# User:Brian P. Josey/Notebook/2010/12/20

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## Helmholtz Coils

Like I noted in my notebook a few weeks ago, I've started working with Andy to find some small projects to do and get some fresh perspective on my ferritin project. One thing that we've talked about was using microcontrollers to create something useful for the lab. Andy offered up creating a device that moves the microscope's stage more precisely, which would be fairly simple. Another idea that I offered up was creating a micro-injector, which could potentially be cheaper than buying one, but it is fairly complicated. For a usable micro-injector you need to be able to move the needle, and supply a pressure to inject whatever you're putting inside of a cell. While simple to understand, there are quite a few engineering problems.

Going back and forth over this, we moved on to designs of electromagnets that I could use for my experiment. There are a couple of things that I want from an electromagnet: to know where it is with respect to the focal plane; how powerful its magnetic field is; and control over as many variables as possible. We talked about putting a curled up wire into a flow cell, but Andy pointed out that flow cells are only ~100 microns thick, and my electromagnet would be thicker. Placing it to the outside of the flow cell, but I don't like this because it would cause problems with knowing the distance between the ferritin and magnet, introducing more variable than necessary. Then I thought about putting a coil of wire with current flowing through it on top of the flow cell opposite of the objective, but the magnetic field would be pointing towards (or away from) the objective, making measurements impossible. Then I thought of just creating a Helmholtz coil, which is basically a solenoid with the middle cut out of it.

My idea was to place one of each ring around the flow cell so that they were centered on the objective's focal plane. This would make it so that the magnetic field is pointing perpendicular to the objective, but still within the focal plane. This way I can see and measure any movement in the direction of the magnetic field, and the force. The only problem is, and I just thought of this when I sat down to type up this section, is that Helmholtz coils a perfect for making nearly uniform magnetic fields. The force acting on a dipole is proportional to the gradient of the magnetic field.

Updated Thoughts

After thinking the constant magnetic field in a Helmholtz coil, I tried two different approaches to generate a gradient. The first one I came up with was to change the amount of current flowing in each of the coils. This will create a gradient in the magnetic field, but Andy pointed out a better solution: simply change the number of coils in the two portions. This has the same effect, however, I do not have to add to the circuit to accomplish this. I modeled a Helmholtz coil with different currents passing through each ring, and different number of coils in each ring. Here is a picture of a coil with different number of turns of wire in each ring:

In this picture, the upper box to the left of the red spot represents the ring with 100 turns of copper wire with 1 A of current running through it. The lower box has 25 turns of copper wire, also with 1 A flowing through it. Clearly there is a difference in the magnetic fields between the two rings. To check this, I measured the magnetic field strength along a 2 cm line running along the center axis of the coil. This produced this graph:

Luckily there is some curve in the magnetic field, and it is not constant, indicating that there will be a force on ferritin if I put some in this coil. Now the only thing left to do is to find the force, and build it to see if it works.