I want to numerically calculate the electric field between two parallel plates with finite length. Where parallel plates are connected to source of constant potential difference:
I have boundary conditions on the edges of numerical area (potential $V = 0$) and "inside-boundary" conditions on parallel plates (for instance, potential on left plate $ V = V_1$, on right plate $V = 0$).
Then I use the FDM method and solve system for Laplace's equations:
For every point within the numerical area. Then, from a value of potential in every point in numerical area, I calculate the electric field.
In theory, always it is OK, but my question is - where must I consider relative permittivity of dielectric medium? In the Laplace equation there is no relative permittivity and I think that my algorithm is contradictory with real physics.
I'd appreciate any help.