Circular core, current for 1 T air gap (mean length)

Given: mean length of magnetic circuit $= 10$ cm (taken to include the gap), $A = 100$ mm$^2 = 10^{-4}$ m$^2$, $l_g = 2$ mm, $N = 600$, $B_g = 1$ T, $\mu_r = 4000$.

Neglecting leakage and fringing, $B$ is 1 T in both iron and gap.

Path lengths

$$l_i = 0.100 - 0.002 = 0.098\ \text{m}$$

Mmf

$$\begin{aligned} F_i &= \frac{B l_i}{\mu_0\mu_r} = \frac{0.098}{4\pi\times10^{-7}\times4000} = 19.50\ \text{AT} \\ F_g &= \frac{B l_g}{\mu_0} = \frac{0.002}{4\pi\times10^{-7}} = 1591.5\ \text{AT} \\ F &= 1611.0\ \text{AT} \end{aligned}$$

Current

$$I = \frac{1611.0}{600} = 2.685\ \text{A}$$

If the 10 cm is taken as the iron length only (gap extra), $F_i = 19.9$ AT and $I = 2.686$ A, so the answer is the same to three figures.

Answer: $I \approx 2.69$ A