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This core has a dumbbell shape so that the magnetic flux is concentrated to the coil winding part of the core. It is well known that the demagnetizing factor strongly depends on the core shape, which defines the effective permeability. Although several researchers have already proposed an approximation for a dumbbell-shaped core, they did not take into account the flange part length. In this paper, a novel approximation for a dumbbell-shaped core is proposed. It is based on the demagnetizing factor and correction terms related to the aspect ratio of both the flange and coil winding part. 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