A 2D axisymmetric two-phase model was developed to study the effect of an arc impingement on the liquid metal inside an electric arc furnace. In addition to the arc flow dynamics, the model covered the heat transfer and magneto hydrodynamics of the arc and the liquid metal. Through a parametric study, three different parameters were considered to predict the most important factors affecting the arc and overall behaviour of the process: the arc gap, the density of the gas, and the total electric current. Understanding the effect of these parameters can show the key factors altering the arc dynamics. The study showed that the total applied current was the most important parameter that influenced the impingement depth and mixing of the liquid metal. The depth of the impingement and strength of the mixing of the liquid bath were directly proportional to the current applied in the furnace. The initial arc gap distance was found to be crucial for sustaining a continuous and stable arc. The value of the gas density was very important for the velocity profile; however, it had no significant effect on the impingement depth. This showed that a constant density could be used instead of a varying gas density with temperature to increase the computational efficiency. The study assessed the effects of the aforementioned factors on the arc impingement depth, velocity magnitude, and arc stability. The conclusions acquired and challenges are also presented.