Reluctance of a conical magnetic pole (${\mathcal{R}}_{\mathrm{taper}}=s/(\mu \pi Rr)$)

For a linear-radius taper from $R$ to $r$ over length $s$, constant absolute permeability $\mu$, and a common approximately axial flux, integrate $dx/[\mu \pi \{R-(R-r)x/s{\}}^2]$ to obtain the displayed reluctance. Leakage, fringing, nonuniform transverse fields and saturation limit this one-dimensional magnetic-circuit approximation.