Re: [femm] Modelling the new discovery of electrostatic rotation

[David Meeker <dmeeker@xxxxxxxx>]

wigstonmagna wrote:
> Apparently if you charge up a sphere to a modest few kilovolts, 
> fixed in place, and then suspend two other spheres close by, the 
> other two spheres rotate. In the experiments described in the 
> references below, they didn't
> actually rotate, but instead torqued up their suspension filaments 
> until the restoring force equalled the torque.
FEMM shouldn't predict a torque about the center of a perfectly
conducting sphere (or infinite in the into-the-page direction cylinder,
either).  If the sphere (or cylinder) is perfectly conducting, the
sphere (or cylinder) is at a constant voltage. This means that at the
surface of the sphere, the only components of E and D are directed
normal to the surface (analogous to flux lines having to enter
perpendicular to the surface of a block of highly permeable iron). 
Consider the electrostatic stress tensor at any point on the surface of
the sphere (or cylinder).  If E and D at a given point are directed
normal to the surface, the force at this point must also be directed
normal to the surface.  The torque about the center of the sphere due
to the force at the point of interest is r cross dF, where r is the
vector from the center of the sphere to the point of interest, and dF
is the force at the point of interest.  Since dF is directed normal to
the surface of the sphere, r and dF are pointing in the same
direction,--their cross-product, and therefore the torque, is zero.

If you actually tried this (say on the cylinders) in FEMM, you'd
doubtless get some small torque--a finite element solution is only
approximate, after all.  However, with increasingly fine meshing, the
computed torque ought to converge to zero.
-- 
David Meeker
dmeeker@xxxxxxxx
http://femm.berlios.de/dmeeker