Electrostatics – Stage 2 (Page 3)

Electric Flux & Gauss’s Law

1️⃣ What is Electric Flux?

Electric flux tells us how much electric field passes through a surface.

Φ = E · A · cosθ

  • θ = angle between E and area vector
  • Flux is scalar

⚠️ IIT Trap: Flux depends on orientation, not on shape.

2️⃣ Area Vector – Small but Critical

  • Magnitude = area
  • Direction = perpendicular outward (closed surface)

For curved surfaces → take small area elements dA.

3️⃣ Special Flux Cases (Must Memorize)

Situation Flux
E ⟂ surface Φ = EA
E ∥ surface Φ = 0
Closed surface, no charge inside Φ = 0

4️⃣ Gauss’s Law (THE GAME CHANGER)

∮ E · dA = Qenclosed / ε₀

Gauss law links:

  • Electric field
  • Charge enclosed
  • Symmetry

This single law solves many otherwise impossible integrations.

5️⃣ When Can We Apply Gauss’s Law Directly?

Only when symmetry exists:

  • Spherical symmetry
  • Cylindrical symmetry
  • Planar symmetry

❌ No symmetry → Gauss law still true, but NOT useful.

6️⃣ Standard Gaussian Surfaces (IIT Favorites)

Charge Distribution Gaussian Surface
Point charge Sphere
Infinite line charge Cylinder
Infinite plane sheet Pill box

7️⃣ Example: Field due to Infinite Line Charge

Choose a cylindrical Gaussian surface:

  • E constant on curved surface
  • Flux through flat ends = 0

E(2πrl) = λl / ε₀

E = λ / (2πε₀r)

8️⃣ Conceptual IIT Question

Q: Does charge outside Gaussian surface contribute to flux?

Answer: NO. Only enclosed charge matters.

9️⃣ IIT Thinking Shortcut

Symmetry → Choose Gaussian surface → Write Gauss law → Solve in 3 lines.

What’s Next?

👉 Stage 2 – Page 4: Electric Field due to:

  • Infinite plane sheet
  • Charged spherical shell
  • Solid sphere

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