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Is it possible to electrically polarize an atom (typically a dielectric) with magnetic field? For example, if dielectric fluid flows near magnetic field, does it shift each atom's positive charge down (nucleus), and negative charge up (electrons) like on the following image?

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My initial thought is the following.

If you're thinking about a classical model of an atom that's just a positive and negative charge bound together, then the equation of motion given by the Lorentz force should tell you that the answer is, I would say, "not really": take your image and continue the trajectories. They'll just go around in circles.

A more quantum mechanical model of the atom involves people talking about an atom's dipole moments in terms of the diagonal matrix elements of the dipole operator. In this case, a DC magnetic field introduces a Zeeman splitting which is a mixing of the original eigenstates of the atom, so in fact "polarization" in the sense of giving the atom a "permanent" dipole moment will occur.

You can reconcile the two by arguing that sending the classical charges on circular trajectories moves their "center" relative to their unperturbed (no B-field) positions.

I could not say the corresponding effect on dielectric solids, but it seems from this argument that it could be possible.

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According to this paper ("The dielectric analogue of magnetohydrodynamics" by Bibhas R. De)

We note, however, that there is here nevertheless a microscopic displacement of the positive and the negative charges bound in the atoms and molecules of the dielectric, and these individual charges are subject to the same Lorentz force as the free electrons in a conductor

From these simple arguments, we are now able to make an important generalization: All substances (conductors and dielectrics) experience the J x B force in a magnetic field. This provides the full complement of the force law to the Maxwell's equations. We will now take the next logical step, and attempt to provide the dielectric counterpart of Alfven's ideas.

Consider for simplicity a pure dielectric fluid (nonconducting, lossless) with a polarizability X and a dielectric constant

e = (1 + X)ε0

placed in a magnetic field B, and moving with a velocity u (assumed nonrelativistic). Then the electric field E' in the body of the moving fluid is related to the field E in the laboratory (or rest) frame by (see, e.g., Stratton, 1941; Section 1.23)

E' = E + u x B,

However, I'm not sure if it's valid when E = 0.

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    $\begingroup$ I think it is valid when E=0. It's a simple relativity argument: electric and magnetic fields in a lab frame mix in a moving frame. You can look to Jackson for this (and maybe a later chapter of Griffiths). But I think it's more interesting (and I assumed this was what you were asking about) to think about something not moving in the lab frame. $\endgroup$ Nov 28 '21 at 2:20

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