Electric Charges and Fields Class 12 Physics Notes 2026-27 | Chapter 1
These Class 12 Physics notes cover the current CBSE 2026–27 scope for Chapter 1, Electric Charges and Fields, under Unit I — Electrostatics. The chapter develops the ideas of electric charge, Coulomb's law, superposition, electric field, field lines, electric dipole, electric flux and Gauss's law, including its specified applications.
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1. Electric Charge
Electric charge is a fundamental property of matter responsible for electrostatic interaction. There are two types of charge: positive and negative. Like charges repel and unlike charges attract.
Basic Properties of Electric Charge
- Additivity: The total charge of a system is the algebraic sum of its individual charges.
- Conservation: In an isolated system, total electric charge remains constant. Charge can be transferred from one body to another but is not created or destroyed.
- Quantisation: Charge on an ordinary isolated body occurs in integral multiples of the elementary charge.
2. Conductors and Insulators
Conductors contain mobile charge carriers that can move relatively freely through the material. Metals are common examples. In insulators, charges are much more strongly bound and do not move freely through the material.
This distinction is important when discussing charging, redistribution of charge and electrostatic equilibrium. Do not confuse the ability of a conductor to redistribute charge with the creation of net charge.
3. Coulomb's Law
Coulomb's law gives the electrostatic force between two point charges. Its magnitude 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.
Coulomb's Law as a Vector Relation
If the position of charge q2 relative to q1 is represented by the vector r, the force must be treated as a vector. This is essential when charges are not arranged along a single straight line.
4. 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 one at a time.
The same principle applies to electric fields: calculate the field contribution of each source charge and then add the contributions vectorially.
5. Continuous Charge Distribution
When charge is spread continuously over a length, surface or volume, charge density is used instead of treating every small charge separately.
- Linear charge density: λ = dq/dl
- Surface charge density: σ = dq/dA
- Volume charge density: ρ = dq/dV
6. Electric Field
The electric field at a point is the electric force experienced per unit positive test charge placed at that point, with the test charge sufficiently small that it does not disturb the source distribution.
Electric field is a vector quantity. Its direction 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.
7. Electric Field Lines
Electric field lines are an imaginary graphical 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.
- 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 indicate a stronger field relative to regions where the lines are more widely separated.
- Electrostatic field lines do not form closed loops.
- The number or density of drawn lines is a representation; it is not itself a physical measurement of charge.
8. Electric Dipole
An electric dipole consists of two equal and opposite point charges separated by a small distance. If the charges are +q and −q and their separation is 2a, the dipole moment is defined as:
The SI unit of dipole moment is coulomb-metre (C m). Its direction is from the negative charge toward the positive charge.
Electric Field Due to a Dipole
The electric field of a dipole depends on the position of the observation point. The two standard positions are the axial line and the equatorial line.
For a dipole with charges +q and −q separated by 2a, the standard axial and equatorial field expressions are:
When the observation distance is much greater than the charge separation (r ≫ a), these reduce to the familiar short-dipole results:
Therefore, at the same far-field distance, the axial field magnitude is twice the equatorial field magnitude. The equatorial field is directed opposite to the dipole moment.
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.
9. Electric Flux
Electric flux measures the extent to which an electric field passes through a surface. For a uniform electric field through a plane surface:
Here θ is the angle between the electric field E and the area vector A. The area vector is normal to the surface.
10. Gauss's Theorem
Gauss's theorem, or Gauss's law, relates the net electric flux through a closed surface to the net charge enclosed by that surface.
For a closed surface, the net flux depends on the net enclosed charge. Charges outside the surface can affect the electric field at points on the surface, but their net contribution to the total closed-surface flux is zero.
How to Choose a Gaussian Surface
- Identify the symmetry of the charge distribution.
- Choose a closed surface that matches that symmetry.
- Determine where the electric field has constant magnitude or a simple direction.
- Evaluate the flux through the relevant surface.
- Use Gauss's law to relate flux to enclosed charge.
11. 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 λ and distance r from the wire.
Uniformly Charged Infinite Plane Sheet
For a uniformly charged infinite plane sheet, a pillbox-shaped Gaussian surface is used. The field is perpendicular to the sheet and, for an ideal infinite sheet, its magnitude is independent of distance from the sheet.
Uniformly Charged Thin Spherical Shell
For a uniformly charged thin spherical shell, spherical symmetry is used.
12. High-Yield Comparisons
| Concept | Key point |
|---|---|
| Charge vs electric field | Charge is a property of matter; electric field describes the force environment created by charges. |
| Electric field vs force | E is force per unit positive test charge; F depends on the test charge. |
| Axial vs equatorial dipole field | For a short dipole at the same far-field distance, axial magnitude is twice the equatorial magnitude. |
| Flux angle | The angle in Φ = EA cos θ is between E and the area vector, not the surface. |
| Open vs closed surface | Gauss's law in its standard flux form applies to a closed surface. |
| Inside spherical shell | For a uniformly charged thin spherical shell, E = 0 inside. |
13. Units, Symbols and Quick Definitions
| Quantity | Symbol | SI unit / meaning |
|---|---|---|
| Electric charge | q | coulomb (C) |
| Electric field | E | N/C or V/m |
| Electric flux | Φ | N m²/C |
| Dipole moment | p | C m |
| Linear charge density | λ | C/m |
| Surface charge density | σ | C/m² |
| Volume charge density | ρ | C/m³ |
| Permittivity of free space | ε₀ | ≈ 8.85 × 10−12 C²/(N m²) |
Notation reminder: dA represents a small area element and dA is the corresponding vector area element normal to the surface. For a closed surface, the flux integral is written as ∮ E·dA.
14. Important Formula Revision
| Concept | Formula |
|---|---|
| Quantisation of charge | q = ne |
| Coulomb's law | F = (1 / 4πε₀) × |q₁q₂| / r² |
| Charge density | λ = dq/dl; σ = dq/dA; ρ = dq/dV |
| Electric field | E = F/q₀ |
| Field of a point charge | E = (1 / 4πε₀) × |q| / r² |
| Dipole moment | p = q × 2a |
| Dipole field, axial | E = (1 / 4πε₀) × 2p/r³ (short dipole) |
| Dipole field, equatorial | E = (1 / 4πε₀) × p/r³ (short dipole) |
| Torque on dipole | τ = pE sin θ |
| Electric flux | Φ = EA cos θ |
| Gauss's law | Φclosed = qenclosed/ε₀ |
| Infinite line charge | E = λ/(2πε₀r) |
| Infinite plane sheet | E = σ/(2ε₀) |
| Thin spherical shell | Outside: E = (1/4πε₀)Q/r²; inside: E = 0 |
15. Quick Answers: Frequently Asked Questions
Coulomb's law gives the electrostatic force between two point charges: F = (1/4πε₀)|q₁q₂|/r².
Electric field at a point is the force experienced per unit positive test charge: E = F/q₀.
It is directed from the negative charge toward the positive charge.
Maximum torque occurs when θ = 90°, because τmax = pE.
The angle between the electric field and the area vector (normal to the surface).
With suitable symmetry, the magnitude and direction of the electric field can become simple over parts of the Gaussian surface, making the flux calculation manageable.
For a uniformly charged thin spherical shell, the electric field is zero at points inside the shell.
16. Common Exam Traps
- Using the angle with the surface instead of the angle with the area vector in electric-flux questions.
- Adding electrostatic forces as ordinary numbers when the forces are not collinear.
- Forgetting that electric field is defined using a positive test charge.
- Giving the dipole moment direction from positive to negative instead of negative to positive.
- Using Gauss's law without first identifying an appropriate symmetry.
- Assuming zero enclosed charge means the electric field is zero everywhere on the Gaussian surface.
- Forgetting that Gauss's law concerns net flux through a closed surface, not flux through an arbitrary open surface.
- Mixing the field of a point charge with the field of an infinite line, plane sheet or spherical shell.
17. Problem-Solving Method
- Draw the arrangement: Mark charges, distances, directions and the required point.
- Choose the physical law: Coulomb's law for point-charge forces/fields, superposition for multiple sources, or Gauss's law when symmetry permits.
- Resolve vectors: Never treat non-collinear forces or fields as simple scalars.
- Check units: Force in newtons (N), field in N/C, flux in N m²/C and dipole moment in C m.
- Check limiting behaviour: For example, point-charge field should fall as 1/r², while the infinite-line result falls as 1/r.
18. Chapter-at-a-Glance
| Topic | What you should be able to do |
|---|---|
| Electric charge | State additivity, conservation and quantisation. |
| Coulomb's law | Calculate magnitude and identify force direction. |
| Superposition | Combine forces or fields vectorially. |
| Continuous charge | Use λ, σ and ρ to describe charge density. |
| Electric field | Relate field to force and determine its direction. |
| Field lines | Interpret direction and relative field strength. |
| Dipole | Use dipole moment, axial/equatorial field and torque. |
| Electric flux | Use Φ = EA cos θ with the correct angle. |
| Gauss's law | Relate closed-surface flux to enclosed charge. |
| Applications | Derive/use fields for line charge, plane sheet and thin spherical shell. |
19. Quick Revision Checklist
- Know the three basic properties of charge: additivity, conservation and quantisation.
- Understand conductors and insulators and the idea of charge redistribution.
- Use Coulomb's law with correct magnitude and direction.
- Apply superposition to multiple charges.
- Know λ, σ and ρ for continuous charge distributions.
- Distinguish electric field from electric force.
- Know field-line rules and what line density represents qualitatively.
- Know dipole moment direction and the axial/equatorial field relations.
- Use τ = pE sin θ and identify maximum/zero torque conditions.
- Use the area-vector convention correctly in electric-flux questions.
- State Gauss's law accurately for a closed surface.
- Practise the three specified Gauss-law applications: infinite wire, infinite plane sheet and thin spherical shell.
20. Complete Chapter 1 Study Resources
Complete Notes: Electric Charges and Fields Class 12 Physics Notes
Important Questions: Electric Charges and Fields Important Questions
MCQs: Electric Charges and Fields MCQs
Numericals: Electric Charges and Fields Numericals
Case-Based Questions: Electric Charges and Fields Case-Based Questions
Assertion–Reason: Electric Charges and Fields Assertion–Reason Questions
PYQs: Electric Charges and Fields PYQs
Formula Sheet: Electric Charges and Fields Formula Sheet & Quick Revision
Chapter Test: Electric Charges and Fields Chapter Test
21. Chapter 2 Connection
Chapter 1 establishes electric field and flux. Chapter 2 develops the related ideas of electric potential, potential energy and capacitance. For the next stage of the Class 12 Physics sequence, continue to:
Electrostatic Potential and Capacitance — Class 12 Physics Hub
22. Official CBSE References
CBSE Physics Curriculum 2026–27: Official Physics Curriculum PDF
CBSE Class XII 2026–27 SQP & Marking Schemes: Official Sample Question Papers and Marking Schemes
Source discipline: The official CBSE Physics 2026–27 curriculum is the authority for syllabus scope. NCERT Chapter 1 is used for conceptual structure and standard definitions/formulas. Competitor pages were reviewed for search intent and student-demand patterns; their rankings or mark claims are not treated as official CBSE information.
23. Short Answers for Search and Revision
It is Chapter 1 of Class 12 Physics and the first chapter of Unit I — Electrostatics. It covers charge, Coulomb's law, electric field, dipole, electric flux and Gauss's law.
Additivity, conservation and quantisation.
The electrostatic force between two point charges is proportional to the product of their charges and inversely proportional to the square of their separation.
The net electric flux through a closed surface equals the net charge enclosed by the surface divided by ε₀.
Electric field due to an infinitely long straight charged wire, a uniformly charged infinite plane sheet, and a uniformly charged thin spherical shell.
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