Low-tension circuit breakers generally rely on the extinction of the electric arc created when the current-carrying contacts separate. The dynamics of the arc has been studied for a number of years using numerical simulations of the coupled fluid dynamics/electromagnetic governing equations. One of the objectives of this thesis is to improve numerical simulation near the wall, where there is a thin boundary layer whose accurate numerical description requires fine meshes, and hence long computing times, unless special measures are taken. Different simulations, based on an existing code, have aided in the development of a two region model, with one region away from the wall and another representing the boundary layer. In the external zone, the full equations are used, but the boundary conditions at the wall are modified by the existence of the thin wall-layer. This external flow forms the outer boundary conditions for a boundary layer calculation. As part of own numerical studies, we have also compared results of simulations with those of experiments. The second topic of the thesis is the stability of an arc column. A basic arc state id perturbed and the growth or decay of the perturbations with time used to determine the stability or otherwise of that basic state. The basic state used was a simple, steady, axisymmetric arc of infinite length, but we found that, in general, to maintain such an arc steady, some means of extracting the heat generated by the arc was necessary, a requirement which was met by introducing a sink of mass at the axis. A study of such arcs, cooled by the influx from outside, showed a variety of families of different solutions, for a given pressure and electric filed strength. Having selected a particular basic state, the linearized equations were solved for the normal modes and their eigenvalues used to examine stability. Different types of unstable and stable modes were found, which were interpreted in terms of magnetic diffusion, acoustics and unstable couples modes.