Class 12 Physics: Electrostatics – Complete Notes

Chapter 1: Electric Charges and Fields

1.1 What is Electrostatics?

Electrostatics is the branch of physics that deals with the study of electric charges at rest. It explores forces, fields, and potentials generated by stationary charges.

1.2 Electric Charge

• Fundamental Property of matter carried by particles like electrons and protons.

• Two types of charges:

  • Positive (e.g., protons)

  • Negative (e.g., electrons)

Properties of Electric Charge:

1. Additivity: Total charge is the algebraic sum of individual charges.

2. Conservation: Charge is neither created nor destroyed.

3. Quantization: Charge (q) is always an integral multiple of elementary charge (e), i.e.,
   q = ±ne, where n is an integer and e = 1.6 × 10⁻¹⁹ C

1.3 Methods of Charging

1. Friction: Rubbing two different materials transfers electrons.

2. Conduction: Direct contact allows charge flow.

3. Induction: Bringing a charged object near a neutral conductor causes redistribution of charges without contact.

1.4 Coulomb’s Law

The electrostatic force (F) between two point charges is:

• Directly proportional to the product of charges

• Inversely proportional to the square of the distance between them

Formula:
F = (1 / 4πε₀) × (q₁q₂ / r²)
Where:

• F = Force between charges

• q₁ and q₂ = Point charges

• r = Distance between them

• ε₀ = Permittivity of free space (8.85 × 10⁻¹² C²/N·m²)

Nature of Force:

• Attractive if charges are opposite

• Repulsive if charges are similar

1.5 Principle of Superposition

The total electrostatic force on a charge due to a number of other charges is the vector sum of all individual forces.

1.6 Electric Field (E)

The region around a charge in which it exerts a force on other charges.

E = F / q
Unit: N/C

Electric Field Due to a Point Charge:
E = (1 / 4πε₀) × (q / r²)

1.7 Electric Field Lines

• Imaginary lines representing the direction of electric field.

• Properties:

  • Start on positive, end on negative charges.

  • Never intersect.

  • Denser lines mean stronger field.

  • Always perpendicular to surface of conductor.

1.8 Electric Dipole

A pair of equal and opposite charges separated by a small distance.

Dipole Moment (p) = q × 2l
(Unit: C·m)

Electric Field Due to a Dipole:

• On Axial Line:
  E = (1 / 4πε₀) × (2p / r³)

• On Equatorial Line:
  E = (1 / 4πε₀) × (p / r³)
  
  

1.9 Torque on a Dipole in a Uniform Electric Field

Torque (τ) = p × E × sinθ
Where:

• p = Dipole moment

• E = Electric field

• θ = Angle between p and E
  
  

1.10 Electric Flux (Φ)

It represents the number of electric field lines passing through a surface.

Φ = E · A · cosθ
Unit: Nm²/C

1.11 Gauss’s Law

The total electric flux through a closed surface is equal to the charge enclosed divided by ε₀:

Φ = q_enclosed / ε₀

Applications of Gauss's Law:

1. Electric Field Due to an Infinite Line Charge:
   E = λ / (2πε₀r)

2. Electric Field Due to an Infinite Plane Sheet of Charge:
   E = σ / (2ε₀)

3. Electric Field Due to a Uniformly Charged Sphere:

   • Outside Sphere (r > R): E = (1 / 4πε₀) × (Q / r²)

   • On Surface (r = R): Same as above

   • Inside Sphere (r < R): E = (1 / 4πε₀) × (Qr / R³)

Chapter 2: Electrostatic Potential and Capacitance

2.1 Electrostatic Potential (V)

Work done in bringing a unit positive charge from infinity to a point in the field.

V = W / q
Unit: Volt (V) = Joule/Coulomb

Potential Due to a Point Charge:
V = (1 / 4πε₀) × (q / r)

2.2 Potential Difference

Work done to move a unit charge between two points.

V = V₁ – V₂

2.3 Relation Between Electric Field and Potential

E = - dV/dx
(Electric field is the negative gradient of potential)

2.4 Equipotential Surfaces

• Surfaces where electric potential is the same at every point.

• Electric field is perpendicular to these surfaces.

• No work is done when moving a charge along the surface.

2.5 Capacitance (C)

The ability of a conductor to store charge.

C = Q / V
Unit: Farad (F)

2.6 Capacitor

A device used to store charge and electrical energy.

Parallel Plate Capacitor:
C = ε₀A / d
Where:

• A = Area of plates

• d = Separation between plates

2.7 Factors Affecting Capacitance

1. Area of plates (directly proportional)

2. Distance between plates (inversely proportional)

3. Nature of dielectric material (via dielectric constant, K)

2.8 Combination of Capacitors

• In Series:
  1/C = 1/C₁ + 1/C₂ + ...

• In Parallel:
  C = C₁ + C₂ + ...

2.9 Energy Stored in a Capacitor

U = ½ CV² = ½ QV = Q² / (2C)

2.10 Dielectrics and Polarization

When a dielectric is placed in a capacitor:

• Increases capacitance:
  C = K × C₀
  (K = Dielectric constant)

• Reduces electric field inside

2.11 Van de Graaff Generator

A high-voltage generator that uses electrostatic principles to generate large potential differences.

Applications: Particle accelerators, nuclear physics experiments

Electrostatics is a foundational chapter that blends theory, mathematics, and logic. It lays the groundwork for future topics in electromagnetism, electric circuits, and more. A strong grasp on Electrostatics is crucial for board exams and entrance tests like NEET and JEE.

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