Problem $3.$ Electric charges are uniformly distributed within a slab region in free space, with volume charge density ${}_v={}_0$ for ${}_v=0zdz0{}_{0}d{}_0=0\mathrm{.}3n\frac{C}{m^3}d=0\mathrm{.}2m(2,-1,-0\mathrm{.}1),P2(3,4,0\mathrm{.}1)(2,-2,0\mathrm{.}3)E_x{E}_z{E}_z{E}_z{E}_{z}V0,$ and $no$ charge outside $of$ the slab, $i.e.,{}_v=0$ for $zdorz0.$ Here ${}_0$ and $d$ are real, positive constants, with ${}_0=0\mathrm{.}3n\frac{C}{m^3},$ and $d=0\mathrm{.}2m.$ Consider three points $P1,P2,$ and $P3,$ with $P1at(2,-1,-0\mathrm{.}1),P2at(3,4,0\mathrm{.}1),$ and $P3at(2,-2,0\mathrm{.}3),(all$ length $in$ meter$).$ Suppose $we$ set the electric potential $atP2tobe0.$

$(a)$ Should the value $of{E}_{x}be$ zero? $(YesorNo).(Q34)$

$(b)$ Should the value $of{E}_z$ depends $ony-$coordinate? $(YesorNo).(Q35)$

$(c)$ Calculate the value $of{E}_{z}at$ point $P1.(Q36)$

$(d)$ Calculate the value $of{E}_{z}at$ point $P2.(Q37)$

$(e)$ Calculate the value $of{E}_{z}at$ point $P3.(Q38)$

$(f)$ Calculate the energy density associated with electrostatic field $at$ point $P3.$ Express the results $inSI$ unit. $(Q39,Q40)$

$(g)$ Calculate the electric potential $Vat$ point $P1.(Q41)$

$(h)$ Calculate the electric potential $Vat$ point $P3.(Q42)$