$(28$ Points$)$ An infinite cylindrical shell is constructed in two non$-$conducting layers. The first layer has an inner radius $R_1,$ an outer radius $R_2,$ and a non$-$uniform charge density $(r)=3r{e}^{-r}+\frac{}{r^2}$ where $$ and $$ are constants. The second layer has an inner radius $R_2,$ an outer radius $R_3,$ and a uniform charge density. The total charge of the structure is arranged such that the electric field is zero for $r>R_3.$

a$.$ What is the total charge contained in the first cylindrical shell?

b$.$ What is the charge density in the second cylindrical shell?

c$.$ What is the magnitude of the electric field strength for $R_2?R_1?$

$d.$ What $is$ the magnitude $of$ the electric field strength for $R_2?$