$($a$)$With reference Gauss's generalization of Faraday's work, determine, Qase$$the total

charge for the following configurations:

$($i$)$On a line L$=12$x$3$Cm$-1$zs$=$z$2$Cm$-2$r$=5\mathrm{.}25$mpv$=3\mathrm{.}05$rsin$,$cm$-10$and with surface charge density is$$s$=$z$2$Cm$-2.$

$($iii$)$Within a splere centered at $$the origin with radias r$=5\mathrm{.}25$m$$if $$its charge

distribution is$$pv$=3\mathrm{.}05$rsin$,$cm$-12$if $$the charge density along the line is$$L$=12$x$3$Cm$-1.$

$($ii$)$On$$an $$uncapped cylinder symmetric along the z$-$axis that is $$defined by

$0$and with surface charge density is$$s$=$z$2$Cm$-2.$

$($iii$)$Within a splere centered at $$the origin with radias r$=5\mathrm{.}25$m$$if $$its charge

distribution is$$pv$=3\mathrm{.}05$rsin$,$cm$-1$