Optically-induced magnetism has drawn considerable interest in the past years for its ability to speed up magnetic processes. For example, static magnetic fields have been demonstrated to be generated in non-magnetic plasmonic (gold) nanoparticles and nano-apertures. Using a simplified hydrodynamic model of the free electron gas of metal, we theoretically investigate the IFE and resulting optomagnetism in a thin gold film as well as in axis-symmetric plasmonic nanostructures under illumination with various focused light. The resulting static magnetic field is found to be maximum and dramatically confined at the corners and edges of the plasmonic structures, which reveals the ability of metallic discontinuities to concentrate and tailor static magnetic fields on the nanoscale. Plasmonics can thus generate and tune static magnetic fields on the nanoscale, potentially impacting small-scale magnetic tweezing and sensing as well as the generation of magneto-optical effects and spin-waves.