I can find equations to give the force of an electromagnet on a piece of iron when the iron touches the electromagnet.But what about when the iron is some distance from the electromagnet? Presumably the force depends on the shape/size of the iron piece as well as the location of the piece away from the magnet.

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Geovanni Shelton · Accepted Answer

Approximate the iron as a collection of dipoles, and calculate the potential energy as      1    2    ∫  (  M  B  )      d    Vover the volume of the iron, where   M is the magnetization and   B is the total field. This becomes impossibly difficult with a nonlinear magnetic material and an asymmetrical magnet. As always, the gradient of potential energy gives force.

Aleah Avery · Accepted Answer

The equation   F  =  (  N  I      )    2        μ    0    A      /    2      g    2   should help. This equation gives the force in Newtons of an electromagnet given the number of turns in the electromagnetic coil (  N), the current flowing through the electromagnet (  I), the magnetic permeability of a vacuum (      μ    0  ), the cross-sectional frontal area of the ferromagnetic material (  A), and the distance of the ferromagnetic material (  g). The units for   A and   g are arbitrary, as long as you&#039;re consistent with the usage.   F will always be in Newtons, and       μ    0   is a constant of nature (sometimes called the magnetic constant).

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