Gauss's Law for Electricity
Maxwell's first equation stating that the net electric flux through any closed Gaussian surface equals the total enclosed charge divided by vacuum permittivity.
Governing formula
Φ_E = ∮ E · dA = Q_enclosed / ε₀, ∇ · E = ρ / ε₀
SI unit
N·m²/C (or V·m)
In depth
Gauss's law provides a powerful method to calculate electric fields for highly symmetric charge distributions (spherical, cylindrical, or planar). It shows that electric charges are the fundamental sources and sinks of electric fields.
Examples in the real world
Proving that the electric field inside a hollow spherical conductor carrying uniform surface charge is identically zero.