The magnetic field of the earth is well known, with a North Pole and a South Pole directing compasses. Magnets also produce magnetic fields and also have poles. The value of a magnetic field is measured in teslas or in gauss, a tesla corresponding to ten thousand gauss. In Paris for instance, the earth’s magnetic field is equal to about half a gauss, less than a ten millionth tesla. On the surface of a NdFeB magnet (made from an alloy of neodymium, iron and boron) such as the ones used in the levitation videos, the magnetic field is equal to 1 tesla. But when you move away from the magnet, the magnetic field strongly decreases and is only equal to a hundredth tesla a few centimetres away from the magnet. The bigger the magnet, the slower the magnetic field decreases when moving away from the magnet.
The magnetism of the magnet comes from its electrons. An electron carries a very small quantum magnet called “spin”. If the electron spins in a material line up parallel to each other, the effect of all these small magnets add up to create an actual magnet. Some materials are not magnets but they cling to magnets, such as steel or iron. These materials are “magnetic”. This phenomenon happens because inside these materials, there are also parallel spins like in an actual magnet, but they are divided in domains. Since these domains are not parallel, the total magnetization is equal to zero. However, when you bring a magnet close to this magnetic material, all the domains become parallel to one another and parallel to the magnet, and the material also becomes a magnet.
In non-magnetic materials, such as noble metals for instance, or the human body, there is nothing of the sort: they do not become magnets when a magnet is brought close to them, neither do they cling to the magnet. Superconductors are not magnets and are generally not magnetic, except in some very particular cases that physicists are still working on.
In order to produce a magnetic field, you can also use inductor coil made of a metal wire in which you apply an electric current. This current will induce a magnetic field perpendicular to the coil. Superconductors can be used to make such coils, hence producing magnetic fields even higher than the best magnets. This is how MRI coils work in hospitals, with a magnetic field of about 1 tesla. In laboratories, it is now possible to create magnetic fields up to a couple dozens teslas.
