User:Brian P. Josey/Notebook/2011/02/08

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FEMM Model Results

Last Tuesday, I attempted to make a model of my newest electromagnet in FEMM, however it failed to work. At the time, I thought that it could be an issue with my computer, until I tried it again. On Thursday, I recreated the model on the lab computer, and it too failed to work properly. After playing with the precision and mesh size, I was able to create a working model. Here is a representative picture of it, taken directly from FEMM:

2.5 Amp model.JPG

2.5 Amps solution This image is the solution created by FEMM of my electromagnet with 2.5 Amps running through the magnetic wire. The colors represent the magnetic field density, |B|, in Tesla. The magnet is represented so that the 325 turn portion of the magnet is the upper large box, while the 25 turn portion is the lower flat box. Clearly the field strength is greatest near the 325 turn portion. The data I collected today was taken from the boxes in the left center of the model.

From this model, I then calculated the magnetic field as a function of the current running through the magnetic wires. From this, I then calculated the force acting on a magnetic dipole placed in the center of the magnet. This time, I am going to do something a little different; I created two different fields over which I took data. The first is a line running along the central axis of the magnet that is 10 mm long. This line is centered at the center of electromagnet, giving 5 mm to either side of the center. The derivative from this is recorded as 10 mm Derivative (T/mm) in the table below. Then I cut this line down again to focus on only the central 4 mm. This data is written down as 4 mm Derivative (T/mm) in the table below. Here is the data:

{{#widget:Google Spreadsheet

key=0AjJAt7upwcA4dFBKNmhxNVJFUU5tR0M5NTVHazNnbkE width=400 height=325


I chose to focus on the derivative and not the force, because the derivative is proportional to the force, and I could use the derivative to calculate the force for many different magnetic particles, not just limited to ferritin. Taking the above data, I then want to graph it directly as a function of the current running through the wires. For the 10 mm section the graph of the derivative looks like this:

Lego 10 mm.png

Graph of Derivative as a Function of Current, 10 mm This graph represents the first derivative of the magnetic field intensity with respect to length for the 10 mm section on the FEMM model.

For the 4 mm section, the graph of the derivative looks like this:

Lego 4 mm.png

Graph of Derivative as a Function of Current, 4 mm This graph is of the derivative of the magnetic field strength as a function of the current flowing through the electromagnet. It should be noted that the graph is nearly identical to the 10 mm case.

I need to point out that the y-axis in the above graphs is the absolute value of the derivatives, and not the derivatives themselves. In the raw data, the derivatives came out negative, as indicated in the table above, but I plotted the absolute value of the derivative, which is proportional to the force. The sign merely indicates which direction the force is pointing, in this case a negative sign means toward the more heavily wrapped magnet.

Since the area the data was taken over is fairly small, and the both sets of data points overlap, the data in both cases is very similar. As suspected, the derivative increases as the current increases, a relationship that appears almost linear. However, it is unclear what this means in terms of the forces that would be applied to ferritin, or any other magnetic moment. Following my gut, I would assume that these numbers are fairly low, but I cannot say just yet. I will come back to this and compare this to some other forces that I've calculated over the last couple of months to get an idea for what is going on.