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Easiest method for magnetic levitation? Answered

i have a ring magnet of about 4 cm diameter and additional magnet pieces. for my science project, i want to suspend one magnet in the air WITH OUT ANY SUPPORT. how can i do it? what are the factors affecting the stability? can anyone tell me the simplest way to perform that? what other shapes of magnet will i need to do that?

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It is impossible to suspend one permanent magnet above another in any stable configuration without support. This is a consequence of Earnshaw's Theorem (which you can look up for yourself).

You can suspend a permanent magnet above a set of electromagnets, by using a feedback circuit to continuously adjust the electromagnets to "push back" the target.

You can suspend a sample of diamagnetic material (look it up) above a permanent magnet configuration.

You can "suspend" a pair of permanent magnet secured at the ends of a "C" shape above a fixed bar magnet, provided you include restraint against sideways motion. See Earnshaw's Theorem.

The answer depends much on what you consider easy.

I am going to guess that those levitation demos based on diamagnetic materials,  like bismuth metal or pyrolytic graphite, are going to be the easiest method to give you a levitating magnet.   Fortunately instructables exist for both those materials.

Here's a bismuth one:
https://www.instructables.com/id/Magnetic-Levitation-Sculpture/

Here's one that uses pyrolytic graphite:
https://www.instructables.com/id/Diamagnetic-Levitation-Experiment/

I think the spin stabilized magnet is going to be more tricky to get it to work. However there exists 'ible(s?) for that one too:
https://www.instructables.com/id/How-to-Build-a-Magnetic-Levitating-Top/

You can use 4 fine threads to anchor the magnet and then your project can discuss Earnshaw's Theorem

Set a smaller magnet spinning over top of a larger magnet. Look at the instructables listed on the right.

Not with permanent magnets. I'll write a longer description as a top-level answer.

how can we make a strong electro magnet?? about number of turns, diameter of cu wire, supply voltage etc etc...

Not without having something that keeps it from flying off to one side. Many mag-lev tricks involve a very thin wire to hold it in place. To get true magnetic levitation without support or spinning would be to use a superconductive material chilled with liquid nitrogen over a strong magnet.