ABSTRACT White dwarf (WD) atmospheres are subjected to gravitational potentials around 105 times larger than occur on Earth. They provide a unique environment in which to search for any possible variation in fundamental physics in the presence of strong gravitational fields. However, a sufficiently strong magnetic field will alter absorption line profiles and introduce additional uncertainties in measurements of the fine structure constant. Estimating the magnetic field strength is thus essential in this context. Here, we model the absorption profiles of a large number of atomic transitions in the WD photosphere, including first-order Zeeman effects in the line profiles, varying the magnetic field as a free parameter. We apply the method to a high signal-to-noise, high-resolution, far-ultraviolet Hubble Space Telescope/Space Telescope Imaging Spectrograph spectrum of the WD G191−B2B. The method yields a sensitive upper limit on its magnetic field of B < 2300 G at the 3σ level. Using this upper limit, we find that the potential impact of quadratic Zeeman shifts on measurements of the fine structure constant in G191−B2B is 4 orders of magnitude below laboratory wavelength uncertainties.