A surface (with real surface area greater than 1/ infinity) would be present for any particle or source that was not by definition a point. As I understand Gauss law this is best illistrated by a infinatly large plane with some surface charge. Suspended above this is a test charged particle. This test charged particle will obtain some finite velocity - the terminal velocity irregardless of how far above the plane it starts. In a video by a MIT professor, this is demonstrated with a metal coated and charged pingball ball suspended next to a ~ 1 meter square metal coated and charged carboard "plane" TGhis is of course not an infinate plane, but so long as the test ball is suspended at a distance somewhat less than the length of the plane, Gauss Law equations better defines the deflection than the inverse square law- which again only absolutely applies to a point source. Or, approximately to a source of a given diameter which is much less to somewhat less (?) than the distance to the test particle.Steven Sesselmann wrote:Dan, can you define a surface?
You might have a EUREKA moment followed by FACEPALM followed by DOH!
The pertinent video lecture is here:
https://www.youtube.com/watch?v=vxasQBBlWmk
As Richard Hull points out, the physics is complicated and dependant on a complex mixture of physical interactions that are difficult to model.
An example of a modeling error involving point like structures (lines) versus real surface area structures that persisted for over a decade is EMC2/ Bussard assumptions (in mathmatical models) that the Polywell Magrid was made up of infinately thin line magnet structures- surface area was thus zero (almost). This allowed for simplification of models and led to a made up feature called the "Funny Cusp" between infinity thin magnets spaced infinity close to each other. This of course was nonsense, but it was not caught by anyone despite multiple reviews, etc. Finally this was corrected (led to WB6). The biggest consequence was that ExB transport across the magnetic fields with subsequent impacts on the real magnet surface areas could not be ignored. This necessitated a compromise in the separation distance between the magnets. The cusps were wider but tolorable, and ExB losses were adequately controlled. Or at least that was the goal.
Also, in the Polywell (the positively charged magrid version), any electron that escaped through a cusp with any outward energy that was below the escape energy (potential on the magrid) would stop, reverse and reenter the same cusp with the potential energy from the magrid (or some consistent energy below that due to other considerations). The electrons that had higher up scattered or down scattered energies (but still below the escape energy- KE greater than the Magrid opposite potential energy/ voltage) would still reenter at at almost the same KE. This is a manifestation of the dominate Gauss Law considerations over the inverse square law considerations.
Dan Tibbets