I would like to find motion equations $m\frac{\text{d}^2}{\text{d}t^2}\vec{x} = -\vec{F}(\vec{x},\dot{\vec{x}},\vec{E},\vec{B})$ or Hamiltonian $\mathcal{H}$ or Lagrange function $\mathcal{L}$ of moving magnetic dipole given by $\vec{m}$ without any charge, e.g. $q=0$, in homogenous magnetic field given by magnetic induction vector $\vec{B}$ and homogenous electric field given by vector $\vec{E}$. I'm mainly interested in magnetic dipole in electric field, thus if there is some complication with magnetic field, feel free to consider $B = 0$. I haven't found explanation about this fenomena only for non-moving magnetic dipole in magnetic field, or quantum physic explanation. My struggle with this is to find the forces from the fields. To sumarize this is what I'm looking for:

  1. Force on moving magnetic dipole due to homogenous electric field.
  2. Force on moving magnetic dipole due to homogenous magnetic field.
  3. Force on moving magnetic dipole due to homogenous electric and magnetic field.
  4. Possible solutions of motion equations given by forces from 1. 2. and 3.

Thanks in advance.

  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Mar 2 at 14:42

1 Answer 1


The force on a magnetic dipole is given by $\vec F=\nabla({\vec m}\cdot{\vec B})$, so there will be no force in a homogeneous field. Movement of the dipole does not change this.


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