Well,I think you asked" the force of the magnetic field "is the interaction of magnetic moments!The essence of microscopic action is potential energy rathan then force, I hope you change it ,the formula of interaction of magnetic moments is
V^(r)=-8/3πui uj δ(r)
V(r)=∫Φ(r)V^(r)Φ(r)dr^3
we could calculate interaction of e-p spins or e spin and orbit ,or you asked e-e spins !