Electric Charges and Fields Class 12 Physics: Complete Notes
These notes cover the topics specified for Chapter 1, Unit I — Electrostatics, in the CBSE 2026–27 Physics syllabus. Use them to build the concepts first, then move to questions, MCQs, numericals and revision practice.
1. Electric Charge
Electric charge is a fundamental property of matter responsible for electric interaction. There are two types of charge: positive and negative. Like charges repel each other, while unlike charges attract each other.
Properties of Charge
- Additivity: The total charge of a system is the algebraic sum of the individual charges.
- Conservation: Electric charge cannot be created or destroyed in an isolated system; it can be transferred from one body to another.
- Quantisation: Charge on an ordinary isolated body occurs in integral multiples of the elementary charge.
2. Coulomb's Law
Coulomb's law gives the electrostatic force between two point charges. The magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
In vacuum, ε₀ is the permittivity of free space. The force acts along the line joining the two charges.
3. Principle of Superposition
When several point charges are present, the net electrostatic force on a charge is the vector sum of the forces exerted by the other charges considered separately.
The same superposition idea is used when calculating the electric field produced by multiple charges.
4. Continuous Charge Distribution
When charge is distributed continuously over a length, surface or volume, the charge can be represented using charge density.
- Linear charge density: λ = dq/dl
- Surface charge density: σ = dq/dA
- Volume charge density: ρ = dq/dV
5. Electric Field
The electric field at a point is defined as the electric force experienced per unit positive test charge placed at that point, provided the test charge does not disturb the source distribution.
The electric field is a vector quantity. Its direction at a point is the direction of the force on a positive test charge.
Electric Field Due to a Point Charge
For a positive source charge, the field is directed radially outward. For a negative source charge, it is directed radially inward.
6. Electric Field Lines
Electric field lines are a visual representation used to show the direction and relative strength of an electric field.
- The tangent to a field line at a point gives the direction of the electric field there.
- Field lines originate from positive charges and terminate on negative charges, or extend to/from infinity where appropriate.
- Two electric field lines do not intersect.
- Closer field lines represent a stronger field relative to regions where they are more widely separated.
- Electrostatic field lines do not form closed loops.
7. Electric Dipole
An electric dipole consists of two equal and opposite point charges separated by a small distance.
The dipole moment is directed from the negative charge toward the positive charge.
Electric Field Due to a Dipole
The field of a dipole depends on the position of the observation point. The two standard positions used in the chapter are the axial line and the equatorial line.
Torque on a Dipole in a Uniform Electric Field
Here θ is the angle between the dipole moment and the electric field. The torque tends to rotate the dipole toward alignment with the field.
8. Electric Flux
Electric flux provides a measure of the electric field passing through a surface.
Here θ is the angle between the electric field and the area vector of the surface.
9. Gauss's Theorem
Gauss's theorem relates the net electric flux through a closed surface to the net charge enclosed by that surface.
For symmetric charge distributions, an appropriately chosen Gaussian surface can make the calculation of the electric field much simpler.
10. Applications of Gauss's Theorem
Infinitely Long Straight Charged Wire
For a uniformly charged infinitely long straight wire, cylindrical symmetry is used. The electric field is radial and its magnitude depends on the linear charge density and distance from the wire.
Uniformly Charged Infinite Plane Sheet
For a uniformly charged infinite plane sheet, a pillbox-shaped Gaussian surface is used. The magnitude of the electric field is independent of the distance from the sheet.
Uniformly Charged Thin Spherical Shell
For a uniformly charged thin spherical shell, spherical symmetry is used.
11. Important Formula Revision
| Concept | Formula |
|---|---|
| Quantisation of charge | q = ne |
| Coulomb's law | F = (1 / 4πε₀) × |q₁q₂| / r² |
| Electric field | E = F/q₀ |
| Field of a point charge | E = (1 / 4πε₀) × |q| / r² |
| Dipole moment | p = q × 2a |
| Torque on dipole | τ = pE sin θ |
| Electric flux | Φ = EA cos θ |
| Gauss's theorem | Φ = qenclosed/ε₀ |
| Infinite line charge | E = λ/(2πε₀r) |
| Infinite plane sheet | E = σ/(2ε₀) |
12. Quick Exam Checklist
- Know the properties and conservation of electric charge.
- Understand Coulomb's law and the direction of electrostatic force.
- Use vector addition for multiple charges through superposition.
- Distinguish electric field from electric force.
- Understand the direction and qualitative meaning of field lines.
- Know electric dipole moment and torque in a uniform field.
- Understand electric flux and the role of the area vector.
- Know the statement and appropriate use of Gauss's theorem.
- Practise the three specified Gauss-law applications: infinite wire, infinite plane sheet and thin spherical shell.
Source basis: CBSE Class XII Physics curriculum for the 2026–27 session. The chapter coverage above follows the topics specified by CBSE for Unit I, Chapter 1.
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