## Spherical Shell

A hollow spherical shell carries charge density $\rho = \frac{k}{r^{2}}$ in the region $a \leq r \leq b$. Find the electric field in the three regions: (i) $r < a$, (ii) $a < r < b$, (iii) $r > b$.

Now I know that for (i) $r < a$, $\bold{E} = 0$ because $Q_{\text{enc}} = 0$. But WHY is this the case? Why is $Q_{\text{enc}} = 0$? What does it physically mean? Is it because the charge density is "above all the points in question" and so it does not produce an electric field?

Then for (ii) we have $\oint \bold{E} \cdot d \bold{a} = E(4 \pi r^{2}) = \frac{1}{\epsilon_{0}} \int \rho \ d \tau$. I eventually get $\bold{E} = \frac{k}{\epsilon_{0}} \left( \frac{r-a}{r^{2}} \right) \hat{\bold{r}}$. And for (iii), a similar result.