The magnetic field of a cuboidal cluster of eight magnetic spheres is measured. It decays with the inverse seventh power of the distance. This corresponds formally to a multipole named a dotriacontapole. This strong decay is explained on the basis of dipole-dipole interaction and the symmetry of the ensuing ground state of the cuboidal cluster. A method to build such dotriacontapoles is provided.

The dipole strength of magnetic particles in a suspension is obtained by a graphical rectification of the magnetization curves based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the particle distribution. It has an advantage compared to the fitting of magnetization curves to some appropriate mathematical model: It does not rely on assuming a particular distribution function of the particles. arXiv:1907.11527v1 [cond-mat.soft]

A R T I C L E I N F O Keywords: ferrofluid magnetogranulometry inverse Langevin function ferrofluid EMG909 from Ferrotec TM Co. A B S T R A C TThe magnetization curve of the ferrofluid EMG909 is measured. It can adequately be described by a superposition of four Langevin terms. The effective dipole strength of the magnetic particles in this fluid is subsequently obtained by a graphical rectification of the magnetization curve based on the inverse Langevin function. The method yields the arithmetic and the harmonic mean of the magnetic moment distribution function, and a guess for the geometric mean and the relative standard deviation. It has the advantage that it does not require a prejudiced guess of the distribution function of the poly-disperse suspension of magnetic particles.

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driven magnet. For other angles, the experiments reveal a more complex dynamical behavior, which is divided in three different classes. This is done by analyzing the deviation from a periodic motion of the driven magnet, and by measuring the total harmonic distortion of this rotation. The experimental results can be understood by a mathematical model based on pure dipole–dipole interaction, with the addition of adequate friction terms.

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