Electric Charges and Fields Class 12 Physics Formula Sheet & Quick Revision 2026-27

Electric Charges and Fields — Class 12 Physics Formula Sheet & Quick Revision
A compact revision resource covering the essential formulas, definitions, directions, standard Gauss-law results, dipole relations and exam traps for CBSE Class 12 Physics.

Class 12 Physics Electric Charges and Fields — Quick Revision

This page is designed for fast revision after completing the chapter. It covers the current CBSE 2026–27 Chapter 1 scope: electric charge, Coulomb's law, multiple charges and superposition, continuous charge distribution, electric field and field lines, electric dipole, torque, electric flux, Gauss's law and its standard applications.

Best use: First revise the formula tables, then test yourself using the checklist at the end without opening your notes.

1. Electric Charge — Essential Facts

Concept	Formula / Fact	Remember
Quantisation	q = ne	n is an integer; e is elementary charge.
Elementary charge	e = 1.6 × 10⁻¹⁹ C	Electron charge = −e; proton charge = +e.
Conservation	Σq = constant	For an isolated system.
Additivity	Q = q₁ + q₂ + ...	Charge is algebraically additive.

2. Coulomb's Law

Magnitude in vacuum:

F = (1 / 4πε₀) |q₁q₂| / r²

In a medium of permittivity ε:

F = (1 / 4πε) |q₁q₂| / r²

Vacuum constant: 1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻².

Relative permittivity: ε = ε_rε₀.

Therefore in a medium: F_medium = F_vacuum/ε_r, for the same charges and separation.

Direction Rules

Like charges repel.
Unlike charges attract.
The force acts along the line joining the two point charges.
The forces on the two charges are equal in magnitude and opposite in direction.

Scaling Shortcuts

If r becomes 2r, force becomes F/4.
If r becomes 3r, force becomes F/9.
If either charge is doubled, force doubles.
If both charges are doubled, force becomes four times.
If the medium has relative permittivity ε_r, force is reduced by a factor ε_r compared with vacuum.

3. Principle of Superposition

For several point charges, calculate each contribution separately and then add the vectors.

F_net = F₁ + F₂ + F₃ + ...

For a continuous distribution, the discrete sum becomes an integral:

dF → integrate dF

Typical charge elements:

Linear: dq = λ dl
Surface: dq = σ dA
Volume: dq = ρ dV

4. Electric Field

Definition:

E = F / q₀

Field due to a point charge:

E = (1 / 4πε₀) |q| / r²

Vector form:

𝐄 = (1 / 4πε₀) (q/r²) r̂

Force on a charge q in an electric field:

𝐅 = q𝐄

SI unit of electric field: N C⁻¹ or V m⁻¹.

Direction

Field due to a positive charge points away from the charge.
Field due to a negative charge points towards the charge.
The direction of E is defined as the direction of force on a positive test charge.

5. Electric Field Lines — Exam Facts

Field lines emerge from positive charges and terminate on negative charges or at infinity.
They do not intersect because the electric field has a unique direction at a point.
Closer field lines represent a stronger field qualitatively.
For electrostatics, field lines do not form closed loops.
The tangent to a field line at a point gives the direction of the electric field there.
Field lines are perpendicular to the surface of a conductor in electrostatic equilibrium.

6. Electric Dipole

Dipole: two equal and opposite charges separated by a small distance.

p = qd

Direction of dipole moment: from negative charge to positive charge.

SI unit: C m.

Electric Field of an Ideal Dipole

For a point far from the dipole compared with its separation:

Axial position:

E_axial ≈ (1 / 4πε₀) (2p/r³)

Equatorial position:

E_equatorial ≈ (1 / 4πε₀) (p/r³)

At the same large distance, the axial field magnitude is twice the equatorial field magnitude.

Torque on a Dipole

τ = pE sin θ

Maximum torque: θ = 90°, so τ_max = pE.
Zero torque: θ = 0° or 180°.
Torque tends to rotate the dipole towards alignment with the field.

7. Electric Flux

Uniform field through a plane surface:

Φ = EA cos θ

Here θ is the angle between E and the area vector, not the surface itself.

General surface:

Φ = ∫ E · dA

SI unit: N m² C⁻¹.

Flux Shortcuts

E perpendicular to surface → θ = 0° → Φ = EA (maximum).
E parallel to surface → θ = 90° → Φ = 0.
Flux can be positive, negative or zero depending on orientation.

8. Gauss's Law

∮ E · dA = q_enclosed / ε₀

Gauss's law relates the net electric flux through a closed surface to the algebraic net charge enclosed by that surface.

Important Interpretation

Charges outside a closed Gaussian surface can contribute to the electric field on the surface, but their net contribution to the total flux through the closed surface is zero.
Zero enclosed charge means zero net flux, not necessarily zero electric field everywhere.
Gauss's law is always valid, but a convenient symmetric Gaussian surface makes field calculations easier.

9. Standard Gauss-Law Results

Charge Distribution	Electric Field	Key Condition
Infinite uniformly charged line	E = λ/(2πε₀r)	Radial field; cylindrical symmetry.
Infinite uniformly charged plane sheet	E = σ/(2ε₀)	Ideal infinite sheet; independent of distance.
Thin uniformly charged spherical shell, inside	E = 0	r < R.
Thin uniformly charged spherical shell, outside	E = (1/4πε₀)Q/r²	r > R; equivalent to a point charge Q at centre.
Thin shell at its surface	E_inside = 0; E_outside = (1/4πε₀)Q/R²	Ideal thin shell; field has a discontinuity across the charged surface.

10. Charge Density Formulas

Linear charge density: λ = dq/dl, so dq = λ dl.
Surface charge density: σ = dq/dA, so dq = σ dA.
Volume charge density: ρ = dq/dV, so dq = ρ dV.

11. Constants and Units

Quantity	Value / Unit
Elementary charge e	1.6 × 10⁻¹⁹ C
Permittivity of free space ε₀	≈ 8.85 × 10⁻¹² C² N⁻¹ m⁻²
Coulomb constant k	1/(4πε₀) ≈ 9 × 10⁹ N m² C⁻²
Electric field	N C⁻¹ = V m⁻¹
Electric flux	N m² C⁻¹
Dipole moment	C m

12. High-Value Exam Traps

Flux angle trap: θ is measured from the area vector, not from the plane of the surface.
Zero flux trap: zero net flux does not imply E = 0 everywhere.
Dipole direction trap: p points from negative to positive charge.
Dipole distance trap: far-field dipole E varies as 1/r³, not 1/r².
Shell trap: field inside a uniformly charged thin spherical shell is zero, while outside it follows the point-charge expression.
Infinite sheet trap: the ideal sheet's field is independent of distance.
Superposition trap: fields and forces are vectors, so they must be added vectorially.
Gauss-law trap: choose a Gaussian surface using symmetry; do not assume Gauss's law automatically makes every field calculation easy.
Charge trap: the sign of charge affects force direction, while the magnitude formula uses |q₁q₂|.

13. 60-Second Formula Checklist

Can I write q = ne?
Can I write Coulomb's law in vacuum and in a medium?
Can I apply superposition to several charges?
Can I convert λ, σ and ρ into dq?
Can I write E due to a point charge?
Can I state the direction of E for positive and negative charges?
Can I write p = qd and state its direction?
Can I write τ = pE sin θ and identify maximum/zero torque?
Can I write Φ = EA cos θ and identify the correct angle?
Can I state Gauss's law for a closed surface?
Can I recall the infinite line, infinite sheet and spherical-shell results?
Can I explain why zero net flux does not necessarily mean zero field?

14. Chapter Resource Path

Use the complete chapter cluster in this order:

Final revision tip: Do not memorise formulas without the conditions under which they apply. In board-style questions, the correct formula often depends on geometry, symmetry, distance, medium and the definition of the angle used.

Curriculum basis: CBSE Class XII Physics 2026–27, Unit I: Electrostatics, Chapter 1: Electric Charges and Fields. The official syllabus includes electric charge, Coulomb's law, multiple charges and superposition, continuous charge distribution, electric field, electric dipole, torque, electric flux and Gauss's theorem with applications to an infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

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