The H-field inside a long solenoid is nI. If there is a vacuum inside the solenoid, the B-field is μoH=μonI. If we now place an iron rod of permeability μ inside the solen...The H-field inside a long solenoid is nI. If there is a vacuum inside the solenoid, the B-field is μoH=μonI. If we now place an iron rod of permeability μ inside the solenoid, this doesn't change H, which remains nI. The B-field, however, is now B=μH. This is greater than μoH, and we can write B=μo(H+M)