Q$.1$ Mandatory

$[$Total: $50$ marks$]$

$($a$)$ A cuboidal sample of intrinsic Silicon is in an electric field that is perpendicular to one face of the sample. The width, height and depth of the sample are $\backslash (30\backslash$mu $\backslash$mathrm$\{$~m$\},40\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash )$ and $\backslash (50\backslash$mu $\backslash$mathrm$\{$~m$\}\backslash )$ respectively.

i$)$ Sketch a diagram of the sample, clearly showing the dimensions. Choose a possible orientation for the electric field $($ensuring it is perpendicular to a face$),$ and indicate: the type and direction of current induced and the movement of all charge carriers.

ii$)$ If the magnitude of the electric field is $\backslash (|\backslash$mathbf$\{$E$\}|=0\mathrm{.}02\backslash$mathrm$\{$Vm$\}^\{-1\}\backslash ),$ calculate the induced current for the orientation in part $($i$).$