Electromagnetic actuator – extension of field beyond coils?
The magnetic field inside a solenoid is very predictable but outside the confines of the solenoid it is weak and divergent: -



Picture from here.

So, to determine what the magnetic flux density is at some point beyond the solenoid coils we use this model (derived from the Biot-Savart law): -




  This obviously depends on how far down the rod (core) the magnetic
  effect extends


Well, you have the formula but I think you'll find that there just won't be sufficient force at any reasonable distance without many tens of amps flowing. To make life easier, use more turns concentrated as close to each other as possible. I think you also need to determine how much flux density needs to be present to create sufficient pulling force.