Electromagnetic actuator – extension of field beyond coils?

Question

In an electromagnet with an iron or similar core, how far down that core, beyond the coil, will the rod be magnetic when the coil is energized?

I'm wondering if I can create an actuator for an object inside a sealed container. The rod would enter the container, with an electromagnet outside the container. A magnetic sleeve on the rod, inside the container, could then be moved toward or away from the end of the container by energizing the electromagnet, if the magnetic force extended a sufficient distance down the rod.

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

Answer 1

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.