Electrostatic
Electric Charges and Fields
Class XII Physics - Comprehensive Notes
1.1 Introduction to Electrostatics
Electrostatics is the branch of physics that studies forces, fields, and potentials arising from stationary electric charges.
Static Charges: Charges that are at rest (do not move or change with time).
Common Examples:
- Sparks when removing synthetic clothes (due to charge discharge)
- Lightning during thunderstorms (natural electric discharge)
- Electric shock when touching a car door or bus handle (charge transfer)
Cause: Charge accumulation occurs through friction between insulating surfaces. When insulating materials rub against each other, electrons transfer from one material to another, creating an imbalance of charges.
1.2 Electric Charge
Charge (q): Fundamental physical property of matter that causes it to experience electromagnetic force.
Unit: Coulomb (C)
Discovery: Thales of Miletus (600 BC) observed that amber rubbed with wool attracts light objects like straw and feathers.
Properties of Electric Charge:
- Two types:
- Positive (+) charge: e.g., glass rod rubbed with silk
- Negative (-) charge: e.g., plastic rod rubbed with fur
- Interaction: Like charges repel; unlike charges attract
- Conservation: Net charge in an isolated system is constant
- Quantisation: q = ne, where:
- n: Integer (positive or negative)
- e: Elementary charge (1.6 × 10⁻¹⁹ C)
Gold-Leaf Electroscope: Instrument that detects electric charge through the divergence of thin gold leaves when charged.
Principle: Charge distribution on conductors causes repulsion between similarly charged leaves.
1.3 Conductors and Insulators
Conductors: Materials that allow free movement of electric charge (e.g., metals, human body).
Charge distribution: Spreads uniformly on the surface.
Insulators: Materials that resist movement of electric charge (e.g., plastic, wood, glass).
Charge distribution: Localized at the point of contact or rubbing.
Semiconductors: Materials with conductivity between conductors and insulators (e.g., silicon, germanium).
Example: A plastic comb gets charged when rubbed through hair, but a metal spoon does not because the charge leaks through the body to the ground.
1.4 Basic Properties of Electric Charge
1. Additivity
Net charge Q = q₁ + q₂ + ... + qₙ (scalar sum)
2. Conservation
Net charge before and after any interaction remains constant.
3. Quantisation
q = ne (n is an integer)
For macroscopic bodies, quantisation is ignored because n is very large.
4. Units
- Coulomb (C): SI unit of charge
- 1 μC = 10⁻⁶ C
- 1 mC = 10⁻³ C
- e = 1.6 × 10⁻¹⁹ C (charge of proton/electron)
1.5 Coulomb's Law
The electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
F = 1⁄4πϵ₀ · |q₁q₂|⁄r²
- ϵ₀: Permittivity of free space (8.854 × 10⁻¹² C²N⁻¹m⁻²)
- r: Distance between charges (m)
- q₁, q₂: Magnitudes of charges (C)
- Direction: Along the line joining the charges
- Repulsive if q₁q₂ > 0
- Attractive if q₁q₂ < 0
Torsion Balance: Instrument used by Charles Coulomb to verify the inverse-square law of electrostatic force.
Key Formulas Summary
Coulomb's Law
F = 1⁄4πϵ₀ · |q₁q₂|⁄r²
q₁, q₂: Charges (C)
r: Distance (m)
ϵ₀: Permittivity constant
Electric Field (Point Charge)
E = 1⁄4πϵ₀ · Q⁄r²
Q: Source charge (C)
r: Distance from charge (m)
Dipole Moment
p = q × 2a
q: Charge magnitude (C)
2a: Separation (m)
Torque on Dipole
τ = pE sinθ
p: Dipole moment (C·m)
E: Field strength (N/C)
θ: Angle between p and E
Gauss's Law
∮E·dS = q⁄ϵ₀
q: Enclosed charge (C)
Field (Infinite Wire)
E = λ⁄2πϵ₀r
λ: Linear charge density (C/m)
r: Radial distance (m)