Last Updated: April 2026
Electrostatic Potential and Capacitance is Chapter 2 of CBSE Class 12 Physics (NCERT Part 1) and one of the most consistently high-weightage chapters in both CBSE Board Exams and competitive exams like JEE and NEET. In the 2025 CBSE Board exam, this chapter contributed 5–7 marks directly through MCQs, short answer and numerical questions. Mastery here is non-negotiable for students targeting 90+ in Physics.
Chapter Overview and CBSE Weightage
| Parameter | Details |
|---|---|
| Chapter Name | Electrostatic Potential and Capacitance |
| NCERT Book | Physics Part I, Class 12 |
| Unit | Unit I — Electrostatics (with Ch. 1) |
| Unit Weightage (2025 Board) | 15 marks (Unit I total) |
| Chapter Weightage (estimated) | 6–8 marks (MCQs + numericals) |
| Difficulty Level | Medium to High |
| JEE/NEET Relevance | Very High |
Key Concepts and Notes
1. Electric Potential
Electric potential at a point in an electric field is defined as the work done per unit positive charge in bringing a small positive test charge from infinity to that point, without any acceleration.
Formula: V = W/q₀ (SI unit: Volt = J/C)
- Electric potential is a scalar quantity.
- Potential due to a point charge: V = kQ/r (where k = 1/4πε₀ = 9×10⁹ N m²/C²)
- Potential due to a system of charges: V = k Σ(qᵢ/rᵢ) — algebraic sum (signs matter!)
- Potential at the surface of a uniformly charged sphere of radius R: V = kQ/R
- Potential inside a uniformly charged sphere = potential at surface = kQ/R (constant inside)
2. Equipotential Surfaces
- A surface on which every point has the same potential is an equipotential surface.
- For a point charge, equipotential surfaces are concentric spheres.
- For a uniform electric field, equipotential surfaces are planes perpendicular to field lines.
- Key property: No work is done in moving a charge along an equipotential surface.
- Electric field is always perpendicular to equipotential surfaces.
3. Relationship Between Electric Field and Potential
E = -dV/dr
The electric field is the negative gradient of potential. In a region where V is constant, E = 0. The direction of E is from higher to lower potential.
4. Potential Energy of a System of Charges
- Potential energy of two charges: U = kq₁q₂/r
- For a system of three charges: U = k[q₁q₂/r₁₂ + q₂q₃/r₂₃ + q₁q₃/r₁₃]
- Potential energy of a charge in an external field: U = qV
- Potential energy of a dipole in uniform field: U = -pE cosθ (minimum at θ=0°, maximum at θ=180°)
5. Capacitance and Capacitors
A capacitor is a device that stores electric charge. Capacitance C = Q/V (SI unit: Farad = C/V).
| Type of Capacitor | Capacitance Formula | Notes |
|---|---|---|
| Parallel Plate (air) | C = ε₀A/d | A = plate area, d = separation |
| Parallel Plate (dielectric) | C = Kε₀A/d | K = dielectric constant |
| Spherical capacitor | C = 4πε₀ab/(b-a) | a = inner radius, b = outer radius |
| Isolated sphere | C = 4πε₀R | R = radius of sphere |
6. Combinations of Capacitors
- Series combination: 1/C_eff = 1/C₁ + 1/C₂ + 1/C₃ (same charge on each, voltage divides)
- Parallel combination: C_eff = C₁ + C₂ + C₃ (same voltage across each, charge divides)
7. Energy Stored in a Capacitor
U = ½CV² = Q²/2C = QV/2
Energy density (energy per unit volume between plates): u = ½ε₀E²
8. Dielectrics and Polarisation
- Polar molecules: Have permanent electric dipole moment (e.g., H₂O, HCl). In absence of external field, dipoles are randomly oriented.
- Non-polar molecules: No permanent dipole moment (e.g., H₂, O₂). External field induces dipole moment.
- Dielectric constant (K): Also called relative permittivity. Always K ≥ 1. For vacuum, K = 1.
- When dielectric is inserted in a capacitor connected to battery: Q increases, V stays same, C increases by factor K.
- When dielectric is inserted after disconnecting battery: Q stays same, V decreases, C increases by factor K.
9. Van de Graaff Generator
A device that can build up high voltages of the order of a few million volts. Uses the principle that charge given to a hollow conductor moves to its outer surface. A comb-shaped conductor sprays charge onto a moving belt which carries it to a large spherical shell. Used in nuclear physics research for accelerating charged particles.
Important MCQs for CBSE Board 2027
Q1. The capacitance of a parallel plate capacitor with air between the plates is 8 pF. If the distance between the plates is reduced by half and the space is filled with a medium of dielectric constant 6, what is the new capacitance?
Solution: C = Kε₀A/d. New C = 6 × ε₀A/(d/2) = 12 × ε₀A/d = 12 × 8 = 96 pF
Q2. Work done in moving a charge of 3 C between two points having a potential difference of 12 V is:
Solution: W = qV = 3 × 12 = 36 J
Q3. Two capacitors of capacitance 4 μF and 6 μF are connected in series. The equivalent capacitance is:
Solution: 1/C = 1/4 + 1/6 = 3/12 + 2/12 = 5/12. C = 12/5 = 2.4 μF
Q4. Energy stored in a capacitor of 5 μF charged to a potential of 400 V is:
Solution: U = ½CV² = ½ × 5×10⁻⁶ × (400)² = ½ × 5×10⁻⁶ × 160000 = 0.4 J
Q5. The electric potential at a point on the axis of an electric dipole depends on the distance r as:
Answer: V ∝ 1/r² (potential on axial line: V = kp/r² where p = dipole moment)
Common CBSE Board Question Patterns
- 1-mark (MCQ/Assertion-Reason): Equipotential surface properties, direction of E field, formula identification.
- 2-mark: Derive C = ε₀A/d; explain dielectric polarisation; draw equipotential surfaces.
- 3-mark: Numerical on capacitor combinations; energy stored calculations; potential at a point due to system of charges.
- 5-mark: Derive expression for energy stored in a capacitor; explain Van de Graaff generator with diagram; derive relationship E = -dV/dr.
Important Formulae — Quick Reference
| Concept | Formula |
|---|---|
| Electric Potential (point charge) | V = kQ/r |
| Work done | W = q(V₁ – V₂) |
| E-V relation | E = -dV/dr |
| Capacitance | C = Q/V |
| Parallel plate (air) | C = ε₀A/d |
| With dielectric | C = Kε₀A/d |
| Series | 1/C = 1/C₁ + 1/C₂ |
| Parallel | C = C₁ + C₂ |
| Energy stored | U = ½CV² = Q²/2C |
| Energy density | u = ½ε₀E² |
| Dipole PE | U = -pE cosθ |
Frequently Asked Questions
How many marks does Electrostatic Potential and Capacitance carry in CBSE Class 12 Board 2027?
Chapter 2 (Electrostatic Potential and Capacitance) is part of Unit I — Electrostatics, which carries 15 marks total in the CBSE Class 12 Physics Board exam. The chapter itself typically contributes 6–8 marks through a combination of MCQs (1 mark each), short answer questions (2–3 marks), and at least one numerical or derivation question (5 marks). It is consistently one of the most important chapters for board exam preparation.
What is the difference between electric potential and electric potential energy?
Electric potential (V) at a point is the work done per unit positive charge in bringing a test charge from infinity to that point — it is a property of the field at that point (unit: Volt). Electric potential energy (U) is the work done in bringing a specific charge q from infinity to that point — U = qV. Potential is a field property; potential energy depends on both the field and the charge placed in it.
What happens to capacitance when a dielectric is inserted?
When a dielectric of constant K is inserted between the plates of a capacitor, the capacitance increases by a factor K — i.e., C_new = KC_original. This happens because the dielectric gets polarised, creating an internal field that opposes the external field, reducing the net field and hence the voltage for the same charge. With less voltage for the same charge, C = Q/V increases. Capacitance always increases with dielectric insertion regardless of whether the capacitor is connected or disconnected from the battery.
What are equipotential surfaces and why are they important for CBSE board exams?
Equipotential surfaces are imaginary surfaces on which every point has the same electric potential. Key properties tested in CBSE boards: (1) No work is done in moving a charge along an equipotential surface (W = q(V₁-V₂) = 0 since V₁ = V₂). (2) Electric field is always perpendicular to equipotential surfaces. (3) For a point charge, equipotential surfaces are concentric spheres. (4) For a uniform field, they are planes perpendicular to field lines. Questions on drawing equipotential surfaces for point charges, dipoles, and uniform fields are asked regularly in 2-mark and 3-mark board questions.
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