⚡ Electrostatics – Electric Charges & Fields
Page 5: Electric Flux (Complete JEE Concept)
1. What is Electric Flux?
Electric flux represents the number of electric field lines passing through a given surface.
It measures how much electric field penetrates a surface.
Symbol: ΦE
2. Mathematical Definition of Electric Flux
For a uniform electric field and a flat surface:
Φ = E · A = EA cosθ
- E = electric field
- A = area vector (perpendicular to surface)
- θ = angle between E and area vector
JEE Tip: Area vector is always normal to the surface.
3. Special Cases of Electric Flux
- θ = 0° → Φ = EA (maximum flux)
- θ = 90° → Φ = 0 (no flux)
- θ = 180° → Φ = −EA (negative flux)
Negative flux means field lines enter the surface.
4. Flux Through a Curved Surface
For a curved surface, flux is calculated by dividing the surface into small area elements.
Φ = ∮ E · dA
This is a surface integral and is mainly used in Gauss’s Law.
5. Electric Flux Through Closed Surface
A closed surface encloses a volume completely.
Φ = ∮ E · dA
- Outward normal is taken as positive
- Used in Gauss’s theorem
6. Important Conceptual Results
- Flux depends on enclosed charge, not shape
- External charges do not affect net flux
- Field may be zero, flux can be non-zero
Frequently tested in JEE Advanced.
7. Electric Flux Due to a Point Charge
Consider a point charge q inside a closed surface.
Φ = q / ϵ₀
- Independent of surface shape
- Sphere, cube, cylinder → same flux
8. Flux Through Cube (JEE Favourite)
If a point charge q is placed at the center of a cube:
Flux through one face = q / (6ϵ₀)
Used repeatedly in JEE Main & Advanced.
9. Units and Dimensions
- SI unit: N·m²/C
- Dimensions: [M L³ T⁻³ A⁻¹]
10. Common Mistakes to Avoid
- Using wrong angle θ
- Confusing area vector direction
- Thinking flux depends on distance
- Ignoring sign of flux
🎯 Page 5 Summary
- Electric flux measures field flow
- Φ = EA cosθ
- Closed surface flux = q / ϵ₀
- Foundation for Gauss’s Law
No comments:
Post a Comment