A sphere of radius $r_2$ is centered on the origin. It has within it a core of radius $r_1$ as shown in the accompanying figure. The material of the core (region 1) is a conducting metal. Region 2 between $r_1 < r < r_2$ is composed of a non-conducting material. The core is charged with a total charge of $Q_o$. Region 2 has a uniform charge density of $\rho_o$.
What is the value of the electric field in the core, region 1, $r < r_1$?
What is the value of the electric field in region 2, $r_1 < r < r_2$?