= Inductance of a toroidal winding
{title2=$L\simeq\mu N^2A/\ell$}
For a slender winding around a <toroid> with $N$ turns, core area $A$, mean magnetic path length $\ell$ and approximately constant <magnetic permeability> $\mu$, <Ampère's law> gives $H\ell=NI$. The linked magnetic flux is $N\Phi=N\mu HA$, so $L=N\Phi/I=\mu N^2A/\ell$. This approximation neglects flux leakage and variation across the core and assumes operation below <magnetic saturation>. With a nonlinear magnetic core, an incremental inductance instead depends on differential permeability at the operating point.
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