(Solved): Problem 5 An infinitely long, infinitely thin, straight wire carries linear charge density \( \lam ...

Problem 5 An infinitely long, infinitely thin, straight wire carries linear charge density \( \lambda_{0} \). It is coaxially surrounded by a thick cylindrical shell of inner radius \( a \) and outer radius \( b \). This cylindrical shell carries a non-uniform volume charge density \( \rho(s)=\beta s \), where \( s \) is the axial distance from the thin wire (i.e. for the shell, \( a \leq s \leq b \) ), and \( \beta \) is a constant. (a) Determine the electric field \( \mathbf{E} \) everywhere. (b) For what value of \( \beta \) is the system as a whole, when view from "outside" (i.e. \( s>b \) ), electrically neutral?