Calculating core length and question regarding B-H curve
I realized that I calculated the core length wrong.


The mid point radius of the core is the average of \$R_0\$ and \$R_1\$: -

$$\dfrac{R_0 + R_1}{2}$$

Therefore the ungapped circumference is: -

$$2\pi\cdot\dfrac{R_0 + R_1}{2}$$


  In the solution, they gave \$l_c=2π(r_o−r_i)\$


That is incorrect.


  Also, if I want to find μ from B-H curve, do I take B/H or dB/dH?


$$\mu\cdot H = B$$

But only in the linear(ish) portion of the curve. My recommendation is to look at the graph and estimate the H-field.