Force and Surface Charge on Sphere
Hi Forum..I have an interesting physics problem I have been working on. I have come up with an answer but I hope someone will confirm my understanding. The physical model is a 1 mm diameter sphere where a gas of tritium is filled inside a CH shell of 10 microns. So the tritium has a radius of 490 microns and the remaning 10 microns is CH that encasses the tritium.
The tritium decays via beta decay where the neutron converts into a proton and emits a 5.7 keV electron and a 13.1 keV anti-neutrino. I have worked out for the 1 mm volume of tritium at 10 atms there are 1e18 molecules. Since the tritium decays it works out to ~ 4e5 (dps). I have found in the literature that most of the electrons easily pass through the CH shell. Maybe someone can confirm this?
I get a little fuzzy in thinking how many of the electrons deposit a charge on the dielectric (CH) shell. I assume that 4e5 electrons are smeared over the surface and I calculated the "work" that is used to assemble those charges. But I am not confident that is correct for my end question.
My end question is that this 1 mm charged sphere is 1mm away from a conducting plane. I am trying to estimate the force between the charged sphere and the conducting wall. I have used the CH shell as a dielectric and the tritium inside as conducting sphere (since the tritium decays into helium3). I would appreactiate any insight on my appraoch. I did come up with a force but I just am not confident I am thinking about this correctly. I will be happy to post my results if anyone is really interested.