Chapter 14, Problem 14.10P

1.2 Magnetic Circuits The figure shows a ferromagnetic core whose mean path length is 40cm. There is a small gap of 0.05 cm in the structure of the otherwise whole core. The cross-sectional area of the core is 12 cm², the relative permeability of the core is 4000, and the coil of wire on the core has 400 turns. Assume that fringing in the air gap increases the effective cross-sectional area of the air gap by 5 percent. Mr = 4000 N=400 turns ·25.4m² Il=0.0005m A=0.0012 m² Given this information: a) Find the total reluctance of the flux path (iron plus air gap). b) Find the current required to produce a flux density of 0.5 T in the air gap. c) Qualitatively describe the effect of the air gap on the magnetic circuit.

> Figure 1 shows a ferromagnetic core whose mean path length is 40 cm. There is a small gap of 0.05 cm in the structure of the otherwise whole core. The cross-sectional area of the core is 12cm2, the relative permeability of the core is 4000 and the coil of wire on the core has 400 turns. Assume that fringing in the air gap increases the effective cross-sectional area of the air gap by 5 percent. Given this information. Find the total reluctance of the flux path (iron plus air gap) and the current required to produce a flux density of 0.5 T in the air gap. N=400 tums 0.05 cm A=12 cm? le-40 cm Figure 1

> Figure 1 shows a ferromagnetic core whose mean path length is 40 cm. There is a small gap of 0.05 cm in the structure of the otherwise whole core. The cross-sectional area of the core is 12cm?, the relative permeability of the core is 4000 and the coil of wire on the core has 400 turns. Assume that fringing in the air gap increases the effective cross-sectional area of the air gap by 5 percent. Given this information. Find the total reluctance of the flux path (iron plus air gap) and the current required to produce a flux density of 0.5 T in the air gap. N=400 0.05 cm A-12 cm - 40 cm Figure 1