\pi\varepsilon_0(a+b) \)
(c) \( 4\pi\varepsilon_0b \)
(d) \( 4\pi\varepsilon_0a \)
Show Answer & Explanation

Answer: (c) \( 4\pi\varepsilon_0b \)

Explanation:
1. On connection the charge goes to the outer shell and the potentials are equal.
2. The system behaves like one sphere of radius b: C = 4πε₀b.

Teacher's Note:
1. Charge resides on the outer surface.

Question 15: 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
Show Answer & Explanation

Answer: (d) no work is done

Explanation:
1. W = q(V_A − V_B) = 0 because the potential is the same along the surface.

Teacher's Note:
1. W = qΔV.

Question 16: Match the types of capacitors in Column I with the expressions of capacitance in Column II.
Column IColumn II
(A) Spherical capacitor (r₂ > r₁)(1) ε₀KA/d
(B) Cylindrical capacitor (r₂ > r₁)(2) ε₀A/d
(C) Parallel plate capacitor, air filled(3) 2πε₀ℓ/ln(r₂/r₁)
(D) Parallel plate capacitor with a dielectric slab filling the gap(4) 4πε₀r₁r₂/(r₂ − r₁)

(a) A-4, B-2, C-3, D-1
(b) A-4, B-3, C-1, D-2
(c) A-4, B-1, C-2, D-3
(d) A-4, B-3, C-2, D-1
Show Answer & Explanation

Answer: (d) A-4, B-3, C-2, D-1

Explanation:
1. A spherical capacitor has C = 4πε₀r₁r₂/(r₂ − r₁) (A-4).
2. A cylindrical capacitor has C = 2πε₀ℓ/ln(r₂/r₁) (B-3).
3. An air-filled parallel plate capacitor has ε₀A/d (C-2), and with a dielectric ε₀KA/d (D-1).

Teacher's Note:
1. Standard capacitances.

Question 17: In a Van de Graaff generator, the breakdown field of air is about
(a) \( 2\times10^{8}\ \text{V/m} \)
(b) \( 3\times10^{6}\ \text{V/m} \)
(c) \( 2\times10^{3}\ \text{V/m} \)
(d) \( 3\times10^{4}\ \text{V/m} \)
Show Answer & Explanation

Answer: (b) \( 3\times10^{6}\ \text{V/m} \)

Explanation:
1. Dry air breaks down at about 3 × 10⁶ V/m.

Teacher's Note:
1. Breakdown field of air.

Question 18: To obtain 3 μF capacity from three capacitors of 2 μF each, they will be arranged
(a) all the three in series
(b) all the three in parallel
(c) two capacitors in series and the third in parallel with the combination of the first two
(d) two capacitors in parallel and the third in series with the combination of the first two
Show Answer & Explanation

Answer: (c) two capacitors in series and the third in parallel with the combination of the first two

Explanation:
1. Two 2 μF in series give 1 μF.
2. Adding the third 2 μF in parallel gives 1 + 2 = 3 μF.

Teacher's Note:
1. Series then parallel.

Question 19: The electric potential at a point on the equatorial line of an electric dipole is
(a) directly proportional to distance
(b) inversely proportional to distance
(c) inversely proportional to the square of the distance
(d) none of these
Show Answer & Explanation

Answer: (d) none of these

Explanation:
1. The potentials of +q and −q cancel on the equatorial line.
2. The potential is zero, so none of the proportionalities holds.

Teacher's Note:
1. V = 0 on the equator.

Question 20: Two vertical metallic plates carrying equal and opposite charges are kept parallel to each other like a parallel plate capacitor. A small uncharged spherical metallic ball is suspended by a long insulated thread such that it hangs freely in the centre of the two plates. The ball is taken slowly towards the positively charged plate and made to touch that plate. Then the ball will
(a) stick to the positively charged plate
(b) come back to its original position and will remain there
(c) oscillate between the two plates touching each plate in turn
(d) oscillate between the two plates without touching them
Show Answer & Explanation

Answer: (c) oscillate between the two plates touching each plate in turn

Explanation:
1. On touching the positive plate the ball becomes positive and is repelled towards the negative plate.
2. It gains negative charge there and returns, so it oscillates touching each plate in turn.

Teacher's Note:
1. Charge transfer by contact.

Question 21: Which of the following about the potential difference between any two points is true? I. It depends only on the initial and final position. II. It is the work done per unit positive charge in moving from one point to the other. III. It is more for a positive charge of two units as compared to a positive charge of one unit.
(a) I only
(b) II only
(c) I and II
(d) I, II and III
Show Answer & Explanation

Answer: (c) I and II

Explanation:
1. The potential difference depends on the positions only and equals the work per unit charge.
2. It does not depend on the test charge, so III is false.

Teacher's Note:
1. ΔV = W/q.

Question 22: A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
(a) decreases
(b) remains unchanged
(c) becomes infinite
(d) increases
Show Answer & Explanation

Answer: (b) remains unchanged

Explanation:
1. The foil adds two capacitors in series, each with a gap whose sum equals the original separation (thickness negligible).
2. The capacitance is unchanged.

Teacher's Note:
1. Series gaps add up to d.

Question 23:
Assertion (A): Polar molecules have a permanent dipole moment.
Reason (R): In polar molecules, the centres of positive and negative charges coincide even when there is no external field.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. The centres of positive and negative charge are separated in polar molecules, so they have a permanent dipole moment.
2. The reason says they coincide, which is false.

Teacher's Note:
1. Separated charge centres.

Question 24:
Assertion (A): The electric potential and the electric potential energy are different quantities.
Reason (R): For a system of a positive test charge and a point charge, electric potential energy equals electric potential.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. Potential is energy per unit charge and the two have different units, so the assertion is true.
2. They are equal only for a unit test charge, so the reason as stated is false.

Teacher's Note:
1. U = qV.

Question 25: The energy required to charge a parallel plate capacitor of plate separation d and plate area of cross-section A such that the uniform electric field between the plates is E, is
(a) \( \varepsilon_0E^2Ad \)
(b) \( \frac12\varepsilon_0E^2Ad \)
(c) \( \frac12\varepsilon_0E^2/Ad \)
(d) \( \varepsilon_0E^2/Ad \)
Show Answer & Explanation

Answer: (b) \( \frac12\varepsilon_0E^2Ad \)

Explanation:
1. Energy density = ½ε₀E² and the volume is Ad.
2. U = ½ε₀E²Ad.

Teacher's Note:
1. u = ½ε₀E².

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