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Break the current in a direct current (DC) network is a challenging theme since the current does not exhibit a zero crossing point, making it difficult to interrupt. Regardless of the method, the physical effect of switching is the formation of an electric arc, causing high levels of temperature, strong magnetic fields, current of several tens of KA, added to mechanical stress and overpressure on the walls. Due to this reason, physical phenomena should be studied to determine a suitable design. This thesis starts by understanding the arc in alternating current (AC), then proceeds to DC. A theoretical description of the electric arc is outlined, based on plasma physics. The Magneto-Hydrodynamic (MHD) model is proposed, which allows modeling a plasma as an electric fluid, allowing coupling the equations of fluid mechanics and magnetic fields.