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We present an alternative approach to analytic force computation in permanent-magnet machines, focusing on the tangential forces that generate the armature and the cogging torque. We extend previously presented methods using conformal mapping to overcome the limits imposed by the singularity of the magnetic flux density at the tooth tip that occurs during the transformation. Using our approach, the cogging and armature torques developed in lightly loaded electric machines can be computed without these limits and without introducing auxiliary parameters. We also revisit Maxwell's stress theory to compute the force on the interface of two materials with different permeabilities, in contrast to the common application to compute the force on a rigid body placed in an electromagnetic field. Using this technique, we then calculate the forces at the slot sides so that the influence of the machine design parameters on the result is directly available.