Electric Flux Calculator
Calculate electric flux through a surface using Φ = E·A·cos(θ).
Also applies Gauss's law to find the enclosed charge from flux.
Electric Flux
Electric flux measures how much electric field passes through a surface:
Φ = E × A × cos(θ)
And Gauss’s law relates flux to enclosed charge:
Φ = Q_enclosed / ε₀
Where:
- Φ = Electric flux (N·m²/C or V·m)
- E = Electric field strength (N/C = V/m)
- A = Area of the surface (m²)
- θ = Angle between the electric field vector and the surface normal
- Q_enclosed = Total charge enclosed by the Gaussian surface (C)
- ε₀ = Permittivity of free space = 8.854 × 10⁻¹² C²/(N·m²)
Understanding the angle θ:
- θ = 0°: Field is perpendicular to the surface (maximum flux)
- θ = 90°: Field is parallel to the surface (zero flux — field “slides along” the surface)
- θ = 180°: Field is anti-parallel to surface normal (negative flux)
Gauss’s Law application: The total electric flux through any closed surface equals the enclosed charge divided by ε₀. This makes calculating electric fields from symmetric charge distributions very easy:
- Sphere of charge: flux = Q/ε₀ regardless of sphere size
- Infinite plane of charge: flux through box = σA/ε₀
Physical intuition: Think of electric flux like counting how many electric field lines pass through a surface. More field lines = stronger field or larger area = more flux.