Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization

Magnetic Field Distribution of an Elliptical Permanent Magnet

“…Furthermore, for educational purposes, this research would assist students in understanding the magnetic field distribution of the elliptical cylinder permanent magnet as an example beyond the common permanent magnets in cuboid, ring, and circular cylindrical shapes, which are commonly found in textbooks [3]. In addition, having in hand a model of the magnetic field of an elliptical cylinder with axial and diametrical magnetizations, the distribution of the magnetic field of an elliptical cylinder with arbitrarily uniform magnetization, which is a combination of the axial and diametrical magnetizations [23], can be predicted, thanks to the superposition principle.…”

Analytical Expression of the Magnetic Field Created by a Permanent Magnet With Diametrical Magnetization

“…Since it can be time-consuming to use Finite Element Method, analytical expressions with minimal computational effort have been attracting attention. This is very useful, especially when modelling dynamic systems, such as the movement of magnetic nanoparticles in a magnetic field gradient [22]. Moreover, a fast-computed analytical expression of the magnetic field can help save computational time to solve an optimization problem with variations over a large number of parameters [23].…”

“…For these magnets, the surface charge density is constant. However, in the case of a diametrically magnetised permanent magnet, this parameter is dependent on the angle φ between the magnetization vector ⃗ J and the normal unit vector ⃗ n to the cylindrical surface which is equal to J cos φ [22]. Therefore, the nonconstant surface charge density needs to be taken into account when deriving the analytical expressions of the magnetic field generated by a permanent magnet with diametrical magnetization.…”

“…However, they are developed only for an infinite cylinder [26,27], or for computing the magnetic field only on the central axis of a finite cylinder [28]. In order to address these limitations, most recently, Caciagli et al [22] presented an analytical model, based on complete elliptic integrals, to calculate the magnetic field created by a diametrically magnetised cylindrical permanent magnet with a finite length, at any point in (3D) space. Nonetheless, in the steps of derivation, the scalar potential is approximately expressed with the complete elliptic integrals; this caused an error associated with the final expressions of the magnetic field, because these final expressions were derived by taking the derivatives of the approximated scalar potential directly.…”

“…The exact final model of the magnetic field was analytically derived, based on geometrical analysis without the need to calculate the scalar potential; and there was no approximation in the derivation steps. All three components of the magnetic field can be expressed using complete and incomplete elliptic integrals that are robust and their computational efforts are minimal [22,[36][37][38][39]. The accuracy of the developed analytical model was validated against 3D FEA results.…”