Calculating Magnetic Force for 5kg Iron Sphere - Magnet Question

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SUMMARY

The discussion focuses on calculating the magnetic force exerted by a magnet on a 5kg iron sphere at varying distances. It is established that the magnetic field strength decreases inversely with the cube of the distance, specifically following the formula for a dipole. For a bar magnet shorter than 10 cm, the force diminishes as 1/r^4, while for longer magnets, the force decreases as 1/r^3. This distinction is crucial for accurate calculations of magnetic attraction at different distances.

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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...
 
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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.
 
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