For the parallel plates separated by a material with conductivity and permittivity $,$ as

given below, suppose a constant charge density

V $=$ $0$

is added between the plates.

$($a$)$ Write down Poisson$$s equation that governs the voltage distribution between the two

parallel plates;

Poisson$$s Equation:

$($b$)$ Write down the boundary conditions for the voltage V on the two parallel plates;

Boundary conditions: V $($z $=$ d$)=$ V $($z $=0)=$