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Force magnetized fluid

  1. Jan 27, 2008 #1
    The force on a single dipole (dipole moment m) can be obtained by taking the gradient of its energy, i.e.

    [tex]\vec{F} = \nabla (\vec{m} \cdot \vec{B})[/tex]

    One also often encounters for the energy of a magnetized material

    [tex]-\mu_0 \vec{M}\cdot \vec{H}[/tex]

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

    [tex] \vec{F}=\mu_0 M \nabla H[/tex]

    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?
    Last edited: Jan 27, 2008
  2. jcsd
  3. Jan 27, 2008 #2


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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.
  4. Jan 27, 2008 #3
    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?
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