# User:Brian P. Josey/Notebook/2010/07/28

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## Application of Magnetic Nanoparticles

I read through an interesting paper titled Application of Magnetic Nanoparticles in Biomedicine by Q Pankhurst et al. It was originally published in 2003, and here is a link to the article. The paper is a review of sorts, covering the essential information concerning magnetic nanoparticles, and discussing some possible uses they can be employed in, like the magnetic separation of cells.

After elaborating on the different types of magnetic nanoparticles, and various types of magnetization, the author derives a new equation that I haven't seen before. The equation relates the force exerted on a magnetic moment to the magnetic field and susceptibility of both the moment and water that it is floating in. The equations is:

$\vec F_m = \frac {V_m \Delta \chi} {\mu_0} (\vec B \cdot \nabla) \vec B$

where:

• Fm is the force acting on the magnetic moment,
• V is the volume of the nanoparticle,
• Δχ is the difference between the susceptibility of water and the nanoparticle, water subtracted from the nanoparticle,
• μ0 is the permeability of free space, and
• B is the magnetic field.

Then the authors apply Gauss's law for magnetization,

$\nabla \cdot \vec B = 0$

to derive a simpler formula for the force acting on a magnetic moment:

$\vec F_m = V_m \Delta \chi \nabla \frac {B^2} {2 \mu_0}$

This is interesting, because I assumed that I could just factor out the magnetic properties of water, and treat it like air, but the authors account for it. However, I should also note that the difference between the susceptibility of water and a vacuum differ on the order of nearly 10-8 m3 kg-1, and is therefore inconsequential, and substituting air or a vacuum for water is not dangerous.