|MadSci Network: Physics|
To answer this new question coherently, I have to present the original question: "If I have a permanent bar magnet, and I place a static charge in the middle, (Imagine a box -the magnet- and a point charge q embedded inside). Then the magnet will produce a static dipole magnetic field, and the static charge will produce a static electric field. If you calculate the direction of the Poynting vector S (ExB), it will seem to be circumferential, ie. it looks like it is circulating around the bar magnet. Now EM fields have a momentum associated with them, in the direction of this Poynting vector S. If you attach a solar sail that is attached to the bar magnet frictionlessly, placed so that it can rotate about the magnet in the same direction as S. Won't the sail be pushed? I understand that it takes work to place the charge inside the magnet, etc. But this is a finite amount of work, and since Magnetic field and Electric field are static, nothing is changing so none of the energy that is stored in their fields, (~Integral[E^2 +B^2]all space) is lost. So where does the energy come from? And does it seem to be infinite?", and my original answer: "You have to be careful in using the EM field momentum vector for static fields. In order for the field momentum to exert an impulse on any object, there must be a traveling wave that reflects from (or is absorbed by) the object. In the calculation for sunlight moving a solar sail, it is the reflection of the traveling wave that produces the impulse. This can also be calculated using the force on currents in the sail induced by the oscillating fields of the wave. If the wave isn't moving or oscillating in time, there will be no force." Now the new answer: Of course static fields can produce forces on matter. An electric charge attracts polarizable matter. But, the original question was about a force of rotation caused by the electromagnetic momentum, and this requires oscillating fields. The stress tensor is brought up in the new question. If the stress tensor is used correctly for the configuration mentioned in the original problem, there is no force of rotation on a sail placed in the field. (But it is a difficult calculation, using the stress tensor.) A misleading impression is made in the source cited. The book suggests that the stress tensor actually corresponds to a stress at a point in space. The derivation shows that the stress tensor must be integrated over a completely closed surface, and only then gives the force on matter inside the surface.
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