## force magnetized fluid

The force on a single dipole (dipole moment m) can be obtained by taking the gradient of its energy, i.e.

$$\vec{F} = \nabla (\vec{m} \cdot \vec{B})$$

One also often encounters for the energy of a magnetized material

$$-\mu_0 \vec{M}\cdot \vec{H}$$

And often the force on a material with magnetization M is written

$$\vec{F}=\mu_0 M \nabla H$$

why the replacement of B with H? Does it have something to do with the fact that part of B is producedby the magnetization (B=mu_0(H+M)) and the material can't excert a force on itself?? Or does one necessarily have to dive into the derivations to get an idea why?

Any intuitive thoughts?

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 Do you have a source for your equations with H? Probably the muzero H just stands for B outside the magnet.
 The force equation with H (M gradH) (Kelvin force) is the standard expression used in ferrohydrodynamics (see e.g. Rosensweig) when dealing with dilute colloids for example. I'm wondering if the use of H instead of B results from the fact that only the external applied magnetic field should be used in evalueating the force because the magnetized material cannot exert a force on itself. Any familiarity with these expressions?