High superconducting bulks made of MgB2 present a very attractive low mass density with a potential strong magnetization that can be used to design compacter, lighter and more efficient electrical machines and levitation systems amongst other applications. However, the manufacturing processes of MgB2 samples still present some challenges that determine the ability of the sample to trap large magnetic fluxes. To identify those technical challenges and characterise the magnetic behaviour of our samples, we studied the trapped magnetic field properties of samples having diameters of 20 mm and 40 mm. These samples were processed by Spark Plasma Sintering which is a reliable method for producing bulk MgB2 of large sizes and in large quantities. For the sample of 40 mm diameter, Field Cooling experiments were carried out at temperatures ranging from 10 K to 30 K, both on a single pellet of 4 mm thick and on a stack of several pellets with the same diameter. With the help of modelling tools, we simulated the behaviour of the MgB2 samples in order to deduce their parameters such as their Jc(B) and their n-value. The magneto-thermal coupled problem was solved and, a parametric analysis was conducted to estimate the parameters that mostly influence the magnetic field produced by the MgB2 bulk. The obtained results show that the trapped magnetic field strongly depends on some of those parameters. Ultimately, they may give clues on the choice of dopants needed to improve MgB2 bulk.