Class 12 Physics Chapter 2: Electrostatic Potential and Capacitance

CBSE 2026–27 | NCERT-aligned free study resource

This chapter connects electric field with energy. It develops electric potential, potential difference, equipotential surfaces, potential energy, conductors, capacitors, combinations of capacitors and energy stored in a capacitor.

1. Electric Potential

Potential at a point is the work done per unit positive test charge in bringing it from infinity to that point without acceleration. V = W/q. For a point charge, V = (1/4πε₀)Q/r.

2. Potential Difference

Potential difference between two points is work done per unit charge in moving a test charge between those points. One volt equals one joule per coulomb.

3. Equipotential Surfaces

An equipotential surface has the same potential everywhere. No work is done in moving a charge along it. Electric field is perpendicular to an equipotential surface.

4. Potential of a System

For several point charges, potential is a scalar sum: V = (1/4πε₀) Σ(qᵢ/rᵢ). Unlike electric field, direction does not have to be considered while adding potentials.

5. Conductors in Electrostatic Equilibrium

• Electric field inside a conductor is zero.
• Excess charge resides on the surface.
• The conductor is an equipotential.
• Electric field just outside a conductor is normal to its surface.

6. Capacitance

A capacitor stores electric charge and energy. Capacitance C = Q/V. For a parallel-plate capacitor with plate area A and separation d in vacuum, C = ε₀A/d. With a dielectric of relative permittivity K, C = Kε₀A/d.

7. Combination of Capacitors

8. Energy Stored

U = ½CV² = ½QV = Q²/(2C). The energy density in vacuum is u = ½ε₀E².

Worked Example

A 4 μF capacitor is connected to 10 V. Q = CV = 40 μC and U = ½CV² = 200 μJ.

Dielectric Concept

Inserting an insulating dielectric between capacitor plates changes capacitance by reducing the effective electric field for a given free charge. The exact changes in V, Q and U depend on whether the battery remains connected.

Common Exam Traps

• Potential is scalar; electric field is vector.
• In series capacitors, charge magnitude is the same; in parallel, voltage is the same.
• Do not use one energy formula without checking which quantity is held constant.

Practice Questions

1. Why is no work done in moving a charge on an equipotential surface?
2. Derive capacitance of a parallel-plate capacitor.
3. Compare series and parallel combinations.
4. A capacitor is disconnected from a battery and then filled with dielectric. Explain changes in Q, V, C and U.
5. Calculate energy stored in a capacitor for given C and V.

Essential Diagrams & Visual Learning

Parallel-Plate Capacitor

For an ideal parallel-plate capacitor, C=ε₀A/d in vacuum. Inserting a dielectric changes the capacitance according to its relative permittivity.

Potential vs Field

Electric field is related to the spatial rate of change of potential. In one dimension, E=−dV/dr. The negative sign indicates that the field points toward decreasing potential.

Worked Numerical

For a capacitor with C=5 μF connected to V=12 V, Q=CV=60 μC and stored energy U=½CV²=360 μJ.

CBSE-Style Practice

1. Calculate potential due to point charges.
2. Compare work done along paths in an electrostatic field.
3. Find equivalent capacitance for series/parallel combinations.
4. Calculate energy stored in a capacitor.
5. Explain the effect of inserting a dielectric.

Common Mistakes to Avoid

• Mixing sign conventions for potential and potential difference.
• Using capacitor series/parallel rules in the wrong arrangement.
• Forgetting the effect of a dielectric on capacitance and stored energy.