Self Assessment Quiz

1. A parallel plate capacitor is filled with a linear dielectric whose dielectric constant varies linearly from the grounded bottom plate to the upper plate located at a distance d, by the relation . If the upper plate is at a potential of , obtain expressions for (a) the potential as a function of z, (b) the electric field in the dielectric and (b) the polarization charge densities  on the plates.

2. The space between the plates of a parallel plate capacitor is filled with two slabs of dielectric material. The dielectric filling the space between the grounded bottom plate at z=0 up to z=d/2 is of dielectric constant  while that filling the space from z=d/2 up to the upper plate at z=d which is maintained at a constant potential  is of dielectric constant . Find an expression for the potential between the plates and the polarization charge density on the two plates.