Force on a magnet inside a short coil

The equations are incredibly difficult, so I'm just after a general idea of how the force on a magnet bellow a coil changes with the distance to the coil. Shown bellow:

Code:
Axial symmetry:

o                 x
o                 x               cross section of coil
o                 x
o                 x
/\
x                      displacement (x)
\/
_
| |
|_|                       cylindrical bar magnet

From intuition, I would say that the force on the magnet is acting in opposite directions when the magnet is above or bellow the coil. So there must be a zero crossing point. It makes sense that this will be in the center of the coil. So in this case the force vs displacement will look something like this, assuming that x=0 is when when the magnet is in the center of the coil. Is this an okay assumption?

How would things change if the magnet had a hollow core: like bellow?

Code:
Axial symmetry:

o                 x
o                 x               cross section of coil
o                 x
o                 x
_         _
| |       | |
|_|       |_|                  cross section of hollow core magnet

Svein