= Inductance of a rectangular-section toroid
{title2=$L=\frac{\mu N^2h}{2\pi}\ln(b/a)$}
For a uniformly permeable <toroid> with inner <radius> $a$, outer <radius> $b$ and axial height $h$, an ideal poloidal winding gives $H_\phi=NI/(2\pi r)$. Integrating the <magnetic flux density> across its section gives $\Phi=\mu NIh\ln(b/a)/(2\pi)$ and hence the displayed <self-inductance>. It retains radial field variation when $b-a$ is not small. For two fully linked windings, replace $N^2$ by $N_1N_2$ to obtain their <mutual inductance>. Discrete turns, leakage and nonlinear core response limit the ideal formula.
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