Experimental results on steady magnetically balanced arcs in supersonic external flows are presented and analyzed, along with investigations elsewhere in subsonic flows, to determine the important similarity parameters. The studies indicate that the steady arc has a central core, impervious to the external flow, within which differential Lorentz forces generate a circulation analogous to that generated by gravity forces in nonuniformly heated gas in a horizontal tube. The conservation equations indicate that a “Lorentz convection parameter,” analogous to the Grashof number in free convection phenomena, is an important similarity parameter over a significant range of arc variables. A “characteristic velocity” for the core circulation is indicated. The similarity parameters that provide the interpolation between the properties of subsonic and supersonic balanced arcs indicate the approximations permissible for a first‐order solution to the internal circulation. It is inferred from the results that to a first approximation the thickness of the enthalpy boundary layer varies linearly with the reciprocal of the Reynolds number of the external flow.