A long solenoid has 850 turns in each metre and carries 0.80 A…

Step 1. The intensity. $H = nI = 850\ \text{m}^{-1} \times 0.80\ \text{A} = 680\ \text{A/m}$.

Step 2. The field with the core. $B = \mu_0\mu_rH = 4\pi \times 10^{-7}\ \text{T m/A} \times 400 \times 680\ \text{A/m} = 0.342\ \text{T}$.

Step 3. The magnetisation. $\chi = \mu_r - 1 = 399$. So $M = \chi H = 399 \times 680\ \text{A/m} = 2.71 \times 10^{5}\ \text{A/m}$.

Step 4. Without the core. $B_0 = \mu_0H = 4\pi \times 10^{-7}\ \text{T m/A} \times 680\ \text{A/m} = 8.55 \times 10^{-4}\ \text{T} = 0.855\ \text{mT}$.