During the smelting process, the sintering quality of self-baked electrodes determines whether the arc furnace can operate normally. Taking the Panzhihua Steel Titanium Slag Three-Phase Arc Furnace as a prototype, this paper establishes a multi-physics field model of the coupled electromagnetic field and temperature field, and develops a quick calculation method for electromagnetic field and temperature field to accelerate computation. A comparative analysis of current density, Joule heat, and temperature distributions during the baking process of solid/hollow self-baked electrodes is conducted. The results show that both solid and hollow electrodes exhibit a "low at the center, high at the edge" current density distribution, namely the skin effect, with the skin effect of hollow electrodes weaker than that of solid electrodes, resulting in a more uniform current distribution. Besides, the baking regions of solid and hollow electrodes are located within the contact area of the conductive components, indicating that the self-baked electrodes have enough strength to meet the baking requirements. Meanwhile, the time to reach baking equilibrium for solid and hollow electrodes is about 13.4 hours and 12.8 hours, respectively, with the baking time of hollow electrodes being 4.3% shorter.