Theoretically, MgB2 bulk samples have very low density of 2.64 g/cm3, compared to REBaCuO samples which are around 6.36 g/cm3, and NdFeB permanent magnets at around 7.60 g/cm3. Practically, this ratio higher than 2-3 is maintained. From the applications point of view, this advantage must be taken into consideration and, the generation of strong magnetic flux densities using MgB2 should be investigated. In this contribution, we have studied the magnetic properties of samples with 20 mm and 30 mm in diameter and a height of 9.7 mm. These samples were processed by the fast spark plasma sintering machine that is able to produce dense and high quality MgB2 samples. Experiments were carried out both on small pieces of the samples using a SQUID-VSM and on big samples performing trapped field measurements in a Field Cooling process. At temperatures between 10 K to 30 K, the results show a strong dependence of the magnetic behavior of the big samples to the applied magnetic field sweep rate, while nothing particular appeared on the small samples. As the magnetic flux density produced by the MgB2 bulks is directly linked to the potential of the applications, we also report the field produced on the surface of one single MgB2 sample of 20 mm diameter, the field produced inside two MgB2 samples of 20 mm in diameter, and finally, the field produced on the surface of one single 30 mm MgB2 sample at various temperatures. A generation of magnetic flux density up to 4.8 T @ 10 K and 3.9 T @ 20 K inside a set of 2 MgB2 samples of 20 mm was observed. The dependence of the flux jumps on the magnetic field sweep rate observed in big samples will be also investigated in detail.