Where can I find how magnetic fields vary with the shape of the magnets?

Answer 1

First, get some magnets which have different shapes. A decent hobby store or physics teacher should be able to help you here. Then get a clear plastic sheet and cover it with iron filings (a file and a nail can set you up here) or small short pins.

When you place each magnet under the sheet, the iron will reveal the shape of the magnetic field.

Answer 2

Just numerically integrate Maxwell's equations. You might want to use finite element methods. Very complex material boundaries will require significant computational resources. In retrospect, if you know what I'm saying, you wouldn't be asking. So, get some iron filings, shake them up in a jar with Karo syrup, and put it next to a magnet constructed with lots of little magnets close to the shape you want. You have to get the syrup/water/filings ratio right, but it works. You can get little strong magnets at a fabric/craft store for cheap. Hope this helps.

Answer 3

Get some iron particles from a workshop or a department store. Put the magnet on a piece of paper and put the dust on the paper and tap the paper.You'll see them adjusting to the field.