Class 12 Physics Notes: Electric Charges and Fields (Chapter 1)
Master Chapter 1 of Class 12 Physics. Understand Electric Charge, Coulomb's Law, Electric Field, Electric Dipole, and Gauss's Law with key formulas and exam PYQs.
1. Introduction to Electrostatics
Look around you. Every piece of plastic you've ever rubbed on your hair, every lightning bolt you've ever seen, and every capacitor inside your smartphone — all operate on one invisible principle: the force between electric charges.
Electrostatics is the study of electric charges at rest — the forces they exert, the fields they create, and the energy they store. It is the first and most important chapter in Class 12 Physics, laying the foundation for Current Electricity, Magnetism, and Electromagnetic Waves.
2. Electric Charge
Definition: An intrinsic property of certain subatomic particles that causes them to experience a force when near other charged particles. Two types: positive (protons) and negative (electrons).
SI Unit: Coulomb (C). Charge of one electron = −1.6 × 10⁻¹⁹ C.
- Quantization: Charge always exists in discrete multiples of e. Formula: q = ±ne, where e = 1.6 × 10⁻¹⁹ C. You cannot have a fraction of an electron's charge.
- Additivity: Total charge of a system is the algebraic (signed) sum of all individual charges.
- Conservation: In an isolated system, total charge is always conserved — it cannot be created or destroyed, only transferred.
3. Coulomb's Law
The fundamental law governing electrostatic force — the electric equivalent of Newton's Law of Gravitation.
Statement: The electrostatic force between two stationary point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Formula: Coulomb's Law
F = k |q₁ q₂| / r²
- k = 1/(4πε₀) ≈ 9 × 10⁹ N·m²/C² (in vacuum/air)
- q₁, q₂ = magnitudes of charges (C)
- r = distance between them (m)
In a medium with relative permittivity εᵣ: F_medium = F_vacuum / εᵣ.
4. Electric Field (E)
A charge creates a field around itself — a region where any other charge experiences a force.
Definition: The electric field at a point is the force per unit positive test charge at that point.
E = F / q₀ = kq / r²
5. Electric Field Lines
These properties are a guaranteed 2-mark question in board exams:
- Originate from positive charges, terminate at negative charges.
- Never cross or intersect — if they did, the field would have two directions at one point, which is impossible.
- The tangent at any point gives the direction of E at that point.
- More densely packed lines = stronger field.
- Always perpendicular to the surface of a conductor.
6. Electric Dipole
A system of two equal and opposite charges (+q and −q) separated by a small distance 2a. Classic example: a water molecule (H₂O).
- Dipole Moment (p): p = q × 2a. Points from negative to positive charge. Unit: C·m.
- Field on Axial Line: E = 2kp / r³ (for r >> a)
- Field on Equatorial Line: E = kp / r³ (for r >> a). Half the axial field, opposite in direction.
7. Gauss's Law — The Star Topic
Statement: The total electric flux (Φ) through any closed surface equals the total enclosed charge divided by ε₀.
Φ = q_enclosed / ε₀
Derivation: Field due to an Infinite Line Charge
Choose a cylindrical Gaussian surface of radius r and length l coaxial with the line charge (linear charge density λ C/m).
Flux through flat ends = 0 (E is parallel to end faces).
Flux through curved surface = E × 2πrl.
Charge enclosed = λl. Applying Gauss's Law: E × 2πrl = λl / ε₀
E = λ / (2πε₀r)
⚠️ Watch Out! — Medium Matters
k = 9 × 10⁹ applies only in vacuum or air. In any other medium with εᵣ, force reduces by a factor of εᵣ.
F_medium = F_vacuum / εᵣ. Always verify the medium before using k = 9 × 10⁹.
Summary: Formula Sheet
| Concept | Formula / Key Value |
|---|---|
| Charge Quantization | q = ±ne, e = 1.6 × 10⁻¹⁹ C |
| Coulomb's Law | F = k|q₁q₂| / r² |
| Coulomb's Constant (k) | 9 × 10⁹ N·m²/C² |
| Electric Field | E = F/q₀ = kq/r² |
| Dipole Moment | p = q × 2a (C·m) |
| Axial Field (Dipole) | E = 2kp / r³ |
| Equatorial Field (Dipole) | E = kp / r³ |
| Gauss's Law | Φ = q_enclosed / ε₀ |
| Electric Flux | Φ = E × A × cosθ |
Practice Questions (PYQs)
- Two point charges of +5 μC and −5 μC are placed 20 cm apart in vacuum. What is the electric field at the midpoint of the line joining the two charges?
- Using Gauss's Law, derive the expression for the electric field due to a uniformly charged spherical shell at a point (i) inside and (ii) outside the shell.
- Why can two electric field lines never cross each other? What would it physically mean if they did?
- An electric dipole consists of charges +2 μC and −2 μC separated by 1 cm. Calculate the dipole moment. Find the electric field at a point on the axial line 10 cm from the centre.
- State and explain the principle of superposition of electric forces. How does it help in calculating the net force on a charge due to multiple other charges?