A toroidal iron core of relative permeability 3000 has a mean radius R = 80 (mm) and a cir...

A toroidal iron core of relative permeability 3000 has a mean radius R = 80 (mm) and a circular cross section with radius b = 25 (mm). An air gap lg= 3 (mm) exists, and a current I flows in a 500-turn winding to produce a magnetic flux of 10-5 (Wb). (See Figure.) Neglecting flux leakage and using mean path length, find

a) the reluctances of the air gap and of the iron core,

---

b) Bg and Hgin the air gap, and Bc and Hc in the iron core,

---

c) the required current I.

Figure: A toroidal iron core with air gap