A spherically symmetric sphere, centered at the origin, has a central core (region 1) of radius $r_1$ surrounded by a thick shell (region 2) between $r_1 < r < r_2$, as shown in the accompanying figure. The core is made of a non-conducting material with a constant charge density of $\rho_1$. The shell is a conducting metal with no additional charge.
What is the electric field for $r_1 < r < r_2$ (region (2)?
What is the electric field for $r> r_2$ (outside of the sphere)?