Electrostatics - Complete Student Theory

Electrostatics

📘 What is Electrostatics?

Electrostatics is the branch of physics that deals with electric charges at rest. It studies the forces, fields, and potentials that arise from stationary charges.

This is different from electrodynamics, which studies moving charges (electric current). In electrostatics, we assume that charges are not in motion.

⚡ Core Concepts in Electrostatics

1. Electric Charge

Charge is a basic property of matter. It can be positive (like protons) or negative (like electrons). Like charges repel, and unlike charges attract.

2. Conductors and Insulators

- Conductors allow electric charge to move freely (e.g. metals).
- Insulators do not allow charges to move freely (e.g. plastic, rubber).

3. Coulomb’s Law

This law gives the force between two point charges. The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

F = k × (q₁ × q₂) / r²

Where:

  • F = Electrostatic force (in Newtons)
  • q₁, q₂ = Charges (in Coulombs)
  • r = Distance between charges (in meters)
  • k = 9 × 10⁹ Nm²/C² (Coulomb's constant)

4. Electric Field (E)

The region around a charged object where it can exert force on other charges is called the electric field.

E = F / q = k × q / r²

Direction: Away from +ve charges and toward -ve charges.

5. Electric Potential (V)

Electric potential at a point is the amount of work done to bring a unit positive charge from infinity to that point.

V = k × q / r

It is a scalar quantity and is measured in volts (V).

6. Relationship Between E and V

The electric field is the negative gradient (rate of change) of electric potential.

E = -dV/dr

7. Gauss's Law

Gauss’s Law relates the electric field on a closed surface to the total charge enclosed inside the surface. It's useful for calculating fields with high symmetry.

∮E ⋅ dA = qenclosed / ε₀

Where ε₀ is the permittivity of free space = 8.85 × 10⁻¹² C²/N·m².

🧪 Daily Life Examples of Electrostatics

  • Lightning: Caused by electrostatic discharge between clouds and the ground.
  • Static on Clothes: Clothes sometimes stick together due to charges during drying.
  • Photocopiers: Use static charges to attract toner powder to paper.
  • Combing Hair: A charged comb can attract small paper pieces.
  • TV Screens: Old CRT screens attract dust due to static charges.
Example: When you walk on a carpet and touch a metal door handle, you feel a small shock. This is static electricity discharging from your body.

📌 Important Equations Summary

F = k × (q₁ × q₂) / r²   →   Coulomb’s Law
E = k × q / r²   →   Electric Field
V = k × q / r   →   Electric Potential
E = -dV/dr   →   Field from Potential
∮E ⋅ dA = q / ε₀   →   Gauss’s Law

✅ Summary for Students

  • Electrostatics deals with stationary charges and their effects.
  • Forces between charges are governed by Coulomb’s Law.
  • Electric fields and potentials describe the space around charges.
  • Gauss’s Law simplifies electric field calculations using symmetry.
  • Electrostatics is part of everyday life — from lightning to photocopiers.
🧠 Tip: Always remember, electrostatic force acts at a distance and obeys the inverse-square law!
electrostatics