The order parameter of a quantum-coherent many-body system can include a phase degree of freedom, which, in the presence of an electromagnetic field, depends on the choice of gauge. Because of the relationship between the phase gradient and the velocity, time-of-flight measurements reveal this gradient. Here, we describe such measurements of initially trapped Bose-Einstein condensates (BECs) subject to an artificial magnetic field. Vortices nucleated in the BEC for artificial field strengths above a critical value, which represented a structural phase transition. By comparing to superfluid-hydrodynamic and Gross-Pitaevskii calculations, we confirmed that the transition from the vortex-free state gives rise to a shear in the released BEC s spatial distribution, representing a macroscopic method to measure this transition, distinct from direct imaging of vortex entry. Shear is also affected by an artificial electric field accompanying the artificial magnetic field turn-off, which depends on the details of the physical mechanism creating the artificial fields, and implies a most natural choice of gauge. Measurements of this kind offer opportunities for studying phase in less-well-understood quantum gas systems.