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

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## Application of Magnetic NanoparticlesI read through an interesting paper titled 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:
where: -
**F**is the force acting on the magnetic moment,_{m} -
**V**is the volume of the nanoparticle, -
**Δχ**is the difference between the susceptibility of water and the nanoparticle, water subtracted from the nanoparticle, -
**μ**is the permeability of free space, and_{0} -
**B**is the magnetic field.
Then the authors apply Gauss's law for magnetization,
to derive a simpler formula for the force acting on a magnetic moment:
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 |