gjk@talcott.UUCP (Greg J Kuperberg) (11/30/84)
In response to Craig Werner's suggestion, I attempt to change the subject by presenting a puzzle: Many of you probably know that momentum in the electromagnetic field is proportional to E cross B. Thus we get net momentum for a plane wave of light, because E and B are perpendicular for light. So suppose you have a cylindrical coil that produces a net magnetic field inside of it. Let the field point upward. Now put two curved capacitor plates around the coil. These capacitor plates will produce a net electric field that points in some horizontal direction. Thus E cross B inside the coil is non-zero, and there is net momentum in the field. Where did this momentum come from? --- Greg Kuperberg harvard!talcott!gjk "Eureka!" -Archimedes
act@pur-phy.UUCP (Alex C. Tselis) (12/01/84)
> So suppose you have a cylindrical coil that produces a net magnetic field > inside of it. Let the field point upward. Now put two curved capacitor > plates around the coil. These capacitor plates will produce a net electric > field that points in some horizontal direction. Thus E cross B inside the > coil is non-zero, and there is net momentum in the field. Where did this > momentum come from? The momentum comes from the fact that in charging up the capacitor plates, you have to impart momentum to the electons in the wires leading up to the plates. Also, there will be a reaction of the electrons carrying current in the coil to the electric field due to the plates. Once these reactions have been taken into account, momentum should balance. (Otherwise, you will have a perpetual motion machine. You could then go to Washington and claim a patent for it, and become very rich, because you will have solved the energy problem.) This puzzle is very similar to one you can find in the Feynman Lectures on Physics, in which there is a similar paradox whose resolution requires the recognition that the electromagnetic field also carries angular momentum. See section 17-4 in the Feynman lectures. Another interesting problem may be found in Oppenheimer's Lectures on Electrodynamics, Section 5, problem 6.