Does the electric flux through a closed loop really count the charge inside it — exactly, whatever the loop's size or shape?
▶ Launch the interactive simulationFix a set of charges in the plane (2-D electrostatics: field E = q·r̂/r), trace the field lines, then tour a measuring loop across the scene and numerically integrate the flux Φ = ∮ E·n̂ dl around it, comparing Φ/2π to the charge the loop encloses.
Gauss's law: Φ/2π equals the enclosed charge EXACTLY — independent of the loop's radius, position, and shape (it jumps in integer steps as the loop swallows charges, and is 0 around the neutral whole) — the integral form of the inverse-distance field ∇·E = 2π·Σqᵢδ²(r−rᵢ)