The problem can be solved without full Legendre polynomials. As a hint, consider an alternate problem of the same uniform electric background field but with a lone +Z dipole at the origin. Find the potential everywhere in space. Is there some dipole magnitude such that the net potential on the...
Homework Statement
A unit sphere at the origin contains no free charge or conductors in its interior or on its boundary. It is, however, embedded in a dielectric medium. The dielectric is linear, but the permitivity varies by angle about the origin. It is constant along any radial direction...
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...
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...
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...
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...
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...
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...
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?
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.
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...
Thanks for thinking about this! You're right that it does have some solution if you can analyze all the world's geometry and solve the Laplace equation everywhere, but as you say, this is likely overkill. But that "oracle" I referred to is in fact doing some math magic that actually does do...
An interesting electrostatics puzzle!
This is a simplification of a real problem I've been hurting my brain on. Luckily the simplification is a fun challenge in its own right.
Homework Statement
There is a 3D rectangular solid object in space. Each face of the solid is a perfect...
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...