This problem has been bugging me for a while, and I really could use a little help understanding the situation. If I can be allowed to think of a permanent magnet DC motor as a magnetic dipole sitting within a constant magnetic field, then it seems to me that the following should occur. If power is applied at the terminals of the motor armature, then the the magnetic dipole should rotate at most 90 degrees before the torque goes to 0. This is because, as I see it, the flux linkage between the dipole and the field is related to the cross product between them. Therefore, simply swapping the polarity at the terminals of the armature would have no effect, as it will still be perpendicular to the field. Now, if we had 4 poles, this problem could be solved by commutating every 90 degrees.

Now, despite the logic applied here, I constantly see examples showing two bar magnets, where one is allowed to rotate 180 degrees before the torque goes to 0. But can the DC motor really be represented this way? In this example it is true that the flux of one magnetic will pass through the other and cause them to allign, but since the rotating magnetic is not sitting between two poles then it doesn't seem to represent what is going on.

Sorry about the long winded analysis, but I desperately want to understand where I am going wrong here. Thanks for any help!