The flux of field lines is the unifying tool for the whole study of the electric field: instead of directly integrating the field over a surface, Gauss’s theorem allows us to count the lines crossing it. Starting from the lemma for open surfaces, we arrive at Gauss’s law for closed surfaces, which links the flux solely to the enclosed charge. When the geometry has a symmetry (spherical, planar, cylindrical), this theorem becomes an extremely fast calculation method for the electric field.