Electrostatics: 40 Must-Practice Questions for CBSE Class 12 Physics 2025

Master CBSE Class 12 Physics Electrostatics for the 2025 Board Exam with 40 critical questions! Includes 10 MCQs, 10 short/long answers, 10 numericals, NCERT-aligned solutions, and competency-based practice. Boost your score with PYQs and expert tips!

Latest Syllabus Coverage
Aligned with CBSE 2024-25 syllabus for Chapters 1 (Electric Charges and Fields) and 2 (Electrostatic Potential and Capacitance). Includes derivations, numericals, and competency-based questions from previous papers.

Objective Questions (MCQs)

1. Gauss’s Law Application:
   Which Gaussian surface is optimal for calculating the electric field of an infinite charged wire?
   (a) Spherical (b) Cylindrical (c) Cubical (d) Planar.
2. Equatorial Potential:
   Electric potential at the equatorial point of a dipole is:
   (a) Maximum (b) Zero (c) Negative (d) Positive.
3. Capacitance with Dielectric:
   Inserting a dielectric slab into a charged capacitor connected to a battery:
   (a) Decreases (b) Increases (c) Remains same (d) Becomes zero.
4. Hollow Conductor Potential:
   Potential at the center of a charged hollow metal sphere is:
   (a) Zero (b) Same as surface (c) Half of surface (d) Double.
5. Equipotential Surfaces:
   Why are equipotential surfaces perpendicular to electric field lines?
   (a) Work done is zero (b) No tangential component of E (c) Charge symmetry (d) Field uniformity.
6. Electric Flux:
   For a closed surface with zero net flux, which statement is true?
   (a) No charges inside (b) Net charge inside is zero (c) E = 0 everywhere (d) Both (b) and (d).
7. Dipole Field Variation:
   Electric field of a dipole varies as:
   (a) 1/r (b) 1/r² (c) 1/r³ (d) 1/r⁴.
8. Capacitor Energy:
   Energy stored in a capacitor is given by:
   (a) CV (b) ½ CV² (c) QV (d) ½ Q²/C.
9. Conductor Shielding:
   Electric field inside a hollow charged conductor is:
   (a) Uniform (b) Zero (c) Radial (d) Non-zero.
10. Dielectric Strength:
    Maximum electric field a medium can withstand without breakdown is called:
    (a) Permittivity (b) Dielectric strength (c) Polarization (d) Conductivity.

Short Answer Questions (2–3 Marks)

1. Gauss’s Law Derivation:
   Derive the electric field due to an infinite charged wire using Gauss’s law.
   Answer: Φ = Q/ε₀ ⇒ E = λ/(2πε₀r).
2. Equipotential Surfaces:
   Explain why work done to move a charge on an equipotential surface is zero.
   Answer: No potential difference ⇒ W = qΔV = 0.
3. Capacitor with Dielectric:
   How does capacitance change when distance between plates is halved and filled with dielectric (K=6)?
   Answer: C’ = 12C₀ (C₀ = 8 pF ⇒ 96 pF).
4. Dipole Axial vs. Equatorial Field:
   Compare electric fields on axial and equatorial lines of a dipole.
   Answer: Axial: 2kp/r³; Equatorial: kp/r³.
5. Electrostatic Shielding:
   Why is potential constant inside a hollow conductor?
   Answer: E = 0 ⇒ No work done ⇒ Uniform potential.
6. Van de Graaff Generator:
   Calculate the minimum radius of a spherical shell (V=15 MV, dielectric strength=5×10⁷ V/m).
   Answer: r = V/E = 0.3 m.
7. Energy in Electric Field:
   Find the volume containing 10⁻⁶ J energy in a field (E=5000 V/m).
   Answer: U = ½ ε₀E²V ⇒ V = 9×10⁻³ m³ 9.
8. Work Done in Square:
   Work done moving 10 µC charge across a square with 500 µC at center?
   Answer: Zero (equipotential points).
9. Capacitors in Series/Parallel:
   Three capacitors (2µF, 3µF, 6µF): Find equivalent capacitance in series and parallel.
   Answer: Series: 1 µF; Parallel: 11 µF.
10. Charge Flow Between Spheres:
    Why does charge flow from a small sphere to a shell when connected?
    Answer: Potential difference depends only on inner charge.

Long Answer Questions (5 Marks)

1. Electric Dipole Field Derivation:
   Derive electric field on the axial line of a dipole. Compare with equatorial field.
   Steps: Superposition of +q and -q fields; E_axial = 2kp/r³, E_equatorial = kp/r³.
2. Parallel Plate Capacitor with Dielectric:
   Derive capacitance when dielectric (thickness t) is inserted.
   Formula: C = ε₀A/(d – t + t/K).
3. Electrostatic Potential Energy:
   Derive energy stored in a capacitor (U = ½ CV²).
   Steps: Integrate work done to transfer charge.
4. Gauss’s Law Applications:
   Use Gauss’s law to find electric field due to a charged spherical shell (inside/outside).
   Derivation: E_inside = 0; E_outside = kQ/r².
5. Equipotential Surfaces Diagram:
   Draw equipotential surfaces for (a) uniform E-field, (b) point charge, (c) dipole.
   Diagrams: Planes, concentric spheres, and asymmetric surfaces.
6. Capacitor with Metal Plate:
   Effect on capacitance when a metal plate (thickness d/2) is inserted.
   Answer: Capacitance doubles (C = 2C₀).
7. Electric Field and Potential Relation:
   Explain why E = -dV/dr. Illustrate with graphs for a charged sphere.
   Explanation: Gradient of potential.
8. Dielectric Polarization:
   How does polarization reduce the effective field in a dielectric?
   Answer: Internal field opposes external field.
9. Energy Density in Capacitor:
   Derive energy density (u = ½ ε₀E²) for a parallel plate capacitor.
   Steps: U = ½ CV²; Substitute C and V in terms of E.
10. Electrostatic Generator Limitation:
    Why can’t a small-shell Van de Graaff generator hold high charge?
    Answer: E = V/r exceeds dielectric strength, causing breakdown.

Numericals (3–5 Marks)

1. Zero Potential Point:
   Two charges (20 µC, -4 µC) 50 cm apart. Find where potential is zero.
   Solution: x = 41.6 cm from 20 µC.
2. Capacitance with Dielectric Slab:
   Air capacitor (C₀ = 8 pF) filled with dielectric (K=6, d’=d/2). Find new capacitance.
   Solution: 96 pF.
3. Force Between Charges:
   Force F between charges at distance d. Find new distance for F/3.
   Solution: √3 d.
4. Work to Dissociate Charges:
   Three charges at triangle vertices: Calculate work to dissociate.
   Solution: W = -2.3 × 10⁻⁸ J.
5. Electric Field Due to Dipole:
   Dipole moment 4×10⁻⁹ Cm. Find field at 0.3 m on axial line.
   Solution: E = 2kP/r³ = 8.89 × 10³ N/C.
6. Energy Stored in Capacitor:
   Capacitor (C=100 µF) charged to 200 V. Calculate energy stored.
   Solution: U = ½ CV² = 2 J.
7. Equilibrium Position of Charge:
   Charges q₁=10 µC and q₂=-2 µC 60 cm apart. Find point where force on q₃=0.
   Solution: 50 cm from q₁.
8. Potential Due to Dipole:
   Dipole (p=2×10⁻⁶ Cm) at 0.5 m on equatorial line. Find potential.
   Solution: V = 0.
9. Capacitor Combination:
   Three capacitors (2µF, 3µF, 6µF) in series/parallel. Find equivalent C.
   Solution: Series: 1 µF; Parallel: 11 µF.
10. Electric Flux and Charge:
    Flux entering ϕ₁=100 Nm²/C, exiting ϕ₂=300 Nm²/C. Find enclosed charge.
    Solution: Q = (ϕ₂ – ϕ₁)ε₀ = 1.77 × 10⁻⁹ C.

Preparation Tips

1. Focus on NCERT: Prioritize derivations (Gauss’s law, capacitance) and diagrams.
2. PYQs Practice: Solve 2015–2023 papers for repeated topics like dipole fields and capacitors.
3. Competency-Based Questions: Practice application-based MCQs from CBSE-released resources.
4. Time Mock Tests: Simulate exam conditions using sample papers.
5. Conceptual Clarity: Use Vedantu and LearnCBSE solutions for numerical steps.