Calculating Magnetic Force for 5kg Iron Sphere - Magnet Question

[MonroeIns]

Hello, please forgive my ignorance. I need help coming up with a formula I can't seem to find on the internet. Assume I have a magnet that can attract a maximum of 5kg iron sphere against gravity from a distance .2m. My question is how much could that same magnet attract at a distance of .1m.

Wikipedia says that generally "the strength of the field falls off inversely with the cube of the distance."

Does that mean you could calculate by Mass * (Change In Distance)^3?

Please help...

 

[Meir Achuz]

Your answer depends on the size and shape of the magnet and size of the iron sphere, compared to 100 cm. If it is a bar magnet of length much smaller than 10 cm and a small sphere, the magnetic field would fall off like 1/r^3, but the force on the sphere would fall off like 1/r^4. This is the force law for a dipole in the field of a dipole.
If the bar magnet is longer than ~10 cm, then force falls off more like 1/r^3.