Confusion in linking H and B in an inductor
These equations don't yield \$ B = \mu \cdot H\$.
\$ \mu \$ is a measure of of the permeability of a magnetic material and is defined as \$ \mu = \frac{B}{H} \$.  This is not always the most useful figure as if we look at a typical B-H curve



You will notice it is not always a simple relationship.  The incremental permeability is often more useful as \$ \mu_i \$ is proportional to the inductance.  For some materials such as air the B-H curve is a straight line so air gaps are often introduced into magnetic materials if you want a defined inductance.