Cast steel ring with air gap, B-H data

For a material given by a $B$–$H$ table, $H$ for the working $B$ is read (interpolated) from the table instead of using $\mu_r$.

Given: section diameter $= 3$ cm, mean circumference $= 80$ cm, $l_g = 1$ mm, $N = 600$, $\Phi_g = 0.75$ mWb.

Flux density (the same in steel and gap, leakage and fringing neglected):

$$\begin{aligned} A &= \frac{\pi}{4}(0.03)^2 = 7.069\times10^{-4}\ \text{m}^2 \\ B &= \frac{0.75\times10^{-3}}{7.069\times10^{-4}} = 1.061\ \text{T} \end{aligned}$$

$H$ for steel at 1.061 T: this lies between (800 AT/m, 0.9 T) and (1000 AT/m, 1.08 T).

$$H = 800 + 200\times\frac{1.061 - 0.9}{1.08 - 0.9} = 978.9\ \text{AT/m}$$

Mmf

$$\begin{aligned} l_i &= 0.80 - 0.001 = 0.799\ \text{m} \\ F_i &= H l_i = 978.9\times0.799 = 782.2\ \text{AT} \\ F_g &= \frac{B l_g}{\mu_0} = \frac{1.061\times0.001}{4\pi\times10^{-7}} = 844.3\ \text{AT} \\ F &= 1626.5\ \text{AT} \end{aligned}$$

Current

$$I = \frac{1626.5}{600} = 2.711\ \text{A}$$

Answer: $I \approx 2.71$ A