Magnetic levitation is really fun to experiment with, and can make a great science fair project. However, it's hard to get dramatic results--the problem goes back to Earnshaw's theorem from 1842. He proved mathematically that any electrical or magnetic levitation would require an extra axis of stabilization...a force from a different direction.
You can show this with ring magnets. Put them on a stick, and they do indeed float over each other. However, the stick is required, that's your extra axis of stabilization--remove it, and the magnets simply flip over and jump to each other, no longer floating. The phenomenon of diamagnetism provides a simple, inexpensive solution to this problem and gives fairly dramatic results.
Most people are familiar with ferromagnetic materials--iron, steel and permanent magnets. These materials are attracted by magnetic fields, and can keep their magnetism after exposure to the field. Diamagnetic materials include carbon-graphite, water, protein, DNA, wood, bismuth, silver, diamond and gold. When exposed to a magnetic field, these materials induce a weak magnetic field in the opposite direction. Superconductors are perfectly diamagnetic, but require liquid nitrogen to work--not something that most folks have a jug of in their fridge!
Diamagnetism is the key to this experiment, and provides the extra stabilizing force needed. We'll be using carbon-graphite and bismuth because they have the strongest diamagnetic effect.
Step 1: Materials needed
This entire project should cost you less than US$20. You may not be able to find all of them locally, but I've provided links and Google search suggestions for any that you might have to order off the internet.
carbon-graphite blocks, 1.5 inches square by 1/4 inch thick, quantity 2 -- carbon-graphite is commonly used in motor and alternator brushes. However, these are generally too small, and some samples are more diamagnetic than others. It's best to look for 'pyrolytic' carbon-graphite, or for samples that are known to be highly diamagnetic by the seller. They should cost under US$7 each.
small rare-earth magnet to levitate -- This magnet should be of neodymium-iron-boron (NdFeB) composition and of at least N40 grade. Cube or disc shapes work well. This magnet should be very small for best results--the one we will use here for the demonstration is a 1/8 inch cube of N40 grade. These magnets cost less than US$1 each.
large magnet for lifting -- This magnet counteracts the force of gravity to allow the week diamagnetic force to work, and does not have to be very powerful. We used a 1.5 inch diameter by 3/4 inch thick ferrite (ceramic) disc magnet, which cost about US$2.
experiment stand -- we built ours out of wood, but it could be as simple as playing cards stacked over platic cassette tape cases. The key here is fine adjustment -- the threaded rod allows very fine adjustments of the distance between the lifting magnet and the graphite plates.