Question

Is we can find the north pole and south pole of ring magnet?

Answer 1

Well, firstly, we can have two possibilities.
1) We carve a spherical magnet from another shape, say a cubic magnet.
In that case, the polarity of the spherical magnet would be in the direction of the polarity of the material from which it's cut. Say you have a cube of a magnetic material with. North at the top, south at the bottom. No matter how you cut it (even if you carve a sphere out of it), north stays at the top and south stays at the bottom

Read What would happen if we created a spherical magnet? for an interesting discussion.

2) In case of a magnet that we assume to be spherical right from the start, there is a simple matter of taking two such magnets and placing them near each other. The point where you have maximum repulsion from each other would be the pole.
Or, place the spherical magnet inside a cup, where it can freely roll around. Place a permanent magnet below the cup and wait for the spherical magnet to rotate and settle down to give you the pole.
One very old-school method, the most common one, IMHO would be to use a compass.