Electric field in two materials

[Gavroy]

Hi

Does anybody know how to find out the potential energy of two equally heavy, equally big and equally charged particles that are placed at the boundary layer of two different media(for example such that mercury is at the bottom and oil is on the top of both spheres( if you know the answer but both substances make you uncomfortable then you should still post your answer) ?

Or is there any way to make a good approximation how the electric field potential energy might look like in this case by referring to the potential energy of both particles being completely in mercury and oil?
Actually tough, I am also interested in good approximations of how to deal with electromagnetic fields in different media.

 

[mfb]

I would use a numerical simulation.
I think your questions are related, so it would be better if you post them all in the same thread, ideally together with some context.

 

[Gavroy]

well, then I am curious whether you could give me an idea, what one would have to solve numerically? for instance in this example. could you just give me an idea about the necessary equations? maybe just choose a similar example that you find comfortable to explain. I would appreciate that very much.

actually, i considered this one to be kind of a new question. although my recent questions were all about electrodynamics I thought that I did not touch this topic explicitely.

 

[mfb]

what one would have to solve numerically?

The Poisson equation, together with boundary conditions (like the potentials on the surfaces)