Electrostatics – Stage 3
Electric Charges & Fields – Page 5
1. Electric Flux – Conceptual Meaning
Electric flux measures how much electric field passes through a surface.
Definition:
Φ = ∮ E · dA
- Vector dot product matters
- Angle between E and area is crucial
2. Flux Through Flat Surface (JEE Favorite)
For uniform field and flat surface:
Φ = EA cosθ
- θ = angle between E and area vector
- Maximum flux when θ = 0°
- Zero flux when θ = 90°
3. Closed Surface – The Big Idea
For a closed surface, flux depends only on enclosed charge.
Key Insight:
Outside charges do NOT affect net flux.
4. Gauss’s Law – Master Formula
∮ E · dA = Qenclosed / ε₀
- True for any closed surface
- Independent of shape
5. JEE Trap – Shape Confusion
Students wrongly believe flux depends on shape.
Trap:
Sphere, cube, cylinder → same flux if same enclosed charge.
6. Charge Inside Surface – Off-Centre Case
Even if charge is not at center:
- Electric field is asymmetric
- Flux remains same
JEE Insight:
Flux depends on charge, not field distribution.
7. Multiple Charges Inside & Outside
- Add only enclosed charges
- Ignore external charges
Φ = (q₁ + q₂ + …) / ε₀
8. Gaussian Surface – When Gauss Law is Useful
| Charge Distribution | Gauss Law Useful? |
|---|---|
| Point charge | Yes |
| Infinite line charge | Yes |
| Infinite plane sheet | Yes |
| Irregular shape | No |
9. PYQ Thinking Method
- Identify symmetry first
- Select Gaussian surface wisely
- Use Gauss law only if E is constant on surface
Stage 3 – Page 5 Completed ✅
Next → Stage 3 – Page 6 (Gauss Law Applications: Line, Sheet & Sphere)
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