We present a new, completely original exact method to determine the permeance between two opposing iron teeth. This configuration is important because it is often encountered in electrical machines and apparatus. The method is based on conformal mapping. The given "tooth-to-tooth" configuration is mapped into a simpler one, in which the same permeance can be analytically determined. We derive an explicit formula for this permeance, and confirm our results using the finite-element method. © 2005 IEEE.