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An axiperiodic quasistatic model to evaluate the magnetic flux density distribution and power loss due to curvature-related radial flux in the laminated core of axial flux machines is presented. It is shown that the relatively low effective permeability in the radial direction and the shielding effect of induced eddy currents result in negligible radial flux density compared to the peak flux densities in the axial and circumferential directions. This justifies the assumption of zero radial flux, which simplifies electromagnetic modelling of axial flux machine cores. The model predicts that power loss due to curvature-related radial flux is insignificant compared to normal eddy-current loss if the core permeability, core conductivity and number of poles are sufficiently high. A laboratory technique is proposed for the practical detection of power loss due to curvature-related radial flux.