I Calculating the field outside a solenoid

[albertrichardf]

Hello.
I know you can calculate the magnetic flux density (B) outside a solenoid using Biot-Savart law, but the law uses the magnetic vacuum permeability.
Suppose that I placed an iron core in the solenoid, but not outside it. How does B outside change?
And now suppose that I place a piece of iron in the solenoid, and I place a piece of iron away from the solenoid, not connected to the first piece. How does that affect B at that point? And does it make a difference if it was one piece of iron, connected to the one inside the solenoid?
Finally if there is no iron inside the solenoid, but there is one outside it, does that affect the magnetic flux density at the iron?

Thank you for answering.

 

[Diegor]

With Biot Savart you should integrate current elements to get magnetic field at a point. Placing iron would affect the field because electrical currents are going on inside it.

 

[Delta2]

In all cases the magnetic field becomes stronger when you put a piece of iron, either in the core or outside the solenoid. The reason is that when putting the iron you have , except the magnetic field due to the current, the additional magnetic field due to the atomic magnetic dipoles of the iron. It doesn't matter where you put the iron, the field becomes stronger, however when you put the iron in the core the field becomes much more stronger than when you put the iron in a point outside.