# Fhd expression bothering me for weeks

1. Feb 3, 2008

### da_willem

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

$$\nabla \int _0 ^H M dH = M \nabla H + \int _0 ^H \nabla M dH$$

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

$$\nabla \int _0 ^H M dH = M \nabla H + \int _0 ^H \frac{\partial M}{\partial T} dH$$

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

$$\int _0 ^H \frac{\partial M}{\partial H} \nabla H dH$$

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