User:Brian P. Josey/Notebook/2010/07/28
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Application of Magnetic NanoparticlesI 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: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \vec F_m = \frac {V_m \Delta \chi} {\mu_0} (\vec B \cdot \nabla) \vec B } where:
Then the authors apply Gauss's law for magnetization, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \nabla \cdot \vec B = 0 } to derive a simpler formula for the force acting on a magnetic moment: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \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} m^{3} kg^{-1}, and is therefore inconsequential, and substituting air or a vacuum for water is not dangerous. |