It will be tempting to write that self-inductance of a winding is the
ratio between the flux of B thru it (with 
) and the
current. The formula makes sense for a linear constant permeability
material like tha air, but cannot be extended for a ferromagnetic
core. One must then use the general definition of self-inductance that
is the derivative of 
with respect to I. Under the
hypotheses yielding to equation (3) of the previous paragraph,
Ampere's law yields 
. Since the chain derivation theorem gives :
we have :
with :
This last value is called appearing permeability or dynamic
permeability. It is the slope of the tangent to the curve B =f(H) at
the winding's biasing point. The relation (4) shows that the
self-induction of the winding can be computed as in the linear case,
but with 
replaced by 
. All ferromagnetic materials
have a flat B=f(H) curve for high absolute values of H : this
implies that self-induction will decrease as the current increases.