P$\mathrm{.}4-1$ The upper and lower conducting plates of a large parallel$-$plate capacitor are separated by a distance $\backslash ($ d $\backslash )$ and maintained at potentials $\backslash ($ V$\_\{0\}\backslash )$ and $0,$ respectively. A dielectric slab of dielectric constant $6\mathrm{.}0$ and uniform thickness $\backslash (0\mathrm{.}8$ d $\backslash )$ is placed over the lower plate. Assuming negligible fringing effect, determine

a$)$ the potential and electric field distribution in the dielectric slab,

b$)$ the potential and electric field distribution in the air space between the dielectric slab and the upper plate,

c$)$ the surface charge densities on the upper and lower plates.

d$)$ Compare the results in part $($b$)$ with those without the dielectric slab.