This paper presents an analytical method based on the coulombian model of a magnet for studying a ferrofluid seal in ironless electrodynamic loudspeakers. Such an approach differs from the ones generally used for studying such geometries because the ferrofluid used is submitted to a magnetic field greater than $1$~T which saturates the ferrofluid. Consequently, its shape and its mechanical properties depend mainly on the magnetic field produced by the permanent magnets that constitute the ironless structure. The motor is constituted of outer stacked ring permanent magnets and the inner moving part is a piston. In addition, one ferrofluid seal is used for centering the moving part and ensuring the airtightness between the loudspeaker faces. The ferrofluid seal also exerts a pull back force on the moving piston. It is noted that this force depends on the lateral shape of the moving piston. Therefore, the piston profile is analytically studied in this paper. A peculiar attention is given to profiles that ensure the axial pull back force to be proportional to the piston displacement. Furthermore, a geometrical method is presented to design the shape of the ferrofluid seal according to the chosen piston profile. It can be noted that such a profile is elliptical in this study. Then, the magnetic energy of the ferrofluid seal is determined with the analytical expression of the magnetic energy density. Such an expression allows us to calculate the axial force created by the ferrofluid seal for a given profile.
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