Stokes’ theorem, in its original form and Cartan’s generalization, is crucial for designing magnetic fields to confine plasma (ionized gas). The paper illustrates its use, in particular to address the question whether quasi-symmetric fields, those for which guiding-centre motion is integrable, can be made with little or no toroidal current.This article is part of the theme issue ‘Stokes at 200 (Part 1)’.