# User:Brian P. Josey/Notebook/2010/02/17

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## Theory and Research

As of writing this, the magnets haven't came in just yet. So I'm taking the time to look into the magnetic separation, and see if I can understand the theory. If I find anything particularly useful or interesting, I will post it here. I might even run back to campus to visit the library.

### Where to go

Since I'm not going to San Francisco next week, I created this mindmap for what I should do between now and next week. I hope it is fairly straight forward, but I can elaborate on anything if needed.

### Griffiths

I'm reading through a part of Koch's copy of Griffiths' Introduction to Electrodynamics to get a better picture of magnetization at the level for the proteins. Here are my notes: When electrons are orbiting around the nucleus of an atom, you can think of them as really small currents and as a magnetic dipole. All magnetic dipoles have an magnetic moment, m. When you apply an external magnetic field to the dipole, you get a torque:

$\vec{N} =\vec{m} \times \vec{B}$

where N is the torque, and B is the external magnetic field.

For an infinitesimal loop with a dipole moment m in a field B you get a force F of:

$\vec{F}= \vec{m} \cdot (\nabla \vec{B})$

This is the important formula for what I'm doing. In essence, what happens is that the force is equal to the magnetic moment, times the magnitude of the magnetic field in its direction.