I would like to solve the Laplacian equation in the following system in order to find out the potential and the Electric field everywhere. I have solved a couple of exercises by solving numerically the Laplacain Equation, but I do not know how to proceed in this one:
I would like to find out $V_1$ and $V_2$ keeping in mind the boundary condition I wrote in the picture.
Could someone give me hint how to proceed in Mathematica. I have no idea how to solve the Laplacian equation for both regions in simultaneous. Furthermore, I have a neumann boundary condition with dependent variables, which in a couple of tries I did without sucess, I have received an alert saying that "NDSolve: Derivatives of dependent variables in boundary conditions are not supported with Finite Element Method in this version of NDSolve"
Thanks in advance