Chapter 23, Problem 88E

(a)

To determine

The expression for $\overrightarrow{E}$ for the regions $r\le a$ and $r\ge a$. Explain why $\overrightarrow{E}$ has only radial component.

(b)

To determine

The expression for $\rho \left(r\right)$ in the two regions $r\le a$ and $r\ge a$.

(c)

To determine

To show: The net charge contained in the volume of a sphere of radius greater than or equal to $a$ is zero and to check whether this result is consistent with the electric field for $r\ge a$ that calculated in part (a).