On the Ewing Model of Magnetism

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As the Scottish physicist James A. Ewing wrote near the end of the nineteenth century [1, p. 348]: "It is extremely helpful… to experiment with a model consisting of a number of short steel magnets pivoted like compass needles on fixed centers and placed near enough to one another to allow their mutual control to be felt." This Demonstration is a mathematical model of Ewing's device (for Ewing, a model was something that came out of a workshop). The main action is to activate the run box. Hover the pointer over the control labels to see tooltips with explanations.

Contributed by: Ulrich Mutze (July 2018)
Open content licensed under CC BY-NC-SA



Snapshot 1: a 3D configuration resulting by decay from a well-aligned configuration

Snapshot 2: a 2D configuration resulting by decay from a well-aligned configuration

Snapshot 3: a 2D configuration resulting by decay from a not-so-well-aligned configuration

Snapshot 4: a 2D configuration resulting by decay from a random configuration

A finite part of a cubic lattice is considered where each lattice point is the center of a freely rotatable, uniformly magnetized spherical particle. Further, the particles are under the influence of a homogeneous magnetic field. The device that holds the particles in place (e.g. ball cages with diamond-coated contact surfaces) is assumed to cause negligible friction. However, friction is introduced by putting the particles into a bath of viscous liquid. This Demonstration gives numerical values (always relative to SI units without a prefix) to all these quantities and follows the time evolution of the particles in a graphic that represents the magnetic dipoles as stylized compass needles.

The dynamical algorithm for the particles makes use of Euler–Rodrigues parameters [3, 4]. 2D lattices of true compass needles were used around 1880 by the Scottish physicist J. A. Ewing for studying the patterns formed by the needles when a homogeneous magnetic field was applied and slowly varied in strength [1]. In Ewing's case, the needles work like pairs of separated magnetic poles. By contrast, uniformly magnetized spheres behave exactly like true dipoles (see [2]). Ewing's needles may have formed more stable chains than those shown in the present model.

The main lesson we learn (which was not clear to Ewing) is that well-aligned fields of magnetic dipoles always decay into ordered domains of only a few dipoles if the aligning field is switched off. Quantum mechanical exchange interaction is needed to allow for large stable, uniformly aligned magnetic domains, such as Weiss's domains in iron.


[1] J. A. Ewing, Magnetic Induction in Iron and other Metals, New York: The D. Van Nostrand Company, 1900. (July 2, 2018) archive.org/details/magneticinductio00ewinrich.

[2] B. F. Edwards, D. M. Riffe, J.-Y. Ji and W. A. Booth, "Interactions between Uniformly Magnetized Spheres," American Journal of Physics, 85(130), 2017. doi: 10.1119/1.4973409.

[3] U. Mutze, "Rigidly Connected Overlapping Spherical Particles: A Versatile Grain Model," Granular Matter, 8(3–4), 2006 pp. 185–194. doi:10.1007/s10035-006-0011-5.

[4] U. Mutze. "Polyspherical Grains and Their Dynamics." (July 2, 2018) www.ulrichmutze.de/articles/07-252.pdf.

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