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I understand the basic idea of how a DC motor works. The current flowing through the coil on the rotor produces a magnetic field; this induced magnetic field then aligns with the permanent magnet's magnetic field. The polarity of the induced magnetic field then flips due to commutator rings and brushes to maintain the rotation of the rotor. I also understand that the current and the induced magnetic field of the coil results in a force or so-called thrust of motion (Flemings left/right-hand rule. I am unclear of the difference and when to use which).

However, I want to know why the motor requires a permanent magnet in which the induced magnetic field has to align itself. Why doesn't the thrust of motion due to the flowing current in the coil rotate the rotor? There are no permanent magnets in a railgun. The current flowing through the rails and projectile induces a magnetic field, and the thrust of motion resulting from the current and induced magnetic field accelerates the projectile. If the thrust of motion is sufficient to accelerate a projectile, wouldn't it also be adequate to rotate the rotor of a DC motor. Am I even understanding these physic concepts, or am I completely off track? Any explanation would be greatly appreciated.

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First, a DC motor can be made without permanent magnets. The permanent magnets on the rotor can be replaced with electromagnets. Then you have both electromagnets on the stator and the rotor.

Second, a railgun's operation is not analogous to a DC motor. It is, however, analogous to an induction motor which also doesn't have magnets, just without the induction part. An induction motor induces a current on the rotor whereas a a railgun directly passes a current through the projectile.

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