Magnetic Force Exerted on a Material

When a magnetic dipole of moment m is subjected to a magnetic field H, the energy changes by an amount  

Introducing the magnetization of the sample M and the total volume of the specimen V we obtain  

If the energy varies along the x coordinate, then the specimen experience a force F equal to  

For a diamagnetic of paramagnetic materials with a magnetic susceptibility, the force can be expressed by  

If we introduce the density of the material p = m/V, we obtain the following equation  

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