The magnetic field distribution of an axially magnetised cylinder with an elliptical profile is analytically modelled and analysed in this paper. An accurate and fast-computed semi-analytical model is developed, based on the charge model and geometrical analysis, to compute three components of the magnetic field generated by this elliptical cylinder in three-dimensional space. The accuracy of the model is verified using Finite Element Analysis. The analytical expressions are efficient for calculating the implementation of the magnetic field, taking less than one millisecond to execute on a modern PC. Using the fast-computed analytical model, the distribution of the magnetic field of an axially magnetised cylinder with different elliptical profiles is studied and compared with that of a circular cylinder. The variations in magnetic field strength of axial, azimuthal and radial components can be used in novel sensing applications. The derived analytical model can be extended to calculate the magnetic field of arc-shaped elliptical and circular cylinders with axial magnetization, which can be used in Halbach arrangements.

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In this paper are presented two formulas, the first, eq. (1), for the mutual inductance of two very thin, disk-shaped, duplicate, coaxial coils, and the second, eq. (2), for the electromagnetic force between the coils.A convergent series for the mutual inductance of two coaxial circles was given by Maxwell.1 This was extended to a considerable number of terms by E. B. Rosa and L. Cohen. 2 By the double integration of the formula for .two circles, formula (1) for two disk coils is obtained. It is shown that for certain shapes and positions of the coils, particularly when they are close together, this formula has distinct advantages.The mutual inductance of two thin, flat, coaxial coils, Fig. 1

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