# Magnetic Field Energy Density Confusion

1. May 20, 2013

### dgreenheck

I am trying to find the approximate force imparted on a piece of iron on the axis of a finite length solenoid. One website said a good approximation was to take the difference of the magnetic field energy from when the piece of iron was directly outside the solenoid and when the piece of iron was inside the solenoid.

The formula for the magnetic field energy density is:
$\frac{1}{2}\frac{B^{2}}{μ}$

So here's the point where I am confused on: The piece of iron is attracted to the solenoid, so the energy has to go down. But I thought that putting a piece of iron in the center of a solenoid made it a stronger electromagnetic, a.k.a. the magnetic field lines are more concentrated with a high permeability core. Wouldn't this imply that the magnetic field energy density goes up, contradicting my first point? I know my fundamentals are messed up somewhere, but I can't quite figure out where.