We present a 3D numerical model capable of simulating hydrogen electric arc. The
numerical model couples the electromagnetic field with hydrogen plasma arc dynamics (flow
and heat transfer). Electric arc operates under the conditions of atmospheric pressure using direct
current (DC) in the presence of external magnetic field. It is found that arc instabilities emerge
spontaneously near the cathode before propagating downwards along the arc jet. Also,
spontaneous splitting into several arcs is observed before merging again into one arc. The
horizontal magnetic field induces arc skewing and directional flow perpendicular to the applied
magnetic field. However, the axial magnetic field induces a rotational flow and arc swirling.