(a) The Figure below shows a ferromagnetic core whose mean path length is 40 cm, with a small air-gap of 0.05 cm in length. The cross-sectional area of the core

is 12 cm2,and the relative permeability ; of the core is 4000. The coil of the wire on the core has 400 turns. Fringing in the air-gap increases the effective cross-sectional area of the air gap by 5%. (i) Find the total reluctance of the flux path (core plus air gap). [5 points]. (ii) Find the current, i, required to produce a flux density of 0.5 T in the air-gap.