# Force between magnet and metal

#### McSquirrel

Hello,

I am trying to calculate the magnitude of the attractive force between a cylindrical magnet and a sheet of iron. A bit of searching found some equations that can be used to calculate the force between two magnets but I could not find anything related to magnetic force on non magnetized materials. I cant link them as this is my first post but searching wikipedia for "force between two magnets" will yield them.

Can you use a similar equation to find the force between a magnet and a metal?

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#### Hassan2

For nearby magnetized surfaces, the equation is given in the same Wiki page. But you need to calculate B in the gap between the two surfaces which usually requires numerical methods. When a magnet is brought very close to an iron sheet, the flux density B approaches $\mu_{0}M$ where M is the magnetization density of the magnet which is constant.
For an accurate calculation of the force for arbitrary shape and distance, you need to find the B distribution in the air region and use Maxwell stress tensor to calculate the total force on the object. see this page: http://www.fieldp.com/documents/stresstensor.pdf

#### McSquirrel

That is quite helpful. Thank you Hassan!

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