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Consider a bunch of magnetic dipoles in $x-y$ plane in an external magnetic field $B(t)=B_0 \hat{z}+B_1(\cos\omega t~\hat{x}+\sin\omega t~\hat{y})$. The dipoles are rotating around $z$ axis and of course they have the dipole-dipole interaction between them that goes like,

$$V=C_d\dfrac{1-3(\hat{d}(t).\hat{r})^2}{r^3},$$

where $r$ is the distance between any two dipoles and $d(t)$ is the magnitude of dipole at time $t$.

I am interested to find out what kind of field the rotating dipoles will create and how it will affect the other dipoles. Will the dipoles also move spatially because of the effect? If yes, then how exactly?

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  • $\begingroup$ I think this would be a case of a classical Heisenberg model and I am not aware that one can solve it in all generality. $\endgroup$ – CuriousOne Sep 3 '15 at 15:25

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