Can a DC motor be made with one magnet?

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In a DC motor as I understand it, a current is passed through a coil of wire within a magnetic field. The magnetic field exerts a force on the current perpendicular to the direction of the current. This force causes the coil to spin. Is the coil is between the north and south poles of 2 magnets. Can the motor work if there is only one magnet? single magnet still produces a magnetic field. Would the field produced by one magnet be too weak?
 

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Janus
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A DC motor works by alternating the attraction and repulsion of the Electromagnet created by the coil.
Here's an image showing the motor at one point of its rotation.
motor1.png

The two arcs are the commutator and are wired to the coil of the armature. The small rectangles are the brushes an are wired to the DC source (not shown)
Here, the current through the brushes and commutator, energize the coil to produce the North and South Poles shown. these are attracted to the respective South and North Poles of the two magnets shown, rotating the armature counter-clockwise.
Eventually the poles align but then the brushes are at the gaps of the commutator, the coil shuts off, and momentum continues the rotation of the armature past the alignment.
When the brushes make contact again, the polarity of the coil is reversed like this:
motor2.png

Now the coil is repulsed by the magnet pole it is near and attracted to the opposite magnet. Once the coil rotates to line up with those poles, the brushes hit the gap again, reverse coil polarity...

You could do this with just one magnet, but then you would be wasting the other pole of the coil and reducing the torque of the motor.
 

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