Answer Happy

Two grounded perfect conducting planes and a dielectric medium
that all lie in the 𝑥𝑧-plane. One conductor is in contact with the
dielectric medium at 𝑦 = 0. The dielectric medium has a thickness
of 𝑏, a uniform positive surface charge density of 𝜌𝑠 and a
permittivity of 3𝜖𝑜. The second conductor is positioned along 𝑦 =
2a. The region between 𝑦 = a and 𝑦 = 2a is free space
with a permittivity of 𝜖𝑜.
1) Which method to use and why? (Coulomb’s, Gauss’, Poisson’s,
or Laplace’s)?
2) Define boundary conditions for the potential at 𝑦 = 0 and
2a and for the electric displacement vector at 𝑦 = a
3) Find the potential for all regions between 0 ≤ 𝑦 ≤ 2a
4) Find electric field for all regions between 0 ≤ 𝑦 ≤
2a
5) Find direction of the polarization vector (𝑃⃗⃗) in the
dielectric medium