White dwarf atmospheres are subjected to gravitational potentials around 10 ^ { 5 } 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 white dwarf 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 HST/STIS spectrum of the white dwarf G191-B2B . The method yields a sensitive upper limit on its magnetic field of B < 2300 Gauss at the 3 \sigma 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 .