Figure 1

(a) Stainless steel spheres roll on a dish made of PS under the influence of the magnetic field produced by a rotating permanent bar magnet, and so separate charge triboelectrically. The forces acting on an isolated sphere are shown in the inset. The curves in (b) give the time average (over one revolution of the magnet) of the radial derivative of the magnetic induction $\partial B_r/\partial r$ as a function of $r$, evaluated at $h=10\mathrm{m}\mathrm{m}$. This average is proportional to the radially directed magnetic force $F_m(r)$ acting on the metallic spheres in the plane of the PS support. (c) The spheres roll on the surface under the influence of the azimuthal component of the rotating magnetic field, and travel one rotation per one revolution of the magnet. The inset has five snapshots showing a rolling motion of a 1 mm sphere that was painted half black and half white.Reuse & Permissions

Figure 2

(a)–(f) Evolution of dynamic ring structures formed by 500 stainless steel spheres rolling over a flat surface of PS at $\Omega =20\mathrm{r}\mathrm{p}\mathrm{m}$ ($\omega =900\mathrm{r}\mathrm{p}\mathrm{m}$). (g) The picture on the left shows a stable, rotating ring structure formed by 500 spheres. In the picture on the right, the spheres were removed, and the surface was dusted with graphite powder. (h) Computer simulation of the evolution of 200 randomly distributed spheres (upper picture) into two rings (lower picture). The charges on the spheres and surface are indicated by shading: uncharged spheres, black; highly charged spheres, dark gray; uncharged surface, white, highly charged surface, light gray.Reuse & Permissions

Figure 3

Formation of noncentrosymmetric patterns of stainless steel spheres on PS surfaces that were modified by making $\sim 100\mu \mathrm{m}$ incisions into them by using a scalpel. The pictures were taken $\sim 3\mathrm{m}\mathrm{i}\mathrm{n}$ after setting the system in motion; the rotation rate $\omega$ of the magnet was 900 rpm. The scale and geometry of the incisions are illustrated schematically by lines adjacent to each image; the locations of the axis of rotation of the magnet are indicated by solid diamonds (◆). The graph in (f) is a Kelvin probe image of a surface charge across the width of an incision charged by rolling 100 spheres over it for 1 min.Reuse & Permissions