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Fhd expression bothering me for weeks

  1. Feb 3, 2008 #1
    Suppose the magnetization of some substance depends on the field H and temperature, i.e. M(H,T) and we have the mathematical identity

    [tex]\nabla \int _0 ^H M dH = M \nabla H + \int _0 ^H \nabla M dH[/tex]

    then it is derived in Ferrohydrodynamics (fhd) by Rosensweig that

    [tex]\nabla \int _0 ^H M dH = M \nabla H + \int _0 ^H \frac{\partial M}{\partial T} dH[/tex]

    but what happend with the dependence of M on H?! Shouldn't the above include a term

    [tex] \int _0 ^H \frac{\partial M}{\partial H} \nabla H dH[/tex]

    or is there some reason this should vanish? Can someone help me out of my misery?
  2. jcsd
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