Abstract: The continuous scrap electric arc furnace adopts a long arc operation for a longer arc length and a larger discharge power. Although the long arc differs from the traditional welding short arc, few reports on long arc simulation research in the field of the electric arc furnace are available. As the main energy source in the electric arc furnace, the long arc is very important for the melting of scrap and heating of molten steel. Due to the complicated physical phenomena in the electric arc furnace, it is difficult to accurately obtain the distribution of various physical fields in the furnace. Therefore, numerical simulation is a frequently used method for studying the arc plasma in the electric arc furnace. In this paper, the magnetohydrodynamic method of the magnetic vector potential was used to establish the numerical model of an arc. Based on this numerical model, the electromagnetic field, temperature field, and flow field were coupled and solved. The effects of current and arc length on the temperature distribution, velocity distribution, arc force, and shear stress of the arc in the electric arc furnace were studied. The results show that the arc plasma in the electric arc furnace is distributed in a long bell shape, and the arc column is slender. As the current increases, the effective arc action range increases, and the arc pressure and shear stress on the anode surface increase. As the arc length increases, the effective arc action range decreases, and the arc pressure and shear stress on the anode surface decrease. The short arc operation has a strong effect on the molten pool, and the long arc operation is relatively stable. A reasonable control of the current and arc length effectively improves the thermal efficiency of the arc.