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Superconductors have revolutionized magnet technology, surpassing the limitations of traditional coils and permanent magnets. This work experimentally investigates the field-trapping ability of a MgB₂ disc at various temperatures and proposes new hybrid (MgB₂-soft iron) configurations using a numerical approach based on the vector potential (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>A</mi><mo>→</mo></mover></semantics></math></inline-formula>) formulation. The experimental characterization consists in measurements of trapped magnetic flux density carried out using cryogenic Hall probes located at different radial positions over the MgB₂ sample, after a field cooling (FC) process and the subsequent removal of the applied field. Measurements were performed also as a function of the distance from the disc surface. The numerical modelling of the superconductor required the evaluation of the critical current density dependence on the magnetic flux density (J<i>_c</i>(B)) obtained through an iterative procedure whose output were successfully validated by the comparison between experimental and computed data. The numerical model, upgraded to also describe the in-field behavior of ARMCO soft iron, was then employed to predict the field-trapping ability of hybrid layouts of different shapes. The most promising results were achieved by assuming a hollow superconducting disc filled with a ferromagnetic (FM) cylinder. With such a geometry, optimizing the radius of the FM cylinder while the external dimensions of the superconducting disc are kept unchanged, an improvement of more than 30% is predicted with respect to the full superconducting disc, assuming a working temperature of 20 K.