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.