Gauss's Law
Definition
A shortcut for electric fields: the total electric flux through any closed surface equals the charge trapped inside divided by ε₀.
Technical definition
∮E·dA = Q_enc/ε₀. One of Maxwell's equations; most powerful for symmetric charge distributions such as spheres, lines, and planes.
Example
Outside a charged metal sphere, Gauss's law gives E = kQ/r² immediately — the sphere behaves as if all its charge sat at the center.
Common confusion
Gauss's law is always true but not always useful. For lumpy charge distributions the integral won't simplify — the law still holds, it just doesn't hand you E directly.