In this second part of the study of electrochemical noise (EN) generated by hydrogen evolution on a vertical cylindrical AISI 4140 steel electrode under galvanostatic control in 0.5 M sulphuric acid, the potential fluctuations induced by the growth and detachment of hydrogen bubbles at the electrode surface were analysed. They could be related to fluctuations of various quantities: electrode active surface due to bubble screening effects, concentration of dissolved hydrogen in the electrolyte close to the electrode surface, and metal-hydrogen interactions (MHI) on or beneath the electrode surface. The existence of MHI and their influence on faradaic potential fluctuations could be revealed by comparing the noise features on steel and platinum. The influence on EN of the charging cathodic current density, the presence of dissolved oxygen in the solution, and the electrode rotation speed was investigated in the absence of stress applied to the electrode. In the third paper of this series, the effect of hydrogen embrittlement on potential fluctuations of stressed electrodes will be examined.