magnetic man
I am trying to find out what is the best arrangement ( rare earth permanent magnets ) to achieve the best magnetic force of catchment ?

I have 16pcs of 50mm x 50mm dimension bar magnet which I hope that by the best arrangement to achieve the catching distance of 100mm without touching the iron fillings. The strength of the bar magnet is around 3000 gauss.

The iron material piece that I am trying to attract is around 3 kg.

mr_homm
Here's my basic suggestion:

Magnetic fields pull on iron only when the field strength is not constant. In other words, iron tends to move toward where the field is stronger, so iron in a uniform field will not be attracted (it will rotate to line up with the field like a compass needle, but it will not move toward the magnet).

To get the greatest distance, you need to have the field extend out from your magnet with only a slow spreading of the field lines, so that the field flares out only after a large distance, not right away. The field will be nearly uniform near the magnet if the magnet has a very large area for its north and south pole faces. Therefore, you want to arrange your 16 magnets in a flat square grid with their north poles facing all the same way (this will be hard to do, because they repel each other, so you will have to attach them to something.

At a guess, I would say to put them close together (touching or almost touching) so that you don't get field lines curling back through the spaces between them. It is not good to make the north pole face larger than the piece of iron you are trying to attract, since the field will then be weaker because it is too spread out.

Basically, stacking the magnets lengthwise (with all north poles facing the same direction) to form a long bar will increase the strength of the field, but it will start to spread out right away, and will be weak at points far from the pole face. On the other hand, attaching the magnets side by side (as I said in the first paragraph) will not make the field stronger, but will prevent it from spreading out so much right away, so that it will not weaken as fast with distance from the pole face.

That means that the best arrangement is probably to put enough magnets side by side to get a pole face that is nearly as big as your piece of iron, but not larger, and then if there are left over magnets, put them behind the first layer to strengthen the field. You won't get a magically super-strong field this way, but I think it is about the best arrangement you can make with a limited number of magnets.

Hope this helps!

--Stuart Anderson
magnetic man