Gauss’s Law (Electric Flux)

Formula

Description

Gauss’s law states that the total electric flux through any closed surface equals the charge enclosed divided by the permittivity of free space. It is one of Maxwell’s equations and lets the field of symmetric charge distributions be found without integration. The flux depends only on the enclosed charge, not on how it is arranged inside the surface.

Variables

• ΦE — Electric flux through the closed surface (V·m)
• Qenc — Net charge enclosed (C)
• ε₀ — Permittivity of free space 8.854×10⁻¹² F/m

Practical Notes

Gauss’s law gives the field of a charged sphere, line, or plane instantly by choosing a symmetric Gaussian surface. It is the electrostatic basis for shielding: no net enclosed charge means zero net flux.