A "normal" motor the magnetic fields
(plural, produced by either physical- or electro-magnets)
are arranged so that they point at
right angles to the axis of rotation.
In a homopolar motor, the magnetic field (singular) points along the axis of rotation.
A battery, a magnet, and a piece of wire is all you need to make these motors.
Until I have my own videos, enjoy these from youtube.
Normally, the centrifugal force tends to cause the rotating wire to fly away from the
magnet.
In this design, the wire near the top of the battery touches the shell
on the opposite side of the electrical contact.
If you drive the magnet, then you will create a homopolar generator
which will produce DC current. As with the homopolar motor, the physics
explaining how it works is a bit controversial.
Basically, the phenomenon can not be explained using classical physics.
In
The Unipolar Generator: A Demonstration of Special Relativity,
two professors at the University of Maryland explain how electrons traveling
at different speeds in a constant magnetic field will undergo length contraction
and produce charge separation - also known as a voltage.
That is an interesting paper, but I still think the jury is out.
When the conductor plate is made to rotate while the magnet is stationary a voltage is generated. And when the magnet and the conductor are both rotated together the voltage is generated. But if the magnet is made to rotate while the conductor is stationary the voltage is not generated.
...
The explanation of this device is perhaps problematic. Many people believe that because there is no change in flux in the wire loop this cannot be an electromagnetic induction effect; the only explanation lies in special relativity. Other theoreticians disagree.