Electrostatic Potential and Capacitance Class 12 Physics Notes 2026-27

Electrostatic Potential and Capacitance — Class 12 Physics Complete Notes
Concept-focused CBSE 2026–27 notes covering electric potential, potential difference, potential energy, equipotential surfaces, conductors, dielectrics, capacitors, combinations of capacitors, parallel-plate capacitors and stored energy.

Electrostatic Potential and Capacitance — Class 12 Physics

Chapter 2 of Class 12 Physics belongs to Unit I: Electrostatics. The current CBSE 2026–27 syllabus includes electric potential and potential difference, potential due to a point charge, dipole and system of charges, equipotential surfaces, electrostatic potential energy, conductors and insulators, dielectrics and polarisation, capacitance, capacitor combinations, parallel-plate capacitors with and without dielectric, and energy stored in a capacitor. CBSE specifies formulae only, with no derivation, for the energy stored in a capacitor.

Exam focus: Do not learn this chapter as a list of formulas. Pay attention to the difference between potential and field, the sign of potential energy, equipotential-surface properties, what changes when a dielectric is inserted, and which quantity remains constant when a capacitor is connected to a battery or isolated.

1. Electric Potential

Electric potential at a point is the work done by an external agent per unit positive test charge in bringing the test charge from infinity to that point, without producing acceleration.

Potential: V = W/q₀

SI unit: volt (V)

1 volt: 1 V = 1 J/C

Electric potential is a scalar quantity. Therefore, potentials due to several charges are added algebraically, including their signs.

Potential Difference

The potential difference between two points A and B is the work done per unit positive test charge in moving the charge from A to B, with the appropriate sign convention.

Potential difference: V_B − V_A = − ∫_A^B E · dl

In a uniform electric field, for displacement d along the field: |ΔV| = Ed. More generally, the sign depends on the direction of displacement relative to the field.

2. Potential Due to a Point Charge

For a point charge q, the electric potential at a distance r in vacuum is:

V = (1/4πε₀) q/r

In a medium of permittivity ε: V = (1/4πε) q/r. Since potential is scalar, the sign of q directly determines the sign of V.

• Positive source charge → positive potential at a finite distance.
• Negative source charge → negative potential at a finite distance.
• At infinity, the reference potential is normally taken as zero.
• Potential varies as 1/r for a point charge.

3. Potential Due to a System of Charges

Since electric potential is scalar, the total potential at a point is the algebraic sum of the potentials produced by all source charges.

V = (1/4πε₀) Σ(q_i/r_i)

Here r_i is the distance of the point from charge q_i. Use the sign of every charge during the algebraic addition.

Common trap: Zero potential does not necessarily mean zero electric field. For example, at a suitable point between equal and opposite charges, the potentials can cancel while the electric fields point in the same direction and add.

4. Potential Due to an Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. Its dipole moment is directed from the negative charge to the positive charge.

Dipole moment: p = qd

SI unit: C m

For a point at distance r from the centre of a short dipole, the potential is:

V = (1/4πε₀) (p cos θ/r²)

This expression is the usual short-dipole / far-field form, where r is much larger than the dipole separation.

Important Special Cases

• Axial line: θ = 0° or 180°, so |V| is maximum for a given r.
• Equatorial line: θ = 90°, so V = 0.
• Zero potential on the equatorial line does not imply zero electric field there.

5. Equipotential Surfaces

An equipotential surface is a surface on which the electric potential has the same value at every point.

• No work is done in moving a test charge along an equipotential surface.
• The electric field is perpendicular to an equipotential surface.
• Two equipotential surfaces cannot intersect, because one point cannot have two different potential values.
• Where equipotential surfaces are closer together, the magnitude of electric field is greater.
• For an isolated point charge, equipotential surfaces are concentric spheres.
• For a uniform electric field, equipotential surfaces are planes perpendicular to the field.

Key relation: Electric field points in the direction of decreasing potential. In one dimension, E = −dV/dx.

6. Electrostatic Potential Energy

Two Point Charges

The electrostatic potential energy of two point charges q₁ and q₂ separated by distance r, taking zero energy at infinite separation, is:

U = (1/4πε₀) q₁q₂/r

• Like charges → U is positive.
• Unlike charges → U is negative.
• Increasing r makes the magnitude of U smaller.

Potential Energy of a Charge in an External Potential

U = qV

Here V is the electric potential at the position of the charge due to the external charges. The charge's own potential is not included when calculating its interaction energy with the external field.

Potential Energy of an Electric Dipole

U = −p · E = −pE cos θ

• At θ = 0°, U = −pE.
• At θ = 90°, U = 0.
• At θ = 180°, U = +pE.

7. Conductors in Electrostatic Equilibrium

In electrostatic equilibrium, free charges in a conductor have reached a state in which there is no net motion of charge inside the conductor.

• Electric field inside the conducting material is zero in electrostatic equilibrium.
• Excess charge resides on the surface of a conductor.
• The electric field just outside a conductor is normal to its surface.
• The conductor is an equipotential body in electrostatic equilibrium.
• No tangential electric field can remain at the surface in electrostatic equilibrium.

Important distinction: “Electric field inside a conductor is zero” refers to electrostatic equilibrium. It is not a general statement about conductors carrying current.

8. Conductors, Free Charges and Bound Charges

Conductors contain mobile charge carriers that can redistribute in response to an electric field. In electrostatic equilibrium, this redistribution continues until the internal electric field in the conducting material becomes zero.

In a dielectric, charges are generally not free to move through the material in the same way. Instead, the applied electric field can cause a small relative displacement of positive and negative bound charges, producing polarisation.

9. Dielectrics and Electric Polarisation

A dielectric is an insulating material that can become polarised in an electric field. Polarisation reduces the effective electric field within the dielectric compared with the corresponding vacuum situation, under the standard capacitor model.

The relative permittivity or dielectric constant is represented by K or ε_r:

ε = Kε₀ = ε_rε₀

For an ideal parallel-plate capacitor completely filled with a dielectric of relative permittivity K: C = K C₀.

10. Capacitor and Capacitance

A capacitor is a system of two conductors separated by an insulating region or dielectric. Its capacitance measures the charge stored per unit potential difference.

C = Q/V

SI unit: farad (F)

Capacitance is determined by the geometry of the conductors and the material between them. For a given capacitor under fixed physical conditions, Q and V can change together while their ratio remains C.

11. Parallel-Plate Capacitor

For two large parallel conducting plates of area A separated by distance d, neglecting edge effects, the capacitance in vacuum is:

C₀ = ε₀A/d

If the space between the plates is completely filled with a dielectric of relative permittivity K:

C = Kε₀A/d = KC₀

Dependence on Geometry

• C increases when plate area A increases.
• C decreases when separation d increases.
• C increases by factor K when a dielectric completely fills the gap.

12. Combination of Capacitors in Parallel

In a parallel combination, all capacitors have the same potential difference.

C_eq = C₁ + C₂ + C₃ + ...

• Potential difference across each capacitor is the same.
• Total charge is the sum of the individual charges.
• The equivalent capacitance is greater than any individual capacitance in the combination.

13. Combination of Capacitors in Series

In a series combination, the magnitude of charge on each capacitor is the same for the ideal isolated series chain.

1/C_eq = 1/C₁ + 1/C₂ + 1/C₃ + ...

• Charge magnitude on each capacitor is the same.
• Total potential difference is the sum of individual potential differences.
• The equivalent capacitance is less than the smallest individual capacitance.

14. Energy Stored in a Capacitor

The CBSE 2026–27 syllabus specifies formulae only, with no derivation for energy stored in a capacitor.

U = ½CV²

Equivalent forms: U = ½QV = Q²/(2C)

These forms are mathematically equivalent because Q = CV. Choose the form that matches the quantities given in the question.

15. What Changes When a Dielectric Is Inserted?

This is one of the most important comparison areas in the chapter. The result depends on whether the capacitor remains connected to a battery or is isolated after charging.

Quantity	Battery Connected	Battery Disconnected / Isolated
Capacitance C	Increases by K	Increases by K
Potential difference V	Remains constant	Decreases by factor K
Charge Q	Increases by K	Remains constant
Stored energy U	Increases by K	Decreases by factor K

Memory rule: Battery connected → V fixed. Battery disconnected → Q fixed.

16. Formula Sheet — Chapter 2 at a Glance

Concept	Formula
Potential	V = W/q0
Point charge potential	V = (1/4πε0)q/r
Potential of charges	V = (1/4πε0)Σ(qi/ri)
Potential difference	VB−VA = −∫E·dl
Dipole moment	p = qd
Far-field dipole potential	V = (1/4πε0)(p cosθ/r²)
Potential energy of charge	U = qV
Two-charge potential energy	U = (1/4πε0)q1q2/r
Dipole potential energy	U = −pE cosθ
Capacitance	C = Q/V
Parallel capacitors	Ceq = ΣCi
Series capacitors	1/Ceq = Σ(1/Ci)
Parallel-plate capacitor	C = ε0A/d
With dielectric	C = Kε0A/d
Stored energy	U = ½CV² = ½QV = Q²/(2C)

17. High-Value Exam Traps

• Potential is scalar: add potentials algebraically, not vectorially.
• Field is vector: a point can have V = 0 while E ≠ 0.
• Equipotential movement: work done by the electrostatic field is zero along an equipotential surface.
• Direction: electric field points toward decreasing potential.
• Conductor: E = 0 inside the conducting material only in electrostatic equilibrium.
• Series: same charge magnitude; voltages divide.
• Parallel: same voltage; charges divide according to capacitance.
• Battery connected: V stays fixed when capacitance changes.
• Battery disconnected: Q stays fixed when capacitance changes.
• Energy formula: use the form matching the known quantities.
• Dielectric: distinguish relative permittivity K from absolute permittivity ε = Kε₀.
• Dipole potential: the p cosθ/r² expression is the short-dipole far-field result, not a universal near-field expression.

18. Quick Self-Check

1. Can I distinguish electric potential from electric field?
2. Can I calculate the potential due to several point charges with correct signs?
3. Can I explain why potential can be zero while field is non-zero?
4. Can I state the properties of equipotential surfaces?
5. Can I calculate potential energy of two point charges?
6. Can I use U = −pE cosθ for a dipole in a uniform field?
7. Can I explain the electrostatic properties of a conductor?
8. Can I distinguish free-charge motion in conductors from polarisation in dielectrics?
9. Can I calculate equivalent capacitance in series and parallel?
10. Can I identify whether Q or V remains constant when a capacitor is isolated or connected to a battery?
11. Can I calculate stored energy using all three equivalent forms?

Chapter 2 Resource Path

Start from the chapter hub and then move through the practice and revision resources as they are published.

Chapter Hub: Electrostatic Potential and Capacitance — Class 12 Physics

Next resources: Important Questions → MCQs → Numericals → Case-Based Questions → Assertion–Reason → PYQs → Formula Sheet & Quick Revision → Chapter Test.

Curriculum basis: CBSE Class XII Physics 2026–27, Unit I: Electrostatics, Chapter 2: Electrostatic Potential and Capacitance. The official syllabus specifically includes potential, potential difference, potential due to a point charge, dipole and system of charges, equipotential surfaces, potential energy, conductors, dielectrics, capacitance, series/parallel combinations, parallel-plate capacitors with and without dielectric, and capacitor energy with formulae only and no derivation.