Hi Newgato,

In this situation, you will have a Zeeman term in the Hamiltonian representing the interaction of the external magnetic field with the material. The force may be calculated by obtaining the negative gradient of the potential energy. In the case of ferromagnetic materials, it is useful to keep in mind that the material is composed of many domains with spins pointing in different directions but with an overall total nonzero magnetization in a specific direction.

I hope this helps.

Hello,

I want to thank both of you for your answers.

Dear Samin, could you please elaborate on whether the force is just the negative gradient of Zeeman energy alone, or the negative gradient of the total potential energy (Zeeman + Anisotropic energy+ exchange energy).

Could you also point me towards a source (if you know one) that treats the force of attraction and repulsion between two dynamic magnetic field alternating.

Thank you in advance

Thank you Thomas for the website I will certainly try do launch some simulations on it, thank you

Dear Newgato,

If you could get a constant magnetic field of 1T on the surface S (in square meters), thus the force would be very easily calculated as

F=S/2μ0

and μ0 is the magnetic permeability of the vacuum in MKS units,

It should be the negative gradient of the total potential energy which, as you correctly point out, may contain contributions from different effects.

To have a force, you need a field gradient. Here is a site where you can find formulas and a scientific paper on this subject.

https://www.kjmagnetics.com/blog.asp?p=magnetic-grates