# User:Brian P. Josey/Notebook/2010/12/22

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## Variable Number of Turns

On Monday I began to design a Helmholtz coil that I could make and mount to the stage on the microscope. One issue that I came up with is that Helmholtz coils are perfect for creating a nearly uniform magnetic field in the center, but magnetic forces depend on the gradient of the magnetic field. The first solution I came up with is to vary the current in each of the rings that makes the Helmholtz coil. The advantage is that I can change the current around however I want, which will vary the strength and direction of the force. However, that can be fairly complicated to implement, and there is a simpler solution.

Andy suggested that I could simply change the number of coils in each of the rings, and then pass the same current through each of the rings. The only advantage that the multiple current model has is that variability in the directions of the forces. However, I am simply trying to create a nice prototype for the time being, so changing the number of coils can be enough for right now. Later, if this works well, I would like to create three different Helmholtz coils with different current sources so that I can create a force and perfectly control it in three dimensions.

### FEMM Model

I created a couple models representing Helmholtz coils with differing number of turns in each of the rings. In all five of the models, I have one ring with 100 turns of 18 AWG wire, with 1 A of current passing through it. The number of turns of wire in the other ring then changes depending on the model. The five models that I created have 1, 25, 50, 75 and 100 turns of the same 18 AWG wire with 1 A flowing through it. I generated this in FEMM, and took data for a line running along the central axis that was 2 cm long and centered on the center of the coil. This area best represents the area I would be looking at through a microscope.

Looking at the data in MATLAB, I was able to calculate the derivative of the magnetic field with respect to the distance, and in turn the force. This confirmed that as the number of turns in each wire changed, the force also changed. Fewer turns in the second coil resulted in a greater gradient and force when compared to nearly identical number of turns in each wire. For example, the force in the 1 turn model was about 100 times larger than the force in the 100 turns model. The only issue is the size of these forces. As with the neodymium magnets from before, the scale of the forces, even in the best case scenario, is only a small fraction of a femtonewton. This of course assumes that all of the ferritin is at its maximum suseptability, and ignores any effects from thermal fluctuations. While it may not be the cure to my small forces blues, it is still worth trying.