Motor/generator solenoid armature

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Joseph M. Zias
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TL;DR
using a solenoid wound armature may in the limit not be a good design.
There are many examples of a 2 pole motor/generator having an armature wound in solenoid fashion, albeit with a steel core. In the limit as the solenoid becomes more perfectly made, long and tightly wound, it would seem not be a good design. An ideal solenoid has zero magnetic field outside and I believe very little field at the ends (correct me if I am wrong). The magnetic field is intense within the core. It would seem that the very good solenoid coil would have difficulty being turned by the permanent magnet of the motor if the field is closely confined. It may work as a generator coil but the current would seem to be a pulse.

What are your thoughts? What shape would make for a better coil?
 
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You need to link to a picture of the two pole motor armature so we know exactly what you mean by solenoid wound. The magnetic path is through the armature material, the two field poles and the casing. The coil will be wound around the armature material.

As a motor it will produce two pulses of torque for each turn.

As a generator, the brushes will rectify the generated current, which will produce two pulses of the same polarity current per turn of the shaft.

It will cost very little.
Joseph M. Zias said:
What shape would make for a better coil?
There are many more efficient and more expensive ways to build a DC motor.