The processor will activate a series of stator coils sequentially to drive the rotor in a given direction,and since there are no brushes, therefore, no gaps for electricity to jump, ergo --nothing TO arc!!
In an old DC motors, the switching was done mechanically by brushes and contactors. you would get a small arc each time the brush would slide from one contact to the other. In the brushless ones, the switching is done by transistors which are semiconductor switches. As long as the transistors are rated properly, the current flow will be extinguished through the silicon material of the transistor. This does not produce an arc. The transistor is like a variable resistors that can quickly change its resistance from a fraction of an ohms to mega ohms within nano seconds. The name transistor comes from TRANS-RESISTOR. In reality the process is more complex than a resistor but the effect is relatively similar.
That being said, if the transistor fails from overload, there is a risk of arcing. A brushless dc motor is not necessarely an explosion proof device.
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