Iron core current for 1 T air-gap flux

The current needed is about 2.69 A. The air gap needs almost all of the mmf because its reluctance is far larger than that of iron.

Given (SI units): iron length lᵢ = 10 cm = 0.1 m; area A = 100 mm² = 1×10⁻⁴ m²; air gap lg = 2 mm = 2×10⁻³ m; N = 600; μr = 4000; B = 1 T; μ0 = 4π×10⁻⁷ H/m.

Assumption: the 10 cm is the length of the iron path and the gap is added to it. Fringing is neglected, so the flux density is the same in iron and gap.

Step 1: flux Φ = B × A = 1 × 1×10⁻⁴ = 1×10⁻⁴ Wb

Step 2: reluctances

Sᵢ = lᵢ/(μ0 μr A) = 0.1/(4π×10⁻⁷ × 4000 × 10⁻⁴)
   = 1.989×10⁵ AT/Wb
Sg = lg/(μ0 A) = 2×10⁻³/(4π×10⁻⁷ × 10⁻⁴)
   = 1.592×10⁷ AT/Wb
S  = Sᵢ + Sg = 1.612×10⁷ AT/Wb

Step 3: mmf and current

mmf = N I = Φ × S = 10⁻⁴ × 1.612×10⁷ = 1611.4 AT
I   = 1611.4 / 600 = 2.686 A

Check by the ampere-turn method: AT(gap) = (B/μ0) lg = 1591.5 AT, AT(iron) = (B/μ0μr) lᵢ = 19.9 AT, total 1611.4 AT.

Answer: I ≈ 2.69 A