I have this problem
The green and the orange blocks are dielectrics of different permittivities $\epsilon_1$ and $\epsilon_2$. They are separated by a very thin conducting plate. I want to know how to calculate the potential in this plate and the charge induced in it.
I am given, also, the conductivities of both dielectrics, so I believe that I have to use the fact that they are not ideal and there is a current density $J$ flowing. However, I have a doubt that is not letting me make any advance.
All the conductors (the one on the top, the one in the middle and the one at the bottom) are neutrally charged originally. So I would expect that to keep happening when equilibrium is reached (except for the one at the bottom, because the ground can lend it some charge). However, if the plate in the middle has no volume (i.e. it has only surface), then there would be a surface charge density $\sigma_m$ there so that electric field exists inside the dielectric. I've seen problems solved like that, but I'm not sure about this because then that conductor would not be neutral as it was in the beginning, and that doesn't make sense to me. Is this correct or is there another way of doing this?