This particular homopolar motor design is ridiculously simple: a pair of neodymium magnets are stuck (by magnetic force only) to the bottom of an AA battery. A wire loop is balanced on the top of the battery, bent so that it touches the magnets on the bottom. When the connection is made, the wire will start to spin immediately, and will in general start spinning so fast that it will flip itself off of its perch. More sophisticated and stable designs exist, but this one is quick and showy.
So how does the homopolar motor work, and the “magneto-electric” train shown in the video? Both of them depend on the relationship between moving electric charges and magnetism, albeit in somewhat different ways.
Our story begins at the birth of what we now call “electromagnetism,” the beginning of a theory of nature that considers electricity and magnetism to be inextricably linked. It began in 1820, when the Danish physicist Hans Christian Oersted demonstrated that a magnetic compass needle can be deflected by an electric current, proving that moving electrical charges produce a magnetic field. Before this stunning experiment, it was generally assumed that electricity and magnetism were two completely separate physical phenomena.
What Oersted discovered, in essence, is that electricity flowing through a long straight wire creates a circulating magnetic field around it, as illustrated below.