(Solved): An iron ring of mean radius \( \mathrm{R} \), permeability \( \mu \) and cross sectional area \( \p ...

An iron ring of mean radius \( \mathrm{R} \), permeability \( \mu \) and cross sectional area \( \pi b^{2} \) contains an air gap of width \( w \) such that \( w \ll b \ll R \). Suppose that there are \( N \) turns of wire carrying a current I wound around the ring as shown in the figure. Calculate the magnetic field near the center of the air gap.