A homopolar motor is of essentially the same construction as a homopolar generator, in general called a homopolar machine. Like most electro-mechanical machines it is reversible so that when electrical energy of a suitable kind is put into its terminals, mechanical energy can be obtained from its motion and vice versa.
Many people are confused by the fact that, unlike other kinds of electric motors, there is no force on the magnet in a homopolar machine. Instead, there are equal and opposite forces or torques on the two parts of the electrical circuit that carry the current, one of which must be able to slide or rotate (the rotor) while remaining in electrical contact with the other (the stator). This confusion has led to erroneous claims of free energy from homopolar machines called "N-machines".
Of course if the magnet is electrically conductive and happens to perform double duty as both the source of the magnetic field and as part of the electrical circuit, it will experience a torque due to its current-carrying function.
Other people are confused about homopolar machine operation because they do not realise that while special relativity says there is no such thing as absolute linear motion, it does recognize absolute rotation, and this is borne out by experiment. This is feature of Mach's Principle which relates inertia to the influence of the mass of distant objects in the universe.
When a magnet with a symmetrical field is rotated about its axis of symmetry (as it may or may not do in a homopolar machine), people often ask whether the field lines rotate with the magnet? The answer is that the question is meaningless, because field lines don't actually exist. They can be a useful visualization-aid in predicting the behaviour of some electro-mechanical machines, but they are very misleading in the case of homopolar machines. There are no field lines mentioned in special relativity or Maxwell's equations or the Lorentz force equation.
A magnetic field merely has a magnitude and direction at every point in space, and is only defined relative to an inertial (non-accelerating, non-rotating) frame of reference. No one has ever succeeded in making a device that can tell whether or not a symmetrical non-conducting magnet, hidden inside a black box, is rotating about its axis of symmetry.
A rotating conductive magnet is however detectable by the electric field produced when its free charges separate radially, due to the Lorentz force produced by (absolute) rotation of the conductor within its own magnetic field. The failure to appreciate this difference between conducting and non-conducting magnets is yet another source of confusion.
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"Homopolar motor".
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