Consider a gallium arsenide sample at T $=300$ K$.$ A Hall effect device has been fabricated with the following geometry; d $=0\mathrm{.}1$ cm$,$ W $=0\mathrm{.}05$ cm$,$ and L $=0\mathrm{.}5$ cm$,$ The electrical parameters are: Ix $=2$ mA$,$ Vx $=2$ V$,$ and Bz $=10$ mT$.$ The Hall voltage is VH $=-10$ mV$.$ Find $($a$)$ the conductivity type, $($b$)$ the majority carrier concentration, $($c$)$ the mobility, $($d$)$ the drift velocity of the majority carriers in the x$-$direction, and $($e$)$ the resistivity.