Coupling of the electromagnetic and heat transfer phenomena in a non-transferred arc plasma torch is generally based on a current density profile and a temperature imposed on the cathode surface. However, it is not possible to observe the current density profile experimentally. To eliminate this boundary condition and be able to predict the arc dynamics in the plasma torch, the electrodes were included in the computational domain, the arc current was imposed on the rear surface of the cathode, and the electromagnetism and energy conservation equations for the fluid and the electrodes were coupled. The solution of this system of equations was implemented in a CFD computer code to model various plasma torch operating conditions. The model predictions for various arc currents were consistent and indicated that such a model could be applied with confidence to plasma torches of different geometries, such as cascaded-anode plasma torches.