Two parallel conducting plates are separated by the distance d, and the potential difference between the plates is maintained at the value (delta) Phi . A slab of dielectric that has dielectric constant k and a uniform thickness d is inserted snugly between the plates. Because it could be inserted, and because it is impossible to make such a slab microscopically smooth, the slab does not quite fill the volume between the plates, but does touch the plates in some regions. The plates are large compared to their separation d, so neglect edge effects in your calculations.
a) Find the electric field (i) in the dielectric and (ii) in the tiny gap (vacuum) between the dielectric and each plate.
b) Find the charge density [Sigma] on that part of the plate in contact with the dielectric.
c) Find the charge density [Sigma] on that part of the plate in contact with vacuum.
d) Find the polarization charge density Sigma,P on the surface of the dielectric slab.