3D Electric Flux and Gauss's Law Simulation
Electric field at left face (x = a):
0 N/C
Electric field at right face (x = 2a):
0 N/C
Theory Explanation
Electric Flux Concept
Electric flux (Φ) is a measure of the electric field passing through a given surface. It's calculated as:
Φ = ∫ E · dA = ∫ E dA cosθ
Where:
- E is the electric field vector
- dA is the differential area element
- θ is the angle between E and the surface normal
Gauss's Law
Gauss's Law relates the electric flux through a closed surface to the charge enclosed:
Φ = ∮ E · dA = Qenc/ε0
Where:
- Qenc is the total charge enclosed
- ε0 is the electric constant (8.85×10-12 C²/N·m²)
This Simulation Demonstrates
1. A non-uniform electric field E = α√x î where α = 800 N/C·m½
2. Flux calculation through a cube (side length a = 0.1m):
Φleft = -E(a)·a² = -αa5/2
Φright = E(2a)·a² = α(2a)½a²
Φnet = a²(E(2a) - E(a)) = αa5/2(√2 - 1)
Φright = E(2a)·a² = α(2a)½a²
Φnet = a²(E(2a) - E(a)) = αa5/2(√2 - 1)
3. The net flux (1.05 N·m²/C) corresponds to enclosed charge:
q = ε0Φ ≈ 9.27×10-12 C
