Question $4(10$ Marks$)$:

A parallel plate capacitor consists of two large metal sheets, as shown in figure $(3).$ The space between the two plates is filled with an isotropic and homogenous dielectric of permittivity $\backslash (\backslash$varepsilon$=3\backslash$varepsilon$\_\{0\}\backslash ).$ The top electrode sheet is maintained at $100$ V and the lower electrode sheet is grounded. Sketch qualitatively, the electric field lines and the equipotential surfaces between the two electrodes and calculate the following:

a$)[3$M$]$ Electric flux density and the electric field intensity in whole space

b$)\backslash ([3$ M$]\backslash )$ The electric potential in the whole space

c$)\backslash ([2\backslash$mathrm$\{$M$\}]\backslash )$ The capacitance of the arrangement.

See

d$)\backslash ([2\backslash$mathrm$\{$M$\}]\backslash )$ The surface charge density on the surfaces of each plate