The magnetic field (B) inside a long solenoid having ' n ' turns per unit length and carrying current ' i ' when iron core is kept in it, is ( ₀= permeability of vacuum, = magnetic susceptibility)

Step-by-step solution

Magnetic field enhancement in a solenoid with an iron core The magnetic field inside a long solenoid with n turns per unit length carrying current i is given by B₀ = ₀ n i . Introducing an iron core changes the permeability from ₀ to , so the field becomes B = n i . The permeability of a magnetic material is defined by = ₀ (1 + ) , where is the magnetic susceptibility. Substituting this into the equation for the magnetic field yields B = ₀ (1 + ) n i .