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This paper focuses on the numerical investigation of arc plasma behavior during the arc motion and splitting process in a low-voltage quenching chamber. The 3-D mathematical model of air arc plasma considering the ferromagnetic splitter plate is built based on the magnetic hydrodynamics theory. The effect of the plasma sheath region, which is not in a state of local thermal equilibrium, is considered by an approximate method. The energy flux equations are introduced to describe the energy balance of the arc-metal interface. The arc motion is described in detail by the distributions of the temperature field and gas flow field in the arc chamber. The arc voltage is also calculated. The phenomenon that the arc root moving of the anode is faster than that of the cathode is observed in the calculation. Moreover, the arc-root formation on the splitter plate is analyzed according to the simulation results. Except for the numerical investigation, the experiment work is also carried out to support the simulation work.