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.

 

[astrokreng]

Hello, thank you for your question. The formula for calculating magnetic force is F = (magnetic field strength) x (magnetic field gradient) x (volume of object) x (magnetic susceptibility). In this case, the magnetic field strength would be the strength of the magnet, the magnetic field gradient would be the change in distance, and the volume of the object would be the volume of the iron sphere. The magnetic susceptibility is a property of the material and can be found in a table or calculated using the material's magnetic permeability and relative permeability.

Using this formula, you can calculate the magnetic force at a distance of 0.1m by plugging in the new distance and keeping all other variables the same. Keep in mind that this formula is an approximation and may not account for all factors, such as the shape of the magnet and the sphere. It is always best to consult a professional or conduct experiments to get more accurate results. I hope this helps!