The cascaded-anode plasma torch makes it possible to get a longer and more stable plasma jet with higher specific enthalpy than conventional plasma torches. It is now used widely, but there are still few models of the cascaded-anode plasma torch. This study developed a 3-D time-dependent model that couples the gas phase and electrodes by encompassing the electromagnetic and heat equations both in the electrodes and gas phase. The model was applied to a commercial plasma spray gun equipped with a single cathode, single cylindrical anode and an inter-electrode insert to fix the average arc length. This paper examines the effect of the boundary conditions for the magnetic vector potential and electric current density on the electromagnetic, velocity and temperature fields of the plasma jet. The model predictions showed that, for such plasma torches where the arc is close to walls, the Biot and Savart formalism is required at the domain boundaries for the magnetic vector potential. They also showed that similar plasma fields could be obtained by imposing an electric current density profile at the cathode tip or by including the electrodes in the computational domain. However, this profile has to be chosen according to the specific design of the cathode, which is not obvious when the cathode has a design different from that of conventional plasma torches with sharp conical tip or rounded tip.