The total electric flux out of any closed surface is proportional to the net charge enclosed by that surface.
All field lines from the enclosed charge must cross the surface — flux counts them.
Φ(E) = Q(enc) / ε₀
Φ(E)
electric flux through the closed surface (V·m)
Q(enc)
net charge enclosed (coulombs)
ε₀
permittivity of free space ≈ 8.85 × 10⁻¹² F/m
In plain English: Imagine charge as a sprinkler and field lines as water: count the lines crossing any bag you draw around it and you know how much charge is inside — the bag's shape doesn't matter.
Where you'll meet it: Derives the field inside coax cable and between capacitor plates, and explains shielding: inside a closed conductor the enclosed charge is zero, so a metal case blocks external fields (the Faraday cage).