Calculating the magnetic field strenght at x distance

[BigShnitsel]

The configuration is hall sensor --- steel rod(3mm radius) --- magnet.
Im trying to make a non mechanical endswitch for a sliding lid and want to determine on what magnets to get and how far apart the hall sensor and the magnet should be for it to work in the proper range.
The hall chip has 0,4 -4,4 mT release and operation point.

How to determine on how much the rod would suck up the magnetic field and how much would pass through etc.
Can anyone direct me to proper sources on how to calculate such stuff?

 

[TJGilb]

When you say "suck up" am I correct in assuming what you're trying to do is determine the strength of the induced magnetic field from the rod? If so this should be able to get you started http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/magpr.html

 

[BigShnitsel]

When you say "suck up" am I correct in assuming what you're trying to do is determine the strength of the induced magnetic field from the rod?

Can you call it induced if the magnet is glued or very near to the rod and both of them don't move?
Im just interested on how much magnetism can pass through that rod and unto that object on the other side of it if the magnet is not connected to it(a la 1mm of separation from the rod).
Or if there are thin metallic structures with a slits or holes etc obstructing the full field of the magnet , how much of it will get passed through?
Or a cuboid , long , iron rod with teeth.If i attach a permanent magnet to one end of it , how will the magnetic field be distributed on the rod etc?
Im talking pure magnetostatics here , 98+% iron objects,permanent magnets and none of them moving.