Magnet Design

using the {non relaxing} Relaxation Method

Dear Boss,

as you know, you gave me the task of designing a magnet using the computer program of my predesessor. It calculates the magnetic field due to two pole pieces one (the upper) held at 10V and the other (the lower) held at 0V. Not wanting to be fired as she was, I made a few changes. The array was boosed from 11X11 to 41X41. And the number of iterations was also increased from her measily 25 to 500.

I also took you suggestion about the boundry conditions. Instead of setting them all to zero, I set the boundry points half way between the poles to 5V (half the distance should have half the value) and I estimated and itterated the values for the other points on the boundry untill the surface looked smooth as the real surface must.

Then I took a look at the poles themselves. Fringing effects bend the field down near the ends of the magnetic region. To get the field more uniform between the two, the magnet was "shimmed" or built up on the edges as illustrated.

In this resolution, the magnet is 16 units across. Originaly it was constructed as a flat surface.

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To reduce the fringing effects the ends were built up on both magnets as follows:

* (1 cell added to the ends 5 rows above the magnet)

** (2 cells added to the ends 4 rows above the magnet)

*** (3 cells added to the ends 3 rows above the magnet)

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*****

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The results were graphed as follows :

The assigment was to get the non-uniformity of the feild to down under .001, but due to the fact my boss took "DOOM" off the computers,[just kidding boss] I had some extra time and managed to get the non-uniformity down to

3.935X10-5

Not that I'm bragging or anything. If you need to take a look at the source program here is the link. So. . . when do I get my bonus ?