The magnetic induction inside a solenoid with a ferromagnetic core depends on the current flowing through the solenoid, the number of turns, the length and also on the permeability of the material used in the core.
The properties of ferromagnetic substances are explained by means of the Domain Theory of Magnetization.
Formula 1
Where:
H is the magnetic induction in gauss (Gs)
I is the current flow through the solenoid in amperes (A)
n is the number of turns
L is the solenoid´s length in centimeters (cm)
µ is the permeability of the material used in the core
Note: materials with µ larger than 1 are called paramagnetic and materials with µ smaller than 1 are called diamagnetic.