Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I'm currently reading material on micromagnetics. In these papers, authors define a quantity called the demagnetizing energy ([itex]E_d[/itex]) as

[tex] E_d = -\frac{1}{2} \int_V \vec{m} \cdot \vec{H}_d\;dV [/tex]

where [itex]\vec{m}[/itex] is the internal magnetization of a material sample of volume [itex]V[/itex] and [itex]\vec{H}_d[/itex] is the demagnetising field. The demagnetizing field itself is defined as the negative derivative of the demagnetizing energy with respect to the material magnetisation, i.e.

[tex] \vec{H}_d = -\frac{dE_d}{d\vec{m}} [/tex]

My problem is that I would like to know how to derive [itex]\vec{H}_d[/itex] by taking the derivative of [itex]E_d[/itex] with respect to [itex]\vec{m}[/itex]. This is as far as I have got (and I'm not too sure that this is correct)

[tex]\frac{dE_d}{d\vec{m}} = \frac{d}{d\vec{m}} \left( -\frac{1}{2}\int_V \vec{m}\cdot\vec{H}_d\;dV \right)[/tex]

[tex]\frac{dE_d}{d\vec{m}} = -\frac{1}{2}\int_V \frac{\partial}{\partial\vec{m}}\left(\vec{m}\cdot\vec{H}_d\right)\;dV=-\frac{1}{2}\int_V\frac{\partial\vec{m}}{\partial \vec{m}} \cdot \vec{H}_d + \vec{m}\cdot\frac{\partial \vec{H}_d}{\partial \vec{m}}\;dV=-\frac{1}{2} \int_V \vec{H}_d\;dV - \frac{1}{2}\int_V \vec{m}\cdot\frac{\partial \vec{H}_d}{\partial \vec{m}}\;dV[/tex]

Could some kind soul please give me some pointers as to how to proceed and/or explain to me where I'm going wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Relationship of the Demagnetizing Energy to the Demagnetizing Field

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**