Acceptable behavior of electrical arc discharges inside high-power arc heaters usually requires the introduction of externally applied magnetic fields near the arc terminations. The strength and spatial distribution of these fields are discussed for a typical configuration. The effects of the Lorentz force produced by these fields on the arc discharge near the electrodes are evaluated in terms of azimuthal, axial, and radial components of the force. In general, there are only two possible states of the Lorentz force interaction with the arc, one of which enhances the gas swirl and the arc attachment, the other opposes the gas swirl and the arc attachment. Simple rules are given for ensuring the proper polarity of the magnetic field to obtain the desired result. An analysis of the proper scaling of the magnetic field strength in conjunction with geometric scaling of the arc heater shows that the magnetic field strength is only weakly dependent on scale.