Class 12 Physics Chapter 1: Electric Charges and Fields

CBSE 2026–27 | NCERT-aligned free study resource

This chapter builds the foundation of electrostatics: electric charge, Coulomb’s law, superposition, electric field, electric flux, Gauss’s law and applications of Gauss’s law. The aim is to understand not only formulas but also why the formulas work and when to use them.

1. Electric Charge

Electric charge is a fundamental property of matter. There are two types: positive and negative. Like charges repel and unlike charges attract. Charge is conserved and quantised: q = ne, where e = 1.6 × 10⁻¹⁹ C.

2. Coulomb’s Law

For two point charges q₁ and q₂ separated by distance r in vacuum, the magnitude of force is F = (1/4πε₀) |q₁q₂|/r². The force acts along the line joining the charges.

3. Principle of Superposition

When several charges are present, the net force or field is the vector sum of the individual contributions. This is one of the most important ideas in electrostatics.

4. Electric Field

Electric field at a point is the force experienced by a unit positive test charge: E = F/q. For a point charge, E = (1/4πε₀) Q/r². Field is a vector quantity.

5. Electric Field Lines

• They start on positive charges and end on negative charges or infinity.
• They never cross.
• The tangent gives field direction.
• Closer lines indicate stronger field.
• Electrostatic field lines do not form closed loops.

6. Electric Dipole

An electric dipole consists of equal and opposite charges separated by a small distance. Dipole moment p = q × 2a and points from negative to positive charge. In a uniform field, a dipole experiences torque τ = pE sinθ.

7. Electric Flux

Electric flux measures the field passing through a surface: Φ = E·A = EA cosθ for a uniform field over a plane surface.

8. Gauss’s Law

∮E·dA = q_enclosed/ε₀. The law connects electric flux through a closed surface with the net charge enclosed by it.

9. Standard Gauss-Law Applications

Worked Example

Two charges 2 μC and 3 μC are 0.30 m apart in vacuum. F = 9×10⁹ × (2×10⁻⁶)(3×10⁻⁶)/(0.30)² = 0.60 N. Because both charges are positive, the force is repulsive.

Common Exam Traps

• Electric field is not the same as electric force; F = qE.
• Use vector addition for multiple charges.
• Dipole moment points from − to +.
• Gauss’s law is always true, but it is easiest to calculate E only when symmetry is high.

Practice Questions

1. Explain charge quantisation and conservation.
2. Derive the electric field on the axial line of a dipole.
3. Why can electric field lines never intersect?
4. Use Gauss’s law to obtain the field due to an infinite plane sheet.
5. Two equal charges are placed symmetrically. Identify the point where net electric field is zero and justify using vectors.

Essential Diagrams & Visual Learning

Electric Field Lines

Field lines point away from positive charges and toward negative charges. Their density represents relative field strength; lines never intersect.

Electric Dipole

Worked Numerical

For a point charge q, electric field magnitude at distance r is E=(1/4πε₀)|q|/r². Substitute the charge in coulombs and distance in metres before calculating.

CBSE-Style Practice

1. Draw field lines for two unlike charges and explain their direction.
2. Use superposition to find the field at a specified point.
3. Derive/use the electric field on the axial line of a dipole as prescribed.
4. Apply Gauss’s law to a symmetric charge distribution.
5. Explain why electrostatic field inside a conductor is zero in equilibrium.

Common Mistakes to Avoid

• Confusing electric field with electric potential.
• Forgetting vector direction while applying superposition.
• Using an incorrect Gaussian surface for a symmetry-based problem.