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1. Research ideas for a high school student

An easy and trendy open-ended theme is rechargable battery efficiency. Charge up some niMH batteries, carefully recording joules needed to charge, and then discharge, measuring joules of work. Experiment with charging schedules, different types of batteries, temperature variations, etc. Wrap...
2. Air temperature in soda bottle pumped to 8 atm

PV = nRT. V is essentially constant. The bike pump may increase pressure by 8 times. This means that n * T is 8 times greater. You can see T is warmer than when you started, but not by that much... mostly what the pump does is put more air molecules into the bottle. Your analysis was...
3. Electric potential of a point charge inside a spheric conductor

An even simpler analysis. The potential of a point charge assuming NO conductors is just q/R. But this thin spherical conductor is symmetric around the charge, so it won't disturb the potential field... there's no induced charge on the conductor at all (by symmerty). So the solution with the...
4. Electric field boundary equation implication at air/earth interface

I am trying to understand how to deal with a boundary value problem when there are multiple dielectrics inside the volume. I'll start with the classic question, then add the dielectric complexity. We want to solve for the potential inside a charge-free axis-aligned 3D rectilinear...
5. Electrostatics: can a positive charge induce negative potential?

That's a good simple proof of the effect of an infinite conductor! But I was referring to proving your statement "All finite distances from the charge will then have a positive potential." It's intuitively true, I certainly can't think of a counterexample, but I don't know how to prove...
6. Electrostatics: can a positive charge induce negative potential?

Isn't induction the case where you have GROUNDED conductors, and when you put charge into the world, the new E field "induces" charge in those grounded conductors to keep their potential at 0? That wouldn't apply to this thought experiment where we're not grounding anything (although I would...
7. Electrostatics: can a positive charge induce negative potential?

This makes sense (unless you had a conductor that connected to infinity, then you'd just have to say nonnegative.) But how could we prove it, ideally with some simple explanation or counterexample?
8. Electrostatics: can a positive charge induce negative potential?

OK, let's fix those loose ends.. I don't think it changes the problem. Let's say that the initial charge was brought in from infinity, and use infinity as our V=0 potential reference.
9. Electrostatics: can a positive charge induce negative potential?

Can a charge, brought into a chargeless world filled with some geometry of conductors and dielectrics, induce a negative potential anywhere in that world? I feel the answer is no. But I cannot think of a good way to prove it, or even attack the problem. More explicitly, imagine a world...
10. Induced charge on a conductive shell, potential theory

There's no electric field inside a conductor, a classic observation of electrostatics. Any field that "should" exist is compensated for by charge redistribution on the surface of the conductor. This produces classic results like shielding since in a hollow conductive shell, the field is still...