Plasma blob dynamics on the high-field side in the proximity of a magnetic field null (X point) is investigated in TORPEX. A significant acceleration of the blobs towards the X point is observed. Close to the X point the blobs break apart. The E x B drifts associated with the blobs are measured, isolating the background drift component from the fluctuating contribution of the blob internal potential dipole. The time evolution of the latter is consistent with the fast blob dynamics. An analytical model based on charge conservation is derived for the potential dipole, including ion polarization, diamagnetic, and parallel currents. In the vicinity of the X point, a crucial role in determining the blob motion is played by the decrease of the poloidal magnetic field intensity. This variation increases the connection length that short circuits the potential dipole of the blob. Good quantitative agreement is found between the model and the experimental data in the initial accelerating phase of the blob dynamics.