⚡ Electrostatics – Electric Charges & Fields
Page 8: Electric Flux, Solid Angle & JEE Advanced Conceptual Traps
1. What is Electric Flux?
Electric flux measures the number of electric field lines passing through a surface.
Φ = ∮ E · dA = EA cosθ
- Scalar quantity
- Depends on angle between E and area vector
2. Area Vector Concept (Very Important)
- Magnitude = Area of surface
- Direction = Normal to surface
- For closed surface → outward normal
⚠ Many students confuse field direction with area vector direction.
3. Special Cases of Electric Flux
| Situation | Flux |
|---|---|
| E ⟂ Surface | Φ = EA |
| E ∥ Surface | Φ = 0 |
| Closed Surface | Φ = qenclosed/ϵ₀ |
4. Electric Flux through Closed Surfaces
By Gauss’s law:
Φtotal = qinside / ϵ₀
- Shape does NOT matter
- Only enclosed charge matters
- Outside charges contribute ZERO net flux
5. Solid Angle Concept (Advanced Level)
Solid angle (Ω) represents the 3D angular spread.
Ω = A / r²
Electric flux due to a point charge:
Φ = (q / 4πϵ₀) · Ω
6. Flux Due to Point Charge & Partial Surface
If a charge lies inside a closed surface:
Φ = q / ϵ₀
If charge is outside:
Φ = 0
This holds true even for irregular surfaces.
7. JEE Advanced Trap Questions
- Flux depends on charge enclosed, not distance
- Field may be zero but flux non-zero
- Flux can be negative (if θ > 90°)
8. Numerical Example (Conceptual)
Question:
A charge q is placed at the center of a cube. What is flux through one face?
Solution:
Total flux = q / ϵ₀
By symmetry, flux through one face:
Φ = q / (6ϵ₀)
9. Flux Through Open Surfaces
- Depends on geometry
- Use solid angle method
- Common in JEE Advanced
10. Exam Tips & Shortcuts
- Always check if surface is closed
- Ignore outside charges for closed surface
- Use symmetry to divide flux
- Remember: Flux ≠ Field
🎯 Page 8 Summary
- Electric flux is scalar
- Gauss’s law simplifies closed surface problems
- Solid angle is key for partial surfaces
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