$\backslash (\backslash \{\backslash )$ Question $2(10$ Marks$)$:

Two point charges $90$ uC and $-90$ uC are placed above a wide earthed conducting plates, as shown in figure $(1).$ The space where the charge exit has a relative permittivity $\backslash (\backslash$varepsilon$\_\{0\}\backslash ).$ Sketch qualitatively the electric field line and the equipotential surfaces in the whole space of $\backslash ($ x y $\backslash )$ plane $\backslash ([1$ M$]\backslash )$ and calculate the following:

a$)\backslash ([3\backslash$mathrm$\{$M$\}]\backslash )$ The electric field intensity at any point on the $\backslash ($ y $\backslash )$ axis

b$)\backslash ([2\backslash$mathrm$\{$M$\}]\backslash )$ The electric potential at any point on the y axis

c$)\backslash ([2\backslash$mathrm$\{$M$\}]\backslash )$ The surface charge density on both sides of conducting plate

d$)[2$M$]$ The force developed on charge of $\backslash (\backslash$operatorname$\{$InC$\}\backslash )$ when it is placed at the following points $\backslash ((0,\backslash$mathrm$\{$~d$\},0)\backslash )$ and $\backslash ((0,-\backslash$mathrm$\{$d$\},0)\backslash )$