Energy of a magnet/iron system (eg. gauss rifle)

[Wxfsa]

Homework Statement

I want to calculate the energy of a system of iron pieces and a magnet on an axis. The configuration can be thought to be like this: http://www.wired.com/images_blogs/wiredscience/2011/12/drawingskey1.jpg

Homework Equations

dE = 1/2B^2/µdv

The Attempt at a Solution

I tried very hard to find a source which explain the calculations of magnet+iron systems but I really couldn't find anything useful. I want to learn to calculate the change in potential energy between the two systems shown in the image above (and possibly more complicated configurations)
I can imagine that the magnetic field wants to go through the iron, making the field stronger when iron is closer to the magnet but i can not even begin to calculate how much.
This may or may not be a problem that can be solved by hand (I am posting this here because I thought this was a homework type question) Reasonable assumptions, and idealizations probably must be made. Shapes of the magnets and iron can be changed for easier calculations.

 

[mfb]

Calculating the potential energy of magnets and magnetic things is messy - you can do a finite element analysis, but this is nothing you want to do just for a toy.