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A 3-D transient model has been developed to investigate plasma current deformation driven by internal and external magnetic fields and their influences on arc stability in a circuit breaker. The 3-D distribution of electric current density is obtained by solving the current continuity equation along with the generalized Ohm's law in the presence of an external magnetic field, while a magnetic field induced by a current flowing through an arc column is calculated by a magnetic-vector-potential equation. The applied external field imposes a rotational electromagnetic force to the arc and influences plasma current deformation which is discussed in this paper. In SF6 circuit breakers, when gas interacts with the arc column, fundamental equations such as Ampere's law, Ohm's law, turbulence model, transport equations of mass, momentum, and energy of plasma flow have to be coupled for analyzing the phenomenon. The coupled interactions between arc and plasma flow are described in the framework of magnetohydrodynamic equations in conjunction with a K - ε turbulence model. Simulations have been focused on sausage and kink instabilities in plasma (these phenomena are related to Bennett relation and electromagnetic fields and define plasma deformations). The 3-D simulation reveals relations between plasma current deformation and instability phenomena, which affect arc stability during operation. Plasma current deformation is the consequence of coupling between electromagnetic forces (resulting from internal and external magnetic fields) and plasma flow that are described in simulations.